New Publications From the Curriculum Department!
Listen to the Article
A Paraeducator’s Handbook for Working with Students with Visual Impairments, 2nd Edition
Authors: Cyral Miller and Debra Sewell (Eds.) (2019), 127 pp.
This publication provides information regarding the paraeducator’s unique role in educational programming for students with visual impairments. Included are:
- Chapters addressing Social Interaction and Self-Determination Skills, Independent Living Skills, Orientation and Mobility Skills, Assistive Technology, other areas of the Expanded Core Curriculum (ECC), Adapting Learning Materials, and Working with Students with Visual and Multiple Impairments
- The paraeducator’s role in these areas of instruction
- Suggestions for working with students
- Resources for Adapted Materials and Equipment
- Print Resources
The Counting Method for the Cranmer Abacus
Authors: Debra Sewell & John Rose (2019)
The Cranmer Abacus is a mathematical tool used for addition, subtraction, multiplication, and division of whole numbers, decimals, and fractions. For the student with a visual impairment, the abacus is comparable to the sighted student’s pencil and paper and should be considered a fundamental component of math instruction. The Counting Method for the Cranmer Abacus (204 pp.) emphasizes the understanding of place value, outlines the importance of this mathematical tool, and gives step-by-step instructions for completion of sample problems using the counting method.


A group of girls doing an experiment at the Kentucky Girls STEM Collaborative "Girls STEM Day" on October 13, 2012 at Western Kentucky University, hosted by the SKyTeach Program & Center for Gifted Studies.
Welcome to the Kentucky Girls STEM Website! We hope this site helps you learn how to help Kentucky girls reach their potential in the fields of science, technology, engineering and mathematics. Although we have made strides in some areas, girls are not succeeding at high enough numbers in careers such as computer science, engineering and physics. Kentucky and the United States will not have enough workers to fill science and engineering jobs if girls are not prepared to succeed in STEM careers.
Feel free to browse through the site, learn more about us and how you can become more involved in helping girls achieve their goals in science, technology, engineering and mathematics.
Thanks for visiting!
Czarena Crofcheck & Sue Scheff, Co-Chairs
Visit us on Facebook: www.facebook.com/KentuckyGirlsStemCollaborative
|Join Our Mailing List|


MATERIAL Art Fair, CDMX
How fast are you moving when standing still? The first thing to consider is the earth’s rotation. The earth is 24,900 miles in circumference at the equator. The earth takes 24 hours to make one rotation. So: 24,900 / 24 = 1,037 MPH. As you move toward the poles that number decreases. At the north pole the speed is zero and you are simply rotating in place at one rotation every 24 hours. So let’s assume you are sitting somewhere in South Florida moving at about 1,000 miles per hour. The Earth orbits around the sun every year. The Earth is roughly 93 million miles (150 million km) away from the sun, giving its orbit a circumference of 584 million miles. That works out to 66,666 MPH. Our solar system itself is also moving in an orbit around the galactic core. The solar system is something like 25,000 light years away from the center of the galaxy, and the galaxy makes one rotation every 250 million years or so. That gives the solar system a speed of something like 420,000 MPH . So there is speculation that the galaxy is moving through the universe at a speed of 1,000 km/s, which means 2,237,000 MPH.
Adding it all up, you get: 1000 + 66,666 + 420,000 + 2,237,000 = 2,724,666 MPH
In other words, you are hurtling through space at 2.7 million MPH even though it feels like you are sitting still while you read this text accompanying some pictures.


So for this round in our math class, we’ve focused a lot in Khan Academy which we use them to learn the news subject. The new subject that we have learned are Transformation, Congruence, Similarity, Rights Triangle & Trigonometry and we also started to learn about Unit Circle but haven’t go in depth into it yet. Using Khan Academy it a unique way of learning which we can learn from watching the video or from the step that it shows how to do it. Also, it was an assignment which we need to get a level five on the subject in Khan Academy to get 20 points for the Activities. At the end of this round, we have a test which includes all the subject that we have learned this round and it a very interesting way to learn by digital.
In my math class, we have a task to do which is to complete all of the section in the heart of Algebra and the reason we do that because to get prepare for the SAT. By doing all of the section we will get a grade for our grade book but is mostly to give chance to the student to practice and get ready for the upcoming SAT. Also, the heart of Algebra is a core section for the next topic that we are going to learn and it Algebra 2. By practicing those skill we will be more prepared to learn the next topic and also to studied what in the SAT so that we can be ready for anything that comes up on the test.
So in the morning, I have one hour of math class and it from 8am to 9 am. My math grade is 7B and we our class arrive the middle of the book. Now we are learning about trapezoid. The new subject that I have done is not really hard and am doing really good on it. Trapezoid has a different equation than other shape and it kind of interesting. I have done many problems already that not just base on the trapezoid.


