Think about some of the most common data visualizations you see in newspapers:
- Graphs showing a country’s GDP growth
- Stock market trends
- Charts that capture business performance year-to-date
- Rates of inflation
While most of these mean different things, they’re all the same at their core—they are all based on time series data.
What Is a Time Series?
A time series is a set of data points that are collected over a period of time, usually at regular intervals.
The most common type of time series data is financial data, such as stock prices or exchange rates. However, time series can also be used to track other types of information, such as meteorological data or sales figures.
Time series can be either univariate or multivariate.
- Univariate Time Series Data: Based on one variable, such as stock prices or the number of cases of a disease
- Multivariate Time Series Data: Based on multiple variables, such as weather data (which could include variables such as temperature, humidity, and rainfall)
Time series are often graphed to visualize the data, and they can be analyzed using statistical methods. Time series analysis can be used for forecasting future values, and it is a powerful tool for understanding complex data.
Types of Time Series Data
There are two main types of time series data:
- Continuous data: This type of data is collected at regular intervals and can be represented by a line on a graph. For example, data from a thermometer would be considered continuous data.
- Discrete data: This type of data is collected at specific points in time and can be represented by a dot on a graph. For example, data from a survey would be considered discrete data.
Continuous data is more common than discrete data since most real-world phenomena are continuous.
For example, the population of a country is a continuous variable that changes over time—it doesn’t jump from one value to another. In contrast, the results of an election are discrete since there are only a finite number of outcomes (e.g., candidate A wins, candidate B wins, etc.).
What Is the Best Way to Visualize Time Series Data?
Time series line graphs are the best way to visualize data that changes over time. This is because line graphs show how a variable changes from one point in time to another, making it easy to see trends and patterns.
For example, consider the following graph of stock prices for Tesla:
The line graph makes it easy to see that the stock prices have been decreasing over the course of the last year.
If the data were presented in a different way, such as a bar graph, it would be much harder to see this trend.
Line graphs are also useful for identifying specific points in time when there was a sudden change in the data (known as an anomaly). For example, the sharp drop in stock prices on October 29th, 1929, is easily visible on the line graph, but it would be much harder to spot on a bar graph.
When to Use Other Temporal Visualizations
Other types of graphs can be used to visualize time series data, but they are less common.
For example, you could use a scatter plot to visualize how two variables are related. This would happen in cases where you have multivariate time series data.
For example, consider the following scatter plot of stock prices and interest rates:
The scatter plot shows that there is a positive relationship between stock prices and interest rates—as one variable increases, the other variable also tends to increase.
This relationship would be much harder to see if the data were presented in a line graph.
Another example would be a bar graph, which could be used to compare different time periods. For example, you could use a bar graph to compare the stock prices of two different companies:
The bar graph makes it easy to see that Company A’s stock price is higher than Company B’s stock price.
However, the bar graph is not as useful for seeing trends over time since it doesn’t show how the data changes from one point in time to another.
Best Platforms to Visualize Data
There are a few different platforms that businesses and data scientists use to visualize data:
- Microsoft Power BI
These platforms are powerful tools that can be used to create complex visuals, but they can also be used to create simple line graphs.
Most analysts and data scientists prefer to visualize data in R, Power BI, or Tableau because these platforms offer more features and flexibility than a platform like Excel or Google Sheets.
However, Excel is still a solid data visualization tool for beginners who want to create simple visuals or who don’t have access to more sophisticated software.
How to Visualize Time Series Data In R
R is a programming language that is commonly used for data analysis and statistical computing.
It’s also a popular choice for data visualization since it has many different packages (i.e., sets of functions) that can be used to create complex visuals.
The most popular packages for data visualization in R are ggplot2, plotly, and leaflet.
These packages can be used to create a variety of different types of graphs, but they are most commonly used to create line graphs.
For an in-depth tutorial on data visualization in R, watch this video.
How to Visualize Time Series Data In Tableau
Tableau is a data visualization platform that is used by businesses and organizations to create complex visuals. It’s a popular choice for data visualization because it’s easy to use and it has many different features.