From the preschool years onward, children with low initial levels of mathematics skills continue to fall further behind their peers.1 To ensure academic success for all children, these widening gaps must be addressed early. In order to help close content-area gaps, we must leverage the way children learn most successfully to lead to better outcomes.
Given the importance of early mathematics development for later success, it is crucial to have pedagogical tools that support mathematics learning from the earliest ages. Playful learning—a broad pedagogical approach encompassing free play, guided play, and games— uniquely supports early learning in mathematics by providing an evidence-based method that effectively supports learning in mathematics (among other areas).2,3
Early mathematics competency is a strong predictor of later achievement and success.4 Yet, across the globe, science, technology, engineering, and mathematics (STEM) skills are rarely introduced adequately in early childhood. Children from lower-income communities experience even lower exposure to STEM related activities than do their middle-income peers—a fact that might account for the gaps in mathematics and spatial competencies present even in early childhood.1
Hirsh-Pasek, Zosh, and colleagues5 recently reviewed the literature from the science of learning—including studies from neuroscience, education, psychology, and cognitive science, —and proposed four pillars of learning that describe the ways in which humans learn best. Learning is optimized when children are 1) mentally active in discovering new knowledge; 2) engaged (not distracted); 3) interacting with material in ways that are meaningful; and 4) socially interactive. Importantly, these four characteristics come together in playful learning.
Playful learning includes both free and guided play as well as games. Free play is child-initiated and child-directed,6 as when children manipulate objects, engage in social interactions with peers or adults, and narrate activities. Even without prompting, many children incorporate mathematics into their independent free play. Seo and Ginsberg,7 for example, reviewed videotapes of 90 four- and five-year-old children as they played for fifteen-minutes to determine the types of mathematics that occurred organically in everyday play. Six categories of mathematical content emerged: classification (grouping or sorting by attribute), magnitude (comparing the size of objects, such as a tower built of blocks), enumeration (saying number words, counting, subtilizing, or reading/writing numerals), dynamics (putting things together or taking things apart), patterns and shape (for example, making a necklace out of beads with a pattern), and spatial location (describing a direction or location). The range of mathematics that was generated in this study was impressive, as was the frequency with which children spontaneously engaged in mathematics activities. Fully 88% of children participated in at least one mathematics activity during the 15 minutes.
Guided play maintains the exploratory nature of free play while also incorporating developmentally appropriate adult scaffolding2—a temporary instructional interaction that supports children’s mastery of a specific learning goal.8 Guided play is, at its core, child-directed. Adults help constrain the discovery of the learning goal by 1) arranging the environment and 2) scaffolding and steering a child to attend to aspects of the environment relevant to the learning goal. For example, a classroom that features a block corner affords children opportunities to learn about spatial rotation. An adult who asks “What happened when you built an even taller tower?” helps the child choose from those alternatives that will favor height as opposed to something like trying to build the longest bridge.
Finally, games that weave content into the course of the play are another playful learning approach. Games offer the potential to increase intrinsic motivation to learn, as well as academic content if that content is integral to the game play, such as the Great Race board game with embedded early mathematics learning.9
Key Research Questions
How can parents, teachers, and caregivers leverage the science of how children learn to create a strong foundation of mathematics knowledge through playful learning?
Recent Research Results
Several successful early childhood mathematics interventions employ elements of playful learning to boost children’s mathematics knowledge. Current work finds that guided, rather than free play, is central to this mission.
The Building Blocks PreK curriculum10 employs games and other play activities to engage children in mathematics learning counting and basic mathematics operations. In one lesson, a teacher and children set up their dramatic play center as a store with a selection of dinosaur toys.11 The students play shopkeeper and collect money (cards with different numbers of dots to represent dollars) in exchange for the dinosaurs. By counting the number of toys to match the dots on the cards, children practice their counting skills and simple arithmetic while engaging in a pretend play scenario. Research demonstrates that children from disadvantaged backgrounds receiving the Building Blocks curriculum improved their early mathematics knowledge more than children in a comparison group using their regular mathematics curriculum.10
With similarly aged children, Ramani and Siegler found that playing a linear number board game—Great Race Game— with an adult for four 15- to 20-minute sessions within a 2-week period increased low-income children’s knowledge in numerical magnitude comparison, number line estimation, counting, and numeral identification. The gains remained even 9 weeks later. By infusing the game with key number sense concepts, the game’s playful and engaging elements helped the children increase their mathematical knowledge more than those children who played a similar game without integrated mathematics content. But, materials must be carefully designed and not just any design will do. Laski and Siegler12 demonstrate that a circular board game that does not emphasize the linearity of number is not effective for extending mathematical learning.
Finally, in spatial learning (an area closely connected to mathematics), Fisher and colleagues13 found that guided play promoted children’s learning about the features of geometric shapes better than didactic instruction or free play. Guided play led to the greatest amount of transfer of shape knowledge to atypical shapes.
During playful learning, children are given a lead role. Adults who have a learning goal in mind constrain the learning space so that the children’s focus lands on the relevant aspects of the material before them. In other words, adults set the mise en place: a term borrowed from the culinary arts, which describes laying out the necessary high quality ingredients before the cooking even starts.14 Children can then generate hypotheses about an end goal within such a constrained space.15 Further research is needed to determine why guided play is so effective and whether it works for different age groups and children with individual learning differences.
Early childhood learning experiences can have a powerful impact on children’s later life outcomes.16 Yet, adding more time for drill and testing has not proven an effective strategy as reflected by both paltry international testing scores for many countries as well as achievement gaps between different demographic groups within the United States. While there is no question that even preschool children profit from a strong curriculum in math, literacy, and science,17 better outcomes are likely if this curriculum is delivered with an age-appropriate playful pedagogy.18 The playful learning approach offers the opportunity to deliver rich mathematics learning through child-directed, adult-supported play activities.6,19 Research from the science of learning indicates that when learners are active, engaged, meaningful, and socially interactive, learning can soar. The challenge then becomes how best to implement this in classrooms and in homes so that all children reach their mathematics potential. By fostering STEM acumen from an early age, societies can increase the likelihood that they will be able to fill the ever-expanding pool of STEM jobs.
Implications for Parents, Services and Policy
Playful mathematics learning is not a novel concept in many of today’s homes, classrooms, and communities, making this approach readily implementable. Children already play with blocks, create pretend play scenarios, and interact with digital apps on a regular, if not daily, basis. By designing these experiences with specific learning goals, child’s play may be transformed into playful learning. Through the application of principles culled from rigorous empirical research in the science of learning, playful learning (i.e., free play, guided play, and games) presents an evidence-based method for sharing mathematical content with young children. By starting early, caregivers and educators can help instill a love of mathematics that may lead children not only to mathematics achievement today but also towards a STEM career tomorrow. Research repeatedly finds that play is more than just fun; it is a valuable educational tool. In particular, adult-supported guided play and games help children learn mathematical concepts in a way that “sticks” and transfers to new problems.
- Jordan NC, Levine SC. Socioeconomic variation, number competence, and mathematics learning difficulties in young children. Developmental Disabilities Research Reviews. 2009;15(1):60-68.
- Weisberg DS, Hirsh-Pasek K, Golinkoff RM, Kittredge AK, Klahr D. Guided play: Principles and practices. Current Directions in Psychological Science. 2016.
- Hassinger-Das B, Toub TS, Zosh JM, Michnick J, Golinkoff R, Hirsh-Pasek K. More than just fun: A place for games in playful learning / Más que diversión: el lugar de los juegos reglados en el aprendizaje lúdico. Infancia y Aprendizaje. 2017;40(2):191-218.
- Duncan GJ, Dowsett CJ, Claessens A, et al. School readiness and later achievement. Developmental Psychology. 2007;43(6):1428-1446.
- Hirsh-Pasek K, Zosh JM, Golinkoff RM, Gray JH, Robb MB, Kaufman J. Putting education in “educational” apps: Lessons from the science of learning. Psychological Science in the Public Interest. 2015;16(1):3-34.
- Hirsh-Pasek K, Golinkoff RM, Berk LE, Singer D. A Mandate for playful learning in preschool: Applying the scientific evidence. Oxford University Press; 2009.
- Seo K-H, Ginsburg HP. What is developmentally appropriate in early childhood mathematics education? Lessons from new research. In: Clements DH, Sarama J, DiBiase AE, DiBiase A-M, eds. Engaging young children in mathematics: Standards for early childhood mathematics education. Hillsdale, Nj: Erlbaum; 2004:91-104.
- Wood, DJ, Bruner JS, Ross G. The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry. 1976;17(2):89-100.
- Ramani GB, Siegler RS. Promoting broad and stable improvements in low-income children’s numerical knowledge through playing number board games. Child Development. 2008;79(2):375-394.
- Clements DH, Sarama J. Effects of a preschool mathematics curriculum: Summative research on the Building Blocks project. Journal for Research in Mathematics Education. 2007;38(2):138-163.
- Sarama J, Clements DH. Building blocks and cognitive building blocks: Playing to know the world mathematically. American Journal of Play. 2009;1(3):313-337.
- Laski EV, Siegler RS. Learning from number board games: You learn what you encode. Developmental Psychology. 2014;50(3):853-864.
- Fisher K, Hirsh-Pasek K, Newcombe N, Golinkoff RM. Taking shape: Supporting preschoolers’ acquisition of geometric knowledge through guided play. Child Development. 2013;84(6):1872-1878.
- Weisberg DS, Hirsh-Pasek K, Golinkoff RM, McCandliss BD. Mise en place: setting the stage for thought and action. Trends in Cognitive Sciences. 2014;18(6):276-278.
- Bonawitz E, Shafto P, Gweon H, Goodman ND, Spelke E, Schulz L. The double-edged sword of pedagogy: Instruction limits spontaneous exploration and discovery. Cognition. 2011;120(3):322-330.
- Fox SE, Levitt P, Nelson CA. How the Timing and Quality of Early Experiences Influence the Development of Brain Architecture. Child Development. 2010;81(1):28-40.
- Hirsh-Pasek K, Golinkoff RM. The great balancing act: Optimizing core curricula through playful learning. In: Zigler E, Gilliam WS, Barnett WS, eds. The pre-K debates: Current controversies and issues. Baltimore, Md: Brookes Publishing Company; 2011:110-115.
- Jenkins JM, Duncan GJ. Do pre-kindergarten curricula matter? In: The Pre-Kindergarten Taskforce, eds. The current state of scientific knowledge on pre-kindergarten effects. Washington, Dc: Brookings Institution and Duke University; 2017:37-44.
- Weisberg DS, Hirsh-Pasek K, Golinkoff RM. Guided play: Where curricular goals meet a playful pedagogy. Mind Brain and Education. 2013;7(2):104-112.
How to cite this article:
Hassinger-Das B, Zosh JM, Hirsh-Pasek K, Golinkoff RM. Playing to Learn Mathematics. In: Tremblay RE, Boivin M, Peters RDeV, eds. Pyle A, topic ed. Encyclopedia on Early Childhood Development [online]. https://www.child-encyclopedia.com/play-based-learning/according-experts/playing-learn-mathematics. Published: February 2018. Accessed December 9, 2023.Text copied to the clipboard ✓


You’ll find lots of career options for a physics major. When considering the own major, keep in mind that mathematics can prepare one for quite a few livelihood. Some of those livelihood choices which are available include working in academia and research software, fabricating research, and several much more.
The ideal place to begin when planning for a livelihood will be in faculty. You should paraphrasing machine always be ready when searching for a job like a student to consider university classes.
There are two areas of science, mathematics and physics, that all students studying physics are required to take. A math major would be able to take calculus, statistics, linear algebra, and probability theory. A physics major, on the other hand, will be taught about some of the more basic mathematical concepts, like polynomials, and Fourier series. The majority of courses students take are lab paraphrasegenerator org courses that require knowledge of a number of basic concepts.
Those who work in academia, including researchers, and university administrators, can benefit greatly from a physics degree. These individuals will need to have excellent math skills and be familiar with all of the advanced topics in physics. In the early stages of a career in this field, a university employee will need to develop their own teaching skills, as well as learn how to relate to both new and experienced faculty members.
Military applications will also be in popular. In the event that you are interested in working out in the armed forces, then the physics level is still your way to go. Application is a fantastic alternative for those who have the chance. Within this scenario, a university employee could be forced to concentrate on academic courses and just have a limited amount of time for you to use for army training. There isn’t any larger profit than knowing how exactly to apply exactly what you have learned from your class http://clubsports.gcu.edu/club-sports/ice-hockey/ room.
For physics is still quite a superior important. Many businesses find it tricky to employ workers who have solid math skills. Then a career in engineering may be your thing to do, if you are somebody who has a background in mathematics or will work nicely with numbers.
Medical applications are increasing fast, so a career in physics is perfect for those who are interested in being associated with study. As a physicist, you may have the opportunity to simply help individuals with ailments such as cancer, Alzheimer’s disease, as well as different ailments. It all can be challenging and enjoyable, at the same time.
Needless to say, in case you have already determined to follow a career in physics, then you definitely have to decide exactly what you want related to your own degree. Additionally, there really are a range of career paths available to a physics key. While you will find numerous choices, there are.
Students who are passionate about math may choose to major in Mathematics or Physical Sciences. This type of degree will provide the student with an education in physics as well as the ability to major in mathematics as well. Students who want to be able to use both fields may want to consider a joint degree.
Might want to settle on a livelihood alternative between Physical Sciences and Engineering. The pupil should be capable of using their understanding of mathematics to produce new technologies to get power. Students might possibly not want to join the two careers because this could confine the student’s talents.
Those who have already completed their degree in physics may choose a career choice in physics. This option will allow the student to continue to work with a particular company or begin a career path in another area. Often, working with a company while completing a degree in physics is a very rewarding experience.
No matter which career selection you produce, it is important to remember that physics classes will gain from participating in labs and mathematics classes. It is a superior concept to ensure that a mathematics major are going to be able to find credit for prior science classes, so that students will possess the essential credits necessary to graduate. In good moment.


Funds and asset managers are increasingly concerned with quantitative and econometric model in order to apply their portfolio models. The main goal of this publication is to study the behavior and the proportions of a stock portfolio from CAC All-Tradable with these kinds of models and compare the results with the historical approach. A GARCH (1,1) process has been used for modelling each asset volatility and Engle dynamic equi-correlation model to forecast covariance matrices. From a small amount of underlying values, the question is raised whether forecasted covariance matrix is more relevant than traditional variance-covariance matrix in a context of minimum variance portfolio model.
Keywords: Volatility - Correlation – Equi-Correlation - GARCH (1,1) - Portfolio Selection - Asset Allocation- Covariance Matrix – Minimum Variance Portfolio.


At secondary level, the two ESF all-through schools, Renaissance College and Discovery College offer the International Baccalaureate Middle Years Programme (IB MYP) from Years 7 to 11.
For the other five ESF secondary schools, the curriculum are aligned to the MYP framework from Years 7 to 9.
Students follow a school-designed curriculum with an approach that is broad and balanced leading to a suite of IGCSE and GCSE qualifications. Subjects include English, mathematics, science, the humanities, creative and performing arts, design technology and an additional language(s) at an appropriate level.
At Years 12 and 13 (post-16), students have the options of taking the IB Diploma programme or the Applied Learning Pathway. At all levels, the curriculum is differentiated to cater for students’ learning needs. Students are supported to choose the most appropriate pathway for future education or career.
Read more about the programmes at these links below:


Our school is committed to developing internationally-minded citizens who aspire to make the world a better place.
Dear parent: You, as a parent, are a voting member of the Association of the International School of Lusaka - which means that you own our...
Maths in Primary! Just before the Christmas break, Year 2 made these amazing shapes in their Maths class! Tesselation and also 3D shapes and nets.
Year 7s made these fun videos of their understanding of fractions using multi link cubes.
What else can we use to explore maths in a fun, colourful way? what maths do you see at home?


(ONE-TIME purchase, no further in-app purchases or continuing fees / tricks.)
Don’t just memorize the odds, *understand* them … This app teaches you a general method for estimating the odds for just about any Texas Hold’em scenario in your head in real time.
*** Pay once and enjoy forever ***
No in-app purchases/fees.
Continual improvement for many years.
New: A user interface upgrade for iPhone X-series models.
This is a challenging app. You need to be pretty good at doing basic math operations in your head. For example, what’s the value of:
16% * 20%
We’ve added a “Math” help button to show you how to calculate this in your head. One way is, 20% means one-fifth. One-fifth of 16% is (16% / 5), which is a little more than 3%. 3.2% to be exact. Or, convert to decimals, multiply, then convert back to %age’s.
This app uses specific hand situations, and some people don’t see the value in this because in real life play we don’t know our opponents’ cards. There’s still value in specific hand situations, because they’re the building blocks that we can use to put together and estimate the odds for more complex hand range situations. For example every good player should know the odds for specific hand situations like AJ vs. QQ pre-flop, or FlushDraw vs. TopPair on the flop. Our other apps e.g. PokerCruncher handle both specific hands and hand ranges.
“… helps players learn some of the math behind poker … teaches a general method of estimating odds for different Texas Hold’em situations.”
Many more great reviews from poker experts, pros, and coaches, and on our TwoPlusTwo forum thread.
(See our website.)
Poker trainers, odds tables, etc. are useful tools but do they help you learn why the odds are what they are or are you just memorizing specific situations? And you can’t use these tools or odds calculators in the middle of a live hand (would you really want to?; could be a “fish” tell :)). This app takes a new and different approach to poker odds – understanding instead of memorizing, so you can handle any situation that comes your way.
Our odds estimation method is a pretty simple 3-step procedure. First you count your outs and estimate your odds of improving (using for example the “Rule of 4&2”; this app shows you how). Then you consider your opponent’s counter-outs. Then you put the two together to come up with a good odds estimate.
We’ve provided about 20 common and important pre-flop and post-flop scenarios for you to practice the method on. This app will take you through the 3 steps for each practice scenario, one screen per step, and will make sure that you’re on track towards a good odds estimate each step of the way, correcting you if needed. We’ve provided info/help buttons for each sub-step.
You might be thinking, how can you cover a game as complex as Texas Hold’em in 20 scenarios? Well, we agree, you can’t! But this app is about learning a general method not many specific situations, and we picked these 20 scenarios to cover a good cross-section of common and important pre-flop and post-flop situations. If you understand how to calculate the odds for say one generic TopPair vs TopPairTopKicker scenario or one representative Pair vs LowerPair pre-flop scenario, you’ll be able to apply your knowledge to other similar situations easily.
Now, we’re not saying that you’re going to master this in 5 or 10 minutes. You’re going to have to practice the method more than a few times, think about the outs and counter-outs, and do simple math operations in your head – basic +, -, *, /; let’s not let our math teachers down :). We hope you feel that acquiring this odds skill and knowledge is more than worth the learning/practice time.
See our website for our strong free app update history over many years.
Follow us on Facebook and Twitter.
App Store reviews are greatly appreciated, thank you.
Also please check out our companion apps Hold’em Odds Quizzer and PokerCruncher.


Board of Secondary Education (BSE) on Monday released the timetable for the Matric exam (Summative-II).
According to the BSE, the examination would be of 80 marks for each subject (50 objective and 30 subjective). Two-hour exam will be held for every subject, barring Mathematics where students will get extra 15 minutes.
Exam will start at 8 AM from April 29-May 7.
April 29: Second Language English/Hindi (8-10 am)
May 2: Mathematics (8-10.15 am)
May 4: Science (8-10 am)
May 5: First Language Odia/Bengali/Hindi/Urdu/Telugu/ alternative English (8-10 am)
May 6: Third Language (8-10 am)
May 7: Social Science