A few benefits of Tableau include:
- It can be used to create interactive visuals
- It has a wide range of built-in charts and graphs
- It integrates with many different data sources, including Snowflake, BigQuery, and Amazon Redshift
To learn how to use Tableau, check out this tutorial.
How to Visualize Time Series Data In Microsoft Power BI
Microsoft Power BI is a platform that many use to create temporal visualizations. Similar to Tableau, its drag-and-drop interface makes it easy to use and it offers a wide range of features.
The main difference between Power BI and Tableau is that Power BI is a part of the Microsoft ecosystem, so it seamlessly integrates with other Microsoft products like Excel and SQL Server.
To learn how to use Microsoft Power BI, watch this tutorial.
7 Time Series Data Visualization Examples
Now that we’ve given you the resources to learn how to visualize time series data and shown you the best platforms to use, we’ll show you seven different visualizations with a dashboard example for each.
- Line Graphs
- Bar Graphs
- Gantt Charts
- Heat Maps
- Stacked Area Charts
1. Line Graphs
Like we mentioned earlier, a line graph is the simplest and most common type of time series data visualization. It uses points to show how a dependent variable and an independent variable change over time.
The independent variable—as the name implies—remains the same, regardless of other parameters. The dependent variable depends on the independent variable and changes based on the relationship between the two variables.
In this graph, the independent variable is time and the two dependent variables are Ireland’s population and Europe’s total population.
In it, you can clearly see the sudden drop in Ireland’s population in the mid-1800s due to the Irish Potato Famine.
In this example, note the two separate y-axis scales—the two dependent variables represent Ireland and the European population as a whole. Europe’s population is considerably higher and is represented as such, but to the viewer, it might seem like they represent the same numerical values.
Use multiple y-axis scales when the dependent variables have different orders of magnitude (i.e., when one is much higher or lower than the other), and use them carefully. Remember to remind your audience that the two figures are presented to show a pattern or relationship, not to make an apples-to-apples comparison.
2. Bar Graphs
You might not think of a bar graph as a means of visualizing time series data, but it can be a helpful tool, especially when comparing multiple variables.
Bar graphs represent data in horizontal or vertical bars, and while they aren’t a good option for representing continuous data, they’re excellent for showing your audience the impact of discrete variables.
To effectively compare multiple variables, use different colors for each set of bars. In this example, note how the color makes it easy to see Turkey’s rapid population growth compared to Germany’s stagnation over the course of a decade.
In some cases, it’s better to use a stacked bar graph view. To show the relative proportions of each sub-group, stack the bars on top of each other.
This stacked bar graph shows the international population from 1990-2030. When comparing the data this way, you can see the steady population growth projection in developing countries as growth in developed countries (i.e., OECD countries) stands still.
Stacked bar graphs are best used when you want to show the proportion of a whole, not the absolute value.
3. Gantt Charts
A Gantt chart is a type of bar graph that’s often used in project management to visually track the progress of tasks over time. Each task is represented by a horizontal bar that starts on the date the task begins and ends on the date the task is completed.
Gantt charts are most commonly used to show project timelines, but they can also be useful for visualizing temporal data. If you need to track short-term data or changes over time, a Gantt chart can give you a high-level overview of what’s happening.
Suppose you’re a data analyst working with a web development team. You might use a Gantt chart to track the progress of different features as they’re being developed.
In this dashboard example, you can see that different activities are attributed to different team members. And each step is meant to be completed in a specific time frame.
When visualizing time series data, use a Gantt chart if your data is represented in a series of discrete steps or if you need to track the progress of tasks over time.
4. Heat Maps
A heat map is a type of graph that’s used to depict how different elements interact with each other. It shows relationships between data points using color to indicate the strength of the relationship.
The most common type of heat map shows how different variables relate to each other in a two-dimensional grid. The darker or more intense colors typically indicate a stronger relationship or larger values.
In this example, you can see how Seattle’s rainfall changes over the month, as well as how many inches of rain it gets per day in that given month.
5. Stacked Area Charts
Stacked area charts are among the most digestible and professional-looking ways to visualize time series data. They essentially take a line graph and turn it on its side, then fill the area between the lines with color.