We are a Teaching for Mastery School
Maths Subject Leaders-Mrs Cookson and Mrs Horn.
Maths Curriculum Intent:
Our maths curriculum is designed with the schools’ vision and ethos at the centre. We aim through our bespoke Mathematics curriculum that our children will be ‘achieving excellence in the light of God.’ Through an environment of Christian love and support, we aim that our children will become confident and independent mathematicians. Using our curriculum driver of Growth Mindset, mistakes in maths are celebrated and used as valuable learning points. By teaching maths with a mastery approach, our children will have deep and broad understanding so because of this be willing to take risks and make informed decisions about their choice of calculation. Staff will be role models of communication in mathematics, teaching the best way to explore and share reasoning. Building on our children’s solid cultural capital, maths teaching will be purposeful, not driven by processes but by meaningful and efficient calculating. By rooting learning in mathematics it is these principles that will allow our children to shine.
Maths Curriculum Implementation:
Key Documentation and links: Note that as we are currently in the mastery embedding stage of our curriculum, our policies are working documents and are constantly being updated as our curriculum develops.
Mathematics will be taught using the long term planning from Maths No Problem as a basis and teachers will use the small steps in learning from here to support the teaching for mastery approach. We also supplement this using the Mastery Development Spines from the National Centre for the Excellence in Teaching of Mathematics or NCETM. Due to the outbreak of Covid 19, teachers are aware that children may have gaps in their learning and will use the new guidance from the Department for Education Ready to Progress Criteria and NCETM Curriculum Prioritisation documents to address this. As we are a Teaching for Mastery School, we also use other resources to support of teaching and allow children to see learning in a variety of ways. It is this that gives the children breadth and depth of understanding. We use Deepening Understanding, NCETM Mastery Assessment Documentation, alongside some resources from White Rose Maths.
Aims of the 2014 National Curriculum:
- Fluency in the fundamentals of mathematics
- Having a deep conceptual understanding of their learning.
- Reasoning mathematically, following a line of inquiry
- Solve problems applying their mathematical skill
What does a mastery approach look like?
We are a member of a Northwest Abacus Teacher Research Group or TRG. Each half term we meet together with a key focus aimed at improving the quality of teaching and learning in mathematics. For academic year 2021/2022.
Our current focus for 2021/2022 (One TRG been held so far in September 2021)
- How are school using the NCETM Curriculum Prioritisation Documents? These documents have been made using guidance from the Department for Education and focuses on key areas of learning to support children’s development after lockdown.
Topics covered in 2020/2021 have been:
- Careful anchor task setting – a worded problem to solve that the lesson is based around. Careful setting and questioning helps bring all children into the discussion at their level, increasing confidence and building mathematical talk.
- Patterns and connections – Connections underpin every area of mastery. If children are encouraged to make connections and apply patterns, they will have a broader and deeper understanding. The use of because is key in our lessons – children can explain their thinking clearly by connecting ideas.
- Representation – How we represent mathematical thinking to the children is key. We need to have consistent representations throughout school in order to unlock the understanding of maths and give children a place to hand their reasoning. If children can have a mental repertoire of practical equipment in their minds, they can tackle challenging problems and explain their thinking visually.
Research has shown that splitting the class into groups of learning based on ability causes widens the gap in achievement. Teaching for mastery focuses on the achievement of all pupils with the class working together at broadly the same pace. Some children will work within age related expectations but need more visual representations of questions, other children will move on to a deeper understanding in their learning.
Practical equipment, used at every stage of learning and regardless of ability, plays a vital role in mathematics in our school. Children who see questions practically and with visual representations have a deeper conceptual understanding and this unlocks the mathematics. Each question will be varied slightly each time, making the children think that little bit more and apply their skill in a different way. Because each question is progressive, next steps in learning are automatically built in through careful question selection. Children are ready for challenge, knowing that each question will stretch their thinking.
During teaching time, children will work in mixed ability groups and share thinking with a partner. Teachers will ask carefully thought-out questions and children will have time to work and feedback. Emphasis will be placed how children have arrived at the answer or how many ways they could arrive at the answer. In this way, children will demonstrate a clear and deep understanding of the concept they have learnt. They will also learn to communicate their thinking in maths clearly and work systematically to arrive at all possibilities.
From years 1 -6 our children are taught in mixed age classes. To focus the lesson on the curriculum objectives for each individual year group. In Years 1 and 2, the children are taught separately as the gap between learning objectives is considerable. One year group will receive their input time whilst the other year group works independently and vice versa. We believe that this allows the teacher to focus on specific learning for that particular year group and learning expectations for all years are clear. In Years 3-4 and Years 5-6, the children are taught together and the younger year group starts their independent activity first in order for the teacher to further the learning for the older year group.
EYFS are using the White Rose Reception scheme and the NCETM spines a basis for their curriculum. The teachers in EYFS also plan the maths provision for the nursery class following this guidance. This is consistent throughout school and the practical equipment and representations flow throughout. White Rose and NCETM use Number Blocks as a basis of understanding of number. This is picked up in Year 1 to ensure continuity of transition. We also use Numberland, which allows the children to explore numbers 1 to 10 in depth and links also to areas such as shape and measure.
Teachers and teaching assistants, circulate effectively during activities to provide immediate feedback to groups of learners or replicate models of calculations on the board at table level. Intervention is conducted as soon as possible that day or as near to the next lesson in order to close gaps quickly.
Children who are working at a greater depth, will have the opportunity again through carefully selected questions to further their thinking. Lessons are not about pace but about deepening understanding. We use the NCETM Mastery with Greater Depth materials and Nrich to support further questioning and challenge.
Pupils with SEND who are working significantly below age-related expectations will be taught using a tailored approach that is right for their specific need.
For all pupils at Hoole St Michael, we believe that we should not put a lid on learning and allow children to maximize their potential. Each lesson, pupils have the opportunity to undertake a deeper learning challenge to stretch their thinking even further.
Daily Fluency Sessions:
We aim for our children to be:
Flexible in their thinking.
Efficient in their calculating.
Accurate in their responses.
We believe that our children should have a fluent recall of the mathematical skills that they need to support them though into adult life. With this in mind, we have daily fluency sessions outside of the maths lesson which gives children the opportunity to recall/embed previous learning and hone their skills. Teachers are currently using the Department for Education Ready to Progress guidance, alongside year group objectives to inform planning for these sessions as well as progressions for mental mathematics. Our fluency sessions are based around fluent recall and reasoning. Children are encouraged in these sessions to make those vital connections and relationships between numbers. We know this because… is a key phrase here.
All our lessons are rooted in practical equipment. We believe that this approach unlocks the understanding of the maths. As children grow in confidence, the equipment is replaced with visual representations such as bar models, part part wholes or place value grids. We ensure that these representations are consistent throughout school by using the Ready to Progress Criteria resources from NCETM and the Spines. This consistency gives our children a place to hang their thinking from, encouraging reasoning and unlocking problem solving.
At Hoole St Michael we have decided on several key representations that we will be using as a school to promote mathematical thinking. These are consistent throughout school. Research has shown, that by providing children with a way to communicate through a visual representation allows children to express their thinking and reason out problems. Our key representations are:
- tens frames
- part whole models
- bar models
- place value counters
- Dienes equipment
Journals – New for 2021/2022:
Through our work with the Mastery Hub, we are now using maths journals to give our children more opportunity to explain their thinking and communicate their maths clearly. We use journal tasks, embedded in a real life context for the children to explore. In their journals, they create their own title. From this the teacher can assess where the children think their learning is heading. The teacher will then reveal the real title at the end of the session.
Impact of our approach to mathematics is regularly and carefully monitored. Assessments are conducted at the end of every topic and exam analysis is used to inform future planning. Termly assessments are focused and test what the children have been learning that term, not end of year expectations. This allows teachers again to accurately future plan for the needs of their children.
The Senior Leadership team regularly monitor the teaching of mathematics through learning walkthroughs, book and planning scrutiny, pupil interviews and lesson observations. The Subject Leader has rigorously assessed the teaching of the mathematics in school and drawn up a focused action plan in order to move the subject forward.
Our children should leave school being high school ready. They calculate with confidence and do not have a reliance on formal, written calculation to solve problems. They have a positive, can do attitude to mathematics and attack challenges with independence and resilience.
Covid 19 Recovery:
We are currently supporting our children using the following two documents to inform our planning and teaching:
We are working carefully with our children to assess their knowledge, analyse our findings and adapt our teaching and learning accordingly that fits the needs of our school.
Maths all Around Us!
Maths Homework at Hoole St Michael:
To support our focus on fluency of skills, our homework across school is designed to foster this.
Each week children will be set:
- an Emile task linked to their National Curriculum objective for maths that week. Teachers can monitor scores and go back through assignments to capture knowledge gaps.
- Numbots for our Year 1 children to encourage a recall of number facts. We also use this further up school for learning support if needed.
- T T Rockstars from Year 2 and up. Each class has an interactive display to encourage speed of recall.
This November marks the start of our popular bar modelling month in school. Bar models are a great tool for us to be able to solve problems independently. Each day in November we will be solving a series of problems using bar modelling. We are aiming to win a champion bar model kit care of White Rose Maths. Watch this space for some photos of bar modelling in action.
National Numeracy Day 13th May 2020
During the time our school was closed, we celebrated National Numeracy Day through our learning from home program. The children saw maths around them and used various activities to explore number, shape and pattern.
As you can see from our photographs, we had a great day!
Focusing on Fluency!
Welcome to Emile. This is primarily a maths program designed to focus on the recall of facts and the increase of calculation speed. This will help children increase their fluency – the skill of answering any question in a certain area of maths no matter how it is presented. Having s solid recall of key facts increases confidence and allows children to make connections quicker between different areas of the subject. Children can also pattern spot and generalise if they are armed with the knowledge to do so.
Emile launched across school formally on the 3rd February and children are using this both in school and at home. Look out on DOJO for details about how to login in and for assignments set by the teacher We will also have whole class and school battles! Which class will be the champions?
Bar Model Stay and Learn November 2019
Look out for our brand new Stay and Learn sessions this half term all about bar modelling. Parents are invited to see how children use bar models to help unpick tricky problems and see how they visually show which calculation to use.
Look out on your child’s class Dojo for booking.
Going APE in maths!
You may have heard your child saying that they have been asked to ape in maths! What does this mean? Reasoning and problem solving questions are asked daily in our lessons. We ask the children not just to say whether a calculation is right or wrong but explain how they know and prove it. Children can prove their thinking through drawings, using practical equipment, calculating or in writing.
Times Table Rockstars!
TT Rock Star Launch Friday 6th September 2019
Wow! We certainly rocked it out during our launch of our brand new times table program! We all had a go at being a rock star and with our wacky hair and inflatable guitars we gave those times tables a thrashing!
Logins are available from your child’s class teacher.
Every Monday each class will add children to our corridor Hall of Fame – we are looking for most improved studio scores and our highest earners.
Go for it guys and rock it out!


Submission possible until: 20th of November 2019, 11:00 am
- Start time:
- Do 14 Nov 2019 12:00:00
- End time:
- Mi 20 Nov 2019 11:00:00
- Task 1 (Conjugate gradient with MPI)
- Your solution should use 44 iterations and end with an error of approximately 0.00459 (as the single process version). Numerical errors may slightly alter the results and iterations! A...
- Task 2 (Asynchronous 2D Jacobi Iteration)
- A possible solution can be found at: https://sauce.zdv.uni-mainz.de/submissions/59749/show Please tell me about any errors or problems you may encounter.


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Our strategies, tools & resources support community colleges in developing innovative teacher preparation programs that boost the number and diversity of students entering the education field, particularly in science, technology, engineering and math (STEM) and career technical education (CTE).


The Mog Bonanza is a number-guessing game in which you pick a five-digit number of your choice. Playing is simple! Purchase a Mog Bonanza marble (*1) from a Bonanza Moogle at designated areas (*2), then have the vendor inscribe your desired five-digit number on it.
The conditions for winning are as follows:
Rank 1 prize: all five digits matching.
Rank 2 prize: the last four digits matching.
Rank 3 prize: the last three digits matching.
Rank 4 prize: the last two digits matching.
Rank 5 prize: the last digit matching.
* The winning number for each prize rank will be drawn separately. In the event that winning numbers overlap for multiple prize ranks, the higher-ranked prize will be given precedence. For example, should the winning numbers for ranks 4 and 5 be "11" and "1" respectively, the holder of a bonanza marble etched with the number "11111" will be awarded with a rank 4 prize.
Up to 10 Mog Bonanza marbles can be purchased per character. You can have the same number inscribed on multiple marbles. This will mean bigger earnings should you have a winning number.
Purchase your Mog Bonanza marbles, check winning numbers, and collect prizes from Bonanza Moogles at Port San d'Oria (I-9), Port Bastok (L-8), Port Windurst (F-6), or the Chocobo Circuit (H-8).