By nature, they are an excellent visualization tool when you need to compare three or more variables over the same period of time.
This stacked area chart reveals how much revenue a company gained by selling different cosmetic produce across the world. The product names and values are placed along the horizontal X axis and vertical Y axis, with the crosshair enabled to help you compare the real-time value of different products from different regions.
If you need to compare multiple variables and show how they develop over time, a stacked area chart is a fantastic option.
But for visualizing a single variable, line graphs are usually the better choice. And for two variables, a scatter plot is usually the better choice.
6. Scatter Plots
Scatter plots are another type of graph used to depict relationships between data points. But unlike heat maps, scatter plots don’t use color to indicate relationship strength. Instead, they use the position of data points on a two-dimensional grid.
Scatter plots are great for visualizing relationships between two variables. They’re mostly used to demonstrate statistical relationships, such as correlation and causation.
This scatter plot shows how the US equity market compares to the 10-year US treasury bond over the course of 25 years. Although the relationship is nonlinear, the data shows a clear negative correlation over time.
7. Waterfall Charts
Waterfall charts show how an initial value is increased or decreased by a series of intermediate values. They’re often used in accounting to visualize the different components of a total income or expense.
This waterfall chart shows how a company’s cash flow increased and decreased over the course of one year. In red, months of net loss are highlighted. In green, revenue is a net positive and the difference between revenue and expenses month-to-month is shown.
If you need to visualize how an initial value changes as a result of intermediate values, a waterfall chart is the way to go.
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Here is a list of Sloan Academic Areas Research Seminars including the Operations Management Seminars.
Other related seminars at MIT include the Applied Math Colloquium, LIDS Seminar Series, CCE Seminars, and CSAIL Seminars.
The Harvard University Center for Mathematical Sciences and Applications also offeres related colloquia and seminars.


Note: The formula for the area of a parallelogram is \displaystyle A=b\times h. Explanation: The base of the parallelogram is 10, while the height is 5.
Area of Parallelograms - How to Find the Area of a Parallelogram
The area of a parallelogram can be calculated by finding the product of its base with the altitude. The base and altitude of a parallelogram are always.
The area of a parallelogram can be found by multiplying the base times the height. The height is the perpendicular distance between two bases. In the above.
Area formula using the base and height The area of a parallelogram is the product of the length of its base (b) and height (h). In the diagram above, △ABE. Note: Parallelograms and rectangles are pretty similar. In fact, you can turn a parallelogram into a rectangle to find the formula for the area of a. Calculates the area and perimeter of a parallelogram given two sides and the angle.


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While most people associate statistics with quantitative information, there are plenty of types of information. In general, data are pieces of information that can be taken for statistical analysis. The definition of “data” pertains to anything that provides a history or perhaps features. For example , if you look at the amount of people who own a certain car, or the amount of money that they earn. Then simply, when a person purchases a new house, that home may be worth more than their original price.