CPM courses are very different from the traditional math courses offered in the United States. This explains why many students search the internet for CPM Math Homework Help. If you too are taking a CPM class and having trouble completing your homework, find the help you need from the experts at MyAssignmenthelp.com.MyAssignmenthelp.com is one of the Internet's leading providers of academic solutions. For more than 10 years, this company has helped thousands of students achieve their academic goals with confidence. If you're also looking for academic success, just use the CPM homework answers from the team of qualified assignment experts at MyAssignmenthelp.com.


Dr. Alexander Engau
Universtiy of Colorado, Denver, USA
Department of Mathematical and Statistical Sciences
A semidefinite cutting-plane approach towards stable set
and the maximum-clique problem
The development of semidefinite programming (SDP) over the last 20 years was largely influenced by the design of efficient interior-point algorithms for convex optimization and their wide applicability also to NP-hard combinatorial problems. Often highlighted by the SDP relaxation for the maximum-cut problem by Goemans and Williamson, for this talk we consider a similarly well-known SDP relaxation for stable set to compute the Lovász theta-number which gives upper and lower bounds on the maximum-clique and the colouring number of a graph, respectively. Although theoretical results have shown that this relaxation can be strengthened using several classes of cutting planes, efficient computational approaches remain largely unexplored. We present our recent progress with a new interior-point cutting-plane method that uses an improved mechanism for the dynamic addition and removal of cut inequalities based on effective warm starts and feasibility indicators at intermediate iterates. This approach does not require to successively solve multiple relaxations and therefore promises to solve most instances in significantly less time than previous methods. This is joint work with Immanuel Bomze (Universität Wien) and Miguel F. Anjos (University of Waterloo) who will focus on the warm-start strategy and related concepts utilized by this method in the Kolloquium on Friday, July 23.


Applications of Matlab:
The current advancements in MATLAB have made it a very competitive tool for Artificial Intelligence, Robotics, Image Processing, Wireless Communication, Machine Learning, Data Analytics, and other fields. MATLAB may be used as a tool for simulating diverse electrical networks. Although it has a wide range of applications, circuit branches and mechanical engineering employ it primarily to tackle a fundamental set of problems. It is a tool that makes it possible to compute, programme, and visually represent the outcomes.
The matrix or array is the fundamental data type in MATLAB, as the name would imply. Professionally constructed MATLAB toolboxes let you materialise your fantasies. Programming in MATLAB is very similar to programming in C, so you just need to brush up on your fundamental programming knowledge.
MATLAB is used in the applications listed below.
Statistics and artificial intelligence (ML)
For programmers, MATLAB's toolbox can be quite useful. It is simple to implement statistical techniques like descriptive or inferential statistics. The same is true for machine learning. Modern challenges can be solved using a variety of models. Big data applications can also utilise the employed methods.
The toolbox for curve fitting aids in the analysis of data distribution patterns. It is possible to anticipate future trends once a specific trend, which can be a curve or surface, has been obtained. Additional graphing, integral and derivative calculations, interpolation, and other tasks are possible.
Control systems of a certain sort are attainable. Bode plots, Nyquist plots, open-loop and closed-loop dynamics, controllability and observability, and other factors can be acquired One can visualise various controlling methods like PD, PI, and PID. Either time or frequency domain analysis is possible.
Processing of Signals
Various engineering disciplines teach signals, systems, and digital signal processing. But MATLAB offers the chance to properly visualise this. On any given signal, different transforms, including Laplace, Z, and others, can be applied. A theorem may be verified. Either time or frequency domain analysis is possible. There are numerous available built-in functions.
There are numerous uses for mapping across numerous industries. For instance, the MapReduce tool, which has numerous real-world applications, is quite important in the field of big data. Analysis of theft or the detection of financial fraud, regression models, and contingency.Data mapping can be used for analysis, social media prediction techniques, data monitoring, etc.
It's a type of machine learning that can be used for picture analysis in medicine, speech recognition, and financial fraud detection. You can use a variety of technologies, including time-series analysis, artificial neural networks (ANN), and fuzzy logic.
Before beginning any project, an entrepreneur must conduct a thorough investigation and a financial analysis to determine the best course of action. All of the necessary tools are contained in MATLAB. It is possible to identify components like profitability, solvency, liquidity, and stability. It is possible to evaluate business valuation, capital budgeting, cost of capital, etc.
The most common application that we observe almost every day are bar.When delivering data from distant satellites and receiving and decoding it in the same manner, digital image processing also plays a significant role. All of these applications can be supported by existing algorithms.
Analysis of text
Sentiment analysis can be performed on the text. Within a few milliseconds of entering any text, Google returns millions of search results. Text analysis makes all of this possible. In forensics, handwriting comparison is possible. One piece of software that can do everything, with no restrictions on applications.
Designing electric vehicles
Used for modeling electric vehicles and analyze their performance with a change in system inputs. Speed torque comparison, designing and simulating of a vehicle, whatnot.
This toolbox in MATLAB is used for analyzing offers resources for speech analysis, acoustic measurement, and audio processing. It also offers methods for extracting audio and speech features and transforming audio signals.
It offers a sizable library of mathematical operations for solving ordinary differential equations and performing linear algebra, statistics, Fourier analysis, filtering, optimization, and numerical integration. It offers tools for creating personalised plots as well as built-in graphics for visualising data.


Every day, millions of single adults, worldwide, visit an online dating site. Many are lucky, finding life-long love or at least some exciting escapades. Others are not so lucky. The industry—eHarmony, Match, OkCupid, and a thousand other online dating sites—wants singles and the general public to believe that seeking a partner through their site is not just an alternative way to traditional venues for finding a partner, but a superior way. Is it? With our colleagues Paul Eastwick, Benjamin Karney, and Harry Reis, we recently published a book-length article in the journal Psychological Science in the Public Interest that examines this question and evaluates online dating from a scientific perspective. We also conclude, however, that online dating is not better than conventional offline dating in most respects, and that it is worse is some respects. Indeed, in the U.
An internationally renowned department within one of the world’s most prestigious universities. The Mathematics department has a regular series of seminars and an active events programme, including the Departmental Colloquia. Find out more. View events organised within and relevant to the Maths Department, including our Colloquia series.
The Junior Mathematical Challenge is a minute, multiple-choice competition aimed at students across the UK. It encourages mathematical reasoning , precision of thought , and fluency in using basic mathematical techniques to solve interesting problems. The problems on the Junior Mathematical Challenge are designed to make students think.
Most are accessible , yet still challenge those with more experience. The competition is aimed at students in schools and colleges based in the UK. Entries must be made by registered UKMT centres , not private tutors, individual students or their parents. We are also extending the Challenges to run over a number of school days to allow you to run the Challenge in smaller sessions to adhere to social distancing requirements, if relevant, in your school. The Challenge date shown on this page is indicative only.
You can order online logins for your students, physical papers or a combination of both. The online and paper Challenge will run over the same number of school days and the results of both combined. This is because all results and your downloadable certificates will be made available on the online Challenge site.
Kangaroo – These will be run over 2 days and you will be sent either a paper or online entry depending on the format the student sat in the previous round. All online entries can be used at home using the same format as would have been used in school.
Now imagine you had a few million friends who could guide you through the thicket with their epic tales of success and failure. They sort and sift, crunch and correlate, catching whatever nuggets of mating wisdom fall out. Then they post a report of their findings — and the resultant dating tips — often with pop culture references, statistical graphs and pictures of half-naked young men and women. We invited experts with serious credentials in the science of mating and dating to weigh in on a few select OkTrend conclusions.
Read on:. Our scientists say: Makes sense.
The Department of Mathematics at Imperial College London is an internationally renowned department within one of the world’s most prestigious universities.
They say love is a numbers game. Bobby Seagull — the mathematician who rose to fame as a finalist on University Challenge in — took them literally. A few years ago, he sat down to try to work out why he had been so unlucky in life. From the total female populations of London and Cambridge — the cities between which he split his time — Seagull selected those roughly his age and up to 10 years younger. Then he reduced that group to the proportion that were likely to be university educated, to reflect the reality of his networks, as a school maths teacher and doctorate student.
Then came a harder parameter: what fraction Seagull might find attractive. That left Seagull with 29, potential girlfriends: as he puts it, a decent-sized crowd at the old West Ham ground at Upton Park. But that did not account for two important factors: his next girlfriend would have to be single — and she would have to find him attractive, too.
Subscriber Account active since. Women fare better when they take the initiative. That’s because women generally message men who are five points more attractive as rated by OKCupid users than they are, while they typically receive messages from men who are seven points less attractive than they are.
A podcast dedicated to sharing our guests’ favorite mathematical online dating site which was differentiating itself from the competition by.
Today I want to talk to you about the mathematics of love. Now, I think that we can all agree that mathematicians are famously excellent at finding love. But it’s not just because of our dashing personalities, superior conversational skills and excellent pencil cases. It’s also because we’ve actually done an awful lot of work into the maths of how to find the perfect partner. Peter Backus tries to rate his chances of finding love.
Now, Peter’s not a very greedy man. Of all of the available women in the UK, all Peter’s looking for is somebody who lives near him, somebody in the right age range, somebody with a university degree, somebody he’s likely to get on well with, somebody who’s likely to be attractive, somebody who’s likely to find him attractive. It’s not looking very good, is it Peter? Now, just to put that into perspective, that’s about times fewer than the best estimates of how many intelligent extraterrestrial life forms there are.
And it also gives Peter a 1 in , chance of bumping into any one of these special ladies on a given night out. I’d like to think that’s why mathematicians don’t really bother going on nights out anymore. The thing is that I personally don’t subscribe to such a pessimistic view. Because I know, just as well as all of you do, that love doesn’t really work like that. Human emotion isn’t neatly ordered and rational and easily predictable.
The Museum is closed due to the current public health situation. MoMath, the National Museum of Mathematics, is an award-winning museum that highlights the role of mathematics in illuminating the patterns and structures all around us. Its dynamic exhibits , galleries , and programs are designed to stimulate inquiry, spark curiosity, and reveal the wonders of mathematics. Learn more and apply now for admission to the Spring semester.
Christian Rudder, a mathematician and co-founder of online dating website OKCupid has spent a decade collecting and analysing data from.
Chris McKinlay was folded into a cramped fifth-floor cubicle in UCLA’s math sciences building, lit by a single bulb and the glow from his monitor. The subject: large-scale data processing and parallel numerical methods. While the computer chugged, he clicked open a second window to check his OkCupid inbox. McKinlay, a lanky year-old with tousled hair, was one of about 40 million Americans looking for romance through websites like Match.
He’d sent dozens of cutesy introductory messages to women touted as potential matches by OkCupid’s algorithms. Most were ignored; he’d gone on a total of six first dates. On that early morning in June , his compiler crunching out machine code in one window, his forlorn dating profile sitting idle in the other, it dawned on him that he was doing it wrong. He’d been approaching online matchmaking like any other user.
Instead, he realized, he should be dating like a mathematician. OkCupid was founded by Harvard math majors in , and it first caught daters’ attention because of its computational approach to matchmaking.
Although it seems as if mobile applications for online dating are mostly about connecting new people, the mathematics used behind the scenes is intriguing. What do we know about the algorithms used for these apps and what does the app know about us? And, more importantly, how is our online dating life influenced by this information? With the availability of online dating applications, it is getting more and more easy to meet and date new people.
For example, using Tinder, you can see the profiles of people around you.
Mathematician Bobby Seagull has tried to use numbers to solve his romantic difficulties. Is he on to something?
Mathematics Research Guide: Podcasts in Mathematics. Recommended Math Podcasts Mathematical Moments from the AMS The American Mathematical Society Mathematical Moments program promotes appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture. My Favorite Theorem A podcast dedicated to sharing our guests’ favorite mathematical results. Follow us on Twitter at myfavethm. A Brief History of Mathematics Professor of Mathematics Marcus du Sautoy reveals the personalities behind the calculations and argues that mathematics is the driving force behind modern science.
Inspired by the fact that women are vast minority in higher mathematics, Women in Math: The Limit Does Not Exist serves to increase enrollment and participation of women in mathematics and STEM courses. The Secrets of Mathematics A series of talks and lectures from Oxford Mathematicians exploring the power and beauty of their subject. These talks would appeal to anyone interested in mathematics and its ever-growing range of applications from medicine to economics and beyond.
Relatively Prime: Stories from the Mathematical Domain. Report a problem.


- Is K nearest neighbor supervised or unsupervised?
- What kind of classifier is K nearest neighbor?
- Is K means the same as K nearest neighbor?
- How many clusters are generated by the K Means algorithm?
- What is K nearest neighbor used for?
- How does Knn determine value of K?
- What is K in the K nearest neighbors algorithm in Python?
- Is Dbscan supervised or unsupervised?
- Can Knn be used for unsupervised learning?
- How is PSO used for unsupervised learning?
- Is CNN supervised or unsupervised?
- What is the use of K means clustering?
- Does K mean unsupervised?
- Is K means supervised or unsupervised?
- Why K means clustering is unsupervised learning?
- Is SVM unsupervised?
- How does K mean?
Is K nearest neighbor supervised or unsupervised?
The k-nearest neighbors (KNN) algorithm is a simple, supervised machine learning algorithm that can be used to solve both classification and regression problems..
What kind of classifier is K nearest neighbor?
K nearest neighbors is a simple algorithm that stores all available cases and classifies new cases based on a similarity measure (e.g., distance functions). KNN has been used in statistical estimation and pattern recognition already in the beginning of 1970’s as a non-parametric technique.
Is K means the same as K nearest neighbor?
K-NN is a Supervised machine learning while K-means is an unsupervised machine learning. K-NN is a classification or regression machine learning algorithm while K-means is a clustering machine learning algorithm. K-NN is a lazy learner while K-Means is an eager learner.
How many clusters are generated by the K Means algorithm?
1) The learning algorithm requires apriori specification of the number of cluster centers. 2) The use of Exclusive Assignment – If there are two highly overlapping data then k-means will not be able to resolve that there are two clusters.
What is K nearest neighbor used for?
In statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric method proposed by Thomas Cover used for classification and regression. In both cases, the input consists of the k closest training examples in the feature space.
How does Knn determine value of K?
The optimal K value usually found is the square root of N, where N is the total number of samples. Use an error plot or accuracy plot to find the most favorable K value. KNN performs well with multi-label classes, but you must be aware of the outliers.
What is K in the K nearest neighbors algorithm in Python?
What does ‘k’ in kNN Algorithm represent? k in kNN algorithm represents the number of nearest neighbor points which are voting for the new test data’s class. If k=1, then test examples are given the same label as the closest example in the training set.
Is Dbscan supervised or unsupervised?
DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a popular unsupervised learning method utilized in model building and machine learning algorithms. … Unsupervised learning methods are when there is no clear objective or outcome we are seeking to find.
Can Knn be used for unsupervised learning?
k-Means Clustering is an unsupervised learning algorithm that is used for clustering whereas KNN is a supervised learning algorithm used for classification.
How is PSO used for unsupervised learning?
For unsupervised learning, an internal clustering index can be used in the fitness function of the ESA optimized clustering method . …  two PSO methods were proposed, one to find the centroids of clusters and another that used K-means clustering to seed the initial swarm.
Is CNN supervised or unsupervised?
Selective unsupervised feature learning with Convolutional Neural Network (S-CNN) Abstract: Supervised learning of convolutional neural networks (CNNs) can require very large amounts of labeled data. … This method for unsupervised feature learning is then successfully applied to a challenging object recognition task.
What is the use of K means clustering?
Introduction to K-means Clustering. K-means clustering is a type of unsupervised learning, which is used when you have unlabeled data (i.e., data without defined categories or groups). The goal of this algorithm is to find groups in the data, with the number of groups represented by the variable K.
Does K mean unsupervised?
K-means clustering is the unsupervised machine learning algorithm that is part of a much deep pool of data techniques and operations in the realm of Data Science. It is the fastest and most efficient algorithm to categorize data points into groups even when very little information is available about data.
Is K means supervised or unsupervised?
What is K-Means Clustering? K-Means clustering is an unsupervised learning algorithm. There is no labeled data for this clustering, unlike in supervised learning.
Why K means clustering is unsupervised learning?
Clustering is the most commonly used unsupervised learning method. This is because typically it is one of the best ways to explore and find out more about data visually. … k-Means clustering: partitions data into k distinct clusters based on distance to the centroid of a cluster.
Is SVM unsupervised?
Support Vector Machines (SVMs) provide a powerful method for classification (supervised learning). Use of SVMs for clustering (unsupervised learning) is now being considered in a number of different ways.
How does K mean?
The k-means clustering algorithm attempts to split a given anonymous data set (a set containing no information as to class identity) into a fixed number (k) of clusters. … The resulting classifier is used to classify (using k = 1) the data and thereby produce an initial randomized set of clusters.


Shape Sorting Box
A modern take on this much-loved classic children's toy from Mushie!
Featuring 12 shapes in soft colors, children will expand their fine motor skills and learn about shapes as they match shapes to their paired cutouts.
- 100% BPA, PVC and Phthalate free
- Shape Sorting Box measures 14.2cm x 14.2cm
- Shapes measure 3.5 cm
- Recommended for ages 10 months+
- Made in Denmark


PhD maths student at Aix-Marseille Université with a passion for music, technology, and language.
Mirroring the classical approach to projective algebraic geometry to study weighted projective spaces and their varieties (summer project under Balázs Szendrői).
As an undergraduate I wrote two dissertations: one full length and one half length.
A translation and accompanying guide to Au-dessous de Spec Z (Toën and Vaquié, 2005) covering the background of this approach to categorical algebraic geometry.
An introduction to a categorical approach to extended persistence homology.
This series of articles is aimed at people who disliked maths at school, or who realise that they don’t really have much of an idea what people who study maths at university are actually even doing — are there really sums so hard that you need a university-level education to solve them?


After high school, the majority of the population throws out their advanced calculators and rejoices in the thought of never having to look at another equation again. That is, until you have to help kids with their homework and your phone’s calculator just doesn't cut it.
Photomath claims to solve all of your maths problems (literally and figuratively) and it's being dubbed a “smart camera calculator”.
It's as simple as pointing your camera at a math problem and the app will produce the answer as well as a step-by-step guide on how to solve the problem. While the app can literally do kids’ homework for them, it can also give them an understanding of the logic behind the answer in a few steps.
The app was created by a company called MicroBlink, which uses text recognition technology that interprets the math problem once it has been scanned – providing instant feedback. Photomath supports basic arithmetics, fractions, decimal numbers, linear equations and several functions like logarithms. The app doesn't recognise handwritten text, for now, meaning that users can only scan textbook equations by placing the equation within the red frame.
There are a few kinks that need to be worked out along the way, aside from only recognising printed text, such as the text recognition technology mistaking an "X" variable for a multiplication symbol, and the red frame limiting the length of the equation that can be scanned.
However, maths equations are just the beginning for MicroBlink as they plan to make advances in using the technology to revolutionise online banking.
Photomath is available on iOS and Android operating systems at no cost!


0.999… is the same as 1. Not just very close, but precisely identical:
a = 0.999…
10a = 9.999…
10a – a = 9.999… – 0.999…
9a = 9
a = 1
There’s no trick here. It’s just a mathematical fact that most people find deeply counterintuitive.
No, there’s no trick, but there is a failure to parse.
Lines 3 and 4 are quite bad, and it looks to me like there’s an implicit assumption being made in line 3 that is the source of all the confusion.
In line 3, the poster seems to be trying to say (in a shorthand way) that 10a — a is the same as 9.999… — 0.999… This is indubitably true, but it also muddies the issue, since it allows the next line to seem sensible:
9a = 9
If that were true, then to solve for a all you’d have to do is divide both sides by 9:
9a / 9 = 9 / 9
Which would make the conclusion, a = 1, make sense. However, the line 10a – a does not make 9a = a. I’m not sure where that assertion even came from, but it doesn’t belong in this algorithm.
What we have here is an example of truncation, basically (which eliminates everything to the right of the decimal), preceded by a multiplication by 10 to bring one digit to the left. (This is something that could actually work with any single-digit infinite repeater from .111… to .999…)
Truncation is something occasionally done in software, but not too often and usually for very specific reasons, because it’s simply false to claim that any truncated decimal is equal to its whole number equivalent. Put another way, 3.1415927* is not equal to 3.
Passing the above example through an accurate analysis, we see the problem more clearly:
a = .999…
10a = 9.999…
10a — a = 9
If we solve for a now (10a = 9), we find that a = .9
Try it again:
a = .222…
10a = 2.222…
10a — a = 2 <— Truncation
a = .2
So, long and short, this really is why it was so important to your algebra teacher that you always showed your work when you did all those math assignments. That’s the only way to step back through an equation’s solution and find where it went off the rails.
* Yes, I actually have memorized pi to the seventh decimal place. More than that would be unnecessary precision, and a waste of time. (This is irony, kids.)
One day I hope to have a phone number equal to pi, within certain limits. Dialers couldn’t miss it, but they might not know when to stop entering numbers. So it goes.
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The first line returns the natural logarithm of 10, and the second line returns the logarithm of 10 to the base 3. The math.gcd() method returns the greatest common denominator for two numbers; we can use it to reduce fractions. They include applying mathematical operations to the data to uncover patterns, trends, and relationships.
It is not a complete listing but is instead a list of numerical libraries with articles on Wikipedia, with few exceptions. This blog post will discuss the `isnan()` method in Python and how it can be used to check if a number is a Not a Number (NaN) or not. We’ll look at an example of using this method, as well as what NaN stands for and why it’s important. We may determine the factorial of a given integer in a one-liner code by using the math.factorial() function. The Python interpreter will send a message if the given number is not integral.
One of the business cards of matplotlib is the hierarchy of its objects. If you have already worked with the matplotlib introductory manual, you may have already called something like plt.plot ([1, 2, 3]). This one line indicates that the graph is actually a hierarchy of Python objects. By “hierarchy” we mean that each chart is based on a tree-like structure of matplotlib objects. The next example shows how to work with linear algebra with NumPy. It is really simple and easy-to-understand for Python users.
Things You Do That Shows You Are Not A Professional Python Developer
Return the natural logarithm of the absolute value of the Gamma
function at x. Int.bit_length() returns the number of bits necessary to represent
an integer in binary, excluding the sign and leading zeros. The IEEE 754 special values of NaN, inf, and -inf will be
handled according to IEEE rules. Specifically, NaN is not considered
close to any other value, including NaN. The algorithm’s accuracy depends on IEEE-754 arithmetic guarantees and the
typical case where the rounding mode is half-even. On some non-Windows
builds, the underlying C library uses extended precision addition and may
occasionally double-round an intermediate sum causing it to be off in its
least significant bit.
- By “hierarchy” we mean that each chart is based on a tree-like structure of matplotlib objects.
- This allows you to easily combine the capabilities of these libraries to perform more advanced operations and analysis.
- First, let’s discuss what Python library is and why it is an integral part of the machine learning and deep learning ecosystem.
- Today, we discuss eight Python libraries data scientists will find helpful.
If k is not specified or is None, then k defaults to n
and the function returns n!. Return the integer square root of the nonnegative integer n. This is the
floor of the exact square root of n, or equivalently the greatest integer
a such that a² ≤ n.
In machine learning and deep learning, Python provides a vast range of libraries that can perform various tasks such as regression, classification, and building neural networks. The Python Math Library is the foundation for the rest of the math libraries that are written on top of its functionality and functions defined by the C standard. Please refer to the python math examples for more information. These libraries save developers time and standardize work with mathematical functions and algorithms, which puts Python code writing for many industries at a very high level. It provides a comprehensive set of result statistics for each estimator, which have been tested against existing statistical packages to guarantee accuracy.
Python Libraries For Math, Data Analysis, ML, and DL
It will be a Python code and examples doing most of the talking. These libraries are all good in their own right but make sure to pick the correct one for your needs. The choice is python math libraries not irreversible but will require quite a lot of work later in a project. Your source code will need to be changed to use a new library and new faults will occur so choose wisely.
Also, if you have not already, consider using Jupyter. It provides you with notebook, documents and a code console on the same workspace. The mpi4py library provides bindings to the standard Message Passing Interface. You need to download a standard parallel library like mpich or openmpi. For functions beyond that, below are some libraries specialized for certain needs.
The Python SciPy library is a collection of mathematical algorithms and convenience functions built on the NumPy extension of Python. It adds significant power to the interactive Python session by providing the user with high-level commands and classes for manipulating and visualizing data. SciPy is organized into sub-packages covering different scientific computing domains. These include special functions, integration, interpolation, optimization, linear algebra, signal and image processing, genetic algorithms, ODE solvers, and others. SciPy also provides many user-friendly and efficient numerical routines such as routines for numerical integration and optimization. A Python library consists of pre-defined custom functions that help write neat and shorter scripts while doing tasks like data visualization, data analysis, machine learning, or deep learning.
File handling and data processing in python
It also has a simple and consistent API, which makes it easy to use and understand. Overall, Scikit-learn is a valuable resource for anyone interested in machine learning and data analysis in Python. One of the main advantages of NumPy is its ability to efficiently manipulate large arrays and matrices of numerical data. NumPy provides functions for creating arrays, reshaping and slicing arrays, and performing element-wise operations on arrays. It also includes functions for performing linear algebra operations, such as matrix multiplication and solving linear systems. From this blog post, it is clear that the `isnan()` method can be used to check if a number is a Not a Number (NaN) or not.
Is there a math module in Python?
Python has a built-in module that you can use for mathematical tasks. The math module has a set of methods and constants.
In data science, math, and data analysis play a vital role in the process of converting raw data into actionable insights. Converting degrees to radians and vice versa is a fairly common function and therefore the developers have taken these actions to the Python library. This allows you to write compact and understandable code.
Trigonometric and Angular Functions
x is not a float, delegates to x.__floor__, which
should return an Integral value. Dask is a Python package that provides flexible, efficient and easy-to-use parallel computing. If you want to perform some kind of computational task on a subset of data across multiple computers or CPUs, Dask will provide the tools to do so.
We already showed you how to work with the four data collection libraries. Matplotlib can be technically and syntactically complex. To create a ready-made diagram, it can take half an hour to google search alone and combine all this hash to fine-tune the graph. However, understanding how matplotlib interfaces interact with each other is an investment that can pay off.
Further, we are comparing a very large floating-point number with positive and negative infinity values. Similarly, it furnishes capabilities to operate on arrays, optimize numerical data, and process images and signals, among other features. You’ll also need to perform mathematical operations on data and analyze it. It allows you to create multidimensional data arrays of the same type and perform operations on them with great speed. Unlike sequences in Python, arrays in NumPy have a fixed size, the elements of the array must be of the same type.
Note that `NaN` stands for `Not a Number`, which is a special value used to represent the result of an invalid mathematical operation, such as dividing by zero. Return the ceiling of x, the smallest integer greater than or equal to x. If x is not a float, delegates to x.__ceil__(), which should return an
Integral value. The functions that are required in representation theory and number theory, such as calculating the factorial of an integer, will be covered in this part. Refer to the below article to get detailed information about the special functions.
To allow other projects to use the NumPy library, its code was placed in a separate package. The framework acts as an IDE but is aimed more at exploring the problems and the software you are developing than traditional IDEs. The simplest use of Python for math is as a calculator. To do this, start Python on the terminal and use the print function. SciPy offers a wide range of algorithms for optimization, integration, interpolation, eigenvalue problems, algebraic equations, differential equations, statistics and more.
One of the most popular uses of Python in mathematics is data analysis. Python’s built-in math module is a useful tool for performing a wide range of mathematical operations in your Python programs. This module contains a variety of functions for performing mathematical calculations, including trigonometric functions, logarithmic functions, and support for complex numbers. By using mathematical methods and algorithms, data scientists can train machine learning and deep learning models to make predictions based on historical data. Importantly, these libraries combine very well with each other; you can build graphs from numpy using matplot, use numpy objects, call the necessary scipy methods. If you look at the problem closely, then the need to write your own methods has already disappeared, except for some special functions and algorithms.
Finally, we will train the model by using the fit method. This trains the model on the training data for 32 epochs, with batch size 10. It also validates the model on the testing data after each epoch.
Our Software Directory features more than 1000 software reviews across all categories. Raises ValueError if x is not integral or
is negative. The gamma() function is used to return the gamma value of the argument. Gcd() function is used to find the greatest common divisor of two numbers passed as the arguments. In this section, we will deal with the functions that are used with number theory as well as representation theory such as finding the factorial of a number.
First, we import the necessary modules from Keras and TensorFlow. Okay, now we will use the fit() function to train the model. It was developed by a team of researchers from INRIA, which is a French institute for computer science and applied mathematics. https://forexhero.info/ This time, we’ll use it with the split() method, select the first element of str, and turn the type into float. The result is then assigned to c and printed to see the result. Then we will calculate transpose by using numpyndarray.T property from NumPy.
What is the difference between numpy and math?
math is part of the python standard library. It provides functions for basic mathematical operations as well as some commonly used constants. numpy on the other hand is a third party package geared towards scientific computing. It is the defacto package for numerical and vector operations in python.


Hot off the press, check out Vsauce’s video aptly titled How Many Photos Have Been Taken, where the team tries to calculate the total number of photographs taken since the invention of the camera (analogue and digital) and also give us some perspective of what these numbers mean.
So, how many photos are on the Lomography site? Over 10,000,000 that’s right, more than ten million. Why can’t we give you the accurate number? Because this very instant, lomographers around the world are still uploading photos to their homes. And how many photos are uploaded every day? Around 10,000 . This calculation stuff and Vsauce's enthusiasm are too contagious!
So, how many photos do you take a day and how many do you upload to your home?


Make better investing decisions when you have access to the Sortino Ratio. With Portfolio Workstation you can easily sort your watch lists by Sortino Ratio over any time window that you like. The better the Sortino Ratio score, the better the risk adjusted returns from that investment in the past. Unlike other well known risk adjusted return measures like the Sharpe Ratio, the Sortino Ratio does not punish upside volatility, so you won’t be overlooking breakout investments.
Understanding the Sortino Ratio calculation is simple. It is made up of three main parts:
- Compounded Return: This is the linear rate of return needed to get you from the starting price on the chart to the ending price on the chart.
- Risk Free Rate: This is what you could earn in T-Bills (or some other cash substitute) instead of making the investment under scrutiny.
- Downside Deviation: Think of this as the volatility of adverse price movement.
These three parts fit together in this way to calculate Sortino Ratio:
Sortino Ratio = (Compounded Return – Risk Free Rate) / Downside Deviation
Portfolio Workstation gives you instant Sortino Ratio calculations on freely available stock market data from Yahoo Finance and Google Finance. Free commodity and stock market index data is also accessible with the included Quandl data connector. Top-down stock market analysis using the Sortino Ratio is easy, simply download and import the Russell 3000 workbook file provided on this website and use Portfolio Workstation’s workbook sorting features.
Better research leads to bigger profits. You might like to learn more about:
Purchase your copy of Portfolio Workstation:
This simulated daily OHLC data was algorithmically generated to portray a hypothetical past for the DGAZ ETN over the period of February 18, 2007 to April 24, 2015. It is strictly intended for informational and testing purposes only.
For more information, please see our introductory post for this data set, DGAZ Price Simulated Back To 2007 Using UNG Prices.


Last week I experienced another one of those precious moments of true teacher satisfaction. I was sitting at the front of the classroom with a group of seven students, while the rest of class was scattered across the room engaged in a variety of activities. We started learning long division this week. Long division can be traumatic for fourth graders. As usual there was a small group that caught on immediately and were eager to move to more challenging problems, while others were lost and overwhelmed by the multi-step process. In order to reduce their stress and mine, we moved into small group instruction. It’s very satisfying to witness the light bulb turning on, as I guide students through the process.
I have been using small group instruction in math for about six years now. I don’t use it every day, and I don’t use it for every skill, but it is definitely one of the best changes I have made to my math instruction. I was first introduced to the idea when I volunteered to represent our school by taking additional district math training. I volunteered because I knew that my math instruction was my weakest area. Ironically, I ended up presenting professional development in math for the next several years. Lots of good things came out of that training. I learned how to make math more fun with skill building games and activities, and I learned a lot about how to differentiate. It improved my own understanding of math, and best of all, I actually like teaching math now.
Small group instruction lets me give guidance to those who are struggling. It allows me to identify where and how their mistakes are occurring. It provides me with opportunities to reassure students that they will get this and that they are growing in their skills. It enables me to correct misperceptions in a non-threatening and non-embarrassing way. It frees the kids up to ask more questions and ask for help as they need it. Recently, I was reminded of all these great advantages, when I read a blog post by Nancy Hniedziejko on her blog Nancy Teaches. (She is @nancyteaches on Twitter.)
I usually introduce a new skill to the whole group. We work for a day or two before I transition to small group instruction. I usually do a mini lesson to start, and then set a focus for the day. After several years of doing small group instruction in math, there are a few things I have learned.
1. Keeping the rest of the class busy and engaged is key. Since students are with me for only 20-25 minutes, it’s imperative that selected activities support math skills. I teach my students to play games that reinforce math facts. We have a math page on our class Read the Web wiki with links to math games. Following their small group time they are responsible for a seatwork assignment. This week, I also had students using the iPads to write a blog post.
2. Use frequent formative assessment to determine student needs. For me that may take the form of an assignment or a quiz. I find that math groups change more often than my reading groups do. I mix up my math groups on a weekly basis.
3. Give yourself permission to not meet with every student every day. It took me a while to come to this conclusion. Since I have 28 students I usually rotate my groups over two days. I work with every student in a small group setting, but it is done over the course of two days and I do spend longer with some groups than others.
4. Adapt your small group approach to meet the needs of the students you have. There’s no doubt about it, success with small groups depends a lot on the make-up of your particular class. With the kids I have this year, it’s easy. These kids work well on their own, and they get along with each other. I have had some years where my materials were destroyed, and kids did not use the time productively. In those years, I still did small group instruction, but I had to do so for a shorter length of time each day.
The best part of all is teaching in small group lets me connect more with my kids. It creates a more relaxing atmosphere, and kids soon realize that math is fun.


This pendulum is mesmerizing to watch as it traces beautiful Lissajous patterns in sand. A favorite of elementary school science tables, it can be used at upper levels to study harmonic motion as energy is transferred from a pendulum swinging in one plane to swinging in another plane at right angles. A Lissajous figure results from the two sine curves meeting at right angles. 21" tall!
Note: The pendulum is sold out, but we still have replacement sand available. Perfect for zen gardens, your science table, and much more!


Welcome to the Offbeat Computation Club! We are a mathematics and computation book club. We pick classics from the field of mathematics and computation and read them together.
To join this club, use one of the links below to log into our IRC channel. All meeting schedule updates are announced here.
Libera chat: #offbeat
Matrix bridge: #offbeat:libera.chat
You only need to join one of these links, not both. Both point to the same channel. If you are not an active IRC user, prefer joining the Matrix bridge because it is more convenient for someone unfamiliar with IRC. For example, you can close your browser or client and your chat session will still stay alive on the Matrix bridge. You can connect back the next day and catch up with the messages. Doing that with IRC requires slightly more work such as setting up IRC bouncers etc.
CSES Problem Solving (starting on Tue, 19 Oct 2021)
Analytic Number Theory (120 meetings from 05 May 2021 to 01 Oct 2021)
Participate in our book club meetings by joining our reading sessions and sharing any insights you have about the reading material.
If you would like to present a talk or host book club meetings for a new book, please join our channel and talk to us.


The Correct Income Tax SchemeWhere e refers to the mathematical constant e, f refers to a flat rate, applied at all income rates, p refers to the maximum rate for infinite income (not including the flat portion, of course), i equals income, pr equals the poverty rate, and c is a constant. Rate = f + p(1 - e^(-(i-pr) * c) I would suggest f should be 3 (varying between 1 and 5), p should be 55, but must be greater than 50, and I have no idea what c should be yet. Why tax people who earn less than the povery rate? The libertarians are basically right about the idea that if you don't pay anything, you won't care how it is spent. c should be crafted so that the logarithmic portion of the rate exceeds 50% at some defined point, perhaps 1,000,000,000 dollars. Below the poverty rate, simply discard the non flat tax portion of the system.
This is the rate for any income, not the overall rate, which would probably be the integral of this, if someone jogged my memory correctly.


The Laboratory for Scientific Computing (LabSC) is a research group at the Department of Physics (Cavendish Laboratory), University of Cambridge.
Research at LabSC is on topical problems of critical importance to industry, the economy and society, such as clean energy, sustainable aviation and aerospace safety.
We specialise in problems involving the nonlinear interaction of the four states of matter at extreme conditions such as supercritical geothermal energy recovery, disruptions in magnetically confined plasma and lightning strike on aerospace composite materials.
To this end, we develop new mathematical models (based on systems of nonlinear, inhomogeneous partial differential equations) to describe the physics of the system, and we build new numerical algorithms and high performance computing methods for their solution.
This allows us to study the physics of complex systems, some of which were previously considered to be intractable.