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Math101-CollegeAlgebra Department of Mathematics Millersville University Description Math 101 is a course for students who need to improve their algebraic skills before taking a higher level course such as Math 151, Math 160, or Math 161. The textbook can be purchased through the Louisiana Tech Bookstore. It is the responsibility of the student to inform the instructor of any necessary accommodations at the beginning of the course. This course is not intended for science, mathematics, or engineering students. RA due refers to Reading Assignments submitted through Wheaton onCourse; WW due refers to WeBWorK Assignments submitted through Wheaton's WeBWorK site. LaGuardia Community College 31-10 Thomson Ave. MATH 101 Intro to Mathematical Analysis I Fall 2016-17 Instructor: Dr. Students are assumed to know some limited physical science and elementary algebra. Math Study Center (MSC) Because of the challenging nature of this course, the Mathematics Department offers a Study Center for the students in Math 111 and 112. " Main Points on the Syllabus. blue/Math_101/exam. However, a calculator/computer should be used as an aid in the learning concepts, not just as a means of computation. MTH 201-202 is a series of mathematics courses focused on the mathematics needed for K-8 teaching. Schedules for both labs are posted in the respective rooms. My 7th Grade Math Classroom; Supply List ; Classroom Expectations; Daily Schedule; Contact Me; Grading Policy; Tutoring; Remind (Communication Through Texting) 7th Grade STAAR Mathematics Chart; 7th Grade Math Year At A Glance (Syllabus) my. Edexcel GCE in Mathematics, Further Mathematics, Pure Mathematics and Further Mathematics (Additional) is designed for use in school and colleges. Topic Outline. Additional Resources Available. Credit will not be given for both Math 1021 and Math 1023. This is the BEST basic electronics course on the internet. Whoops! There was a problem previewing MTM 101&102 SYLLABUS. Click the "Important Syllabus Information" link to access more information that is relevant to your courses this semester. Math 108Q, Fundamentals of Mathematics I - Chance Program (Fall semester only. _____ I attended the first lecture in Psych 101, I received a copy of the syllabus, and the course requirements were explained to me. Course topics include Newtonian mechanics, fluids, heat, vibrations, electricity and magnetism, light and sound, quantum phenomenon, nuclear radiation, relativity, and cosmology. The purpose of this lab is to give you practice programming small programs related to the constructs and conceptual ideas covered in lecture. NJIT Academic Integrity Code: All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. Come to office hours, visit the Math Tutorial Center or go to the Supplemental Instruction sessions when you have questions or need help. The main topics of PHY-101 are Newton's Laws of Mechanics, Conservation of Energy, and Basic Electromagnetism. (heat, work and engines), waves, and fluids. com 10:00 - 12:00. Background should include two semesters of high school algebra. This course presents principles to develop appropriate and effective communication strategies in one-to-one and small group communication settings. "The Mathematics Program in the College of Sciences at King Fahd University of Petroleum and Minerals is accredited by the National Commission for Academic Accreditation & Assessment for the Period May 2015 to April 2022 and agrees to uphold the NCAAA Standards for the Quality Assurance and accreditation of Higher Education Programs. Students with a documented disability may contact Liberty University Online's Office of Disability Academic Support (ODAS) at. The searches below only return course versions Fall 2000 and forward. Because the fundamentals of Set Theory are known to all mathemati-cians, basic problems in the subject seem elementary. and Math Proofs Week 2 – 3 Each student is to gather 2-3 logic puzzles and 2 mathematical proofs. For more details on individual sections of Math 111, please contact the instructor of that section. Academic Services maintains a file of detailed course content summaries for courses offered at Northern Virginia Community College. The intended audience for Math 115 College Algebra is the student who needs a background in college algebra to help prepare him/her for either of the one-semester calculus courses, Math 130 or 135, or for other quantitative courses, such as statistics or mathematics for elementary teachers. Reviews the various mathematics reform efforts over the past 170 years. Course Description for Math 1314. Math101-CollegeAlgebra Department of Mathematics Millersville University Description Math 101 is a course for students who need to improve their algebraic skills before taking a higher level course such as Math 151, Math 160, or Math 161. As this is a relatively new course, the instructor reserves the right to adjust/augment the syllabus as needed throughout the semester. If you miss it due to incapacitating illness, severe domestic affliction or other compelling reasons you can apply for an excused absence. Math Study Center (MSC) Because of the challenging nature of this course, the Mathematics Department offers a Study Center for the students in Math 111 and 112. Course Title: Mathematics for General Studies. Must have a passing grade. Homework problems will be posted on the Stat 101 course web site and on Blackboard. MTH 102 does not have designated tutors in the math learning center. Now check NDA 2019 mathematics syllabus details below. In schools, these subjects are often taught to students who are not planning a university education. Right of Change. Milton Nash is the Acting Dean of the Mathematics, Statistics, and Data Science area. The Limit of a Function. Everything we discuss in class will be rigorously proved. And it does—up to a point; we will prove theorems shedding light on this issue. The challenge must be emailed to the instructor, with detailed justi cation, within one week of the date the grade is available. I have received a copy of the Department of Psychology's Student Responsibility Code. UCLA computer science and mathematics Professor Rafail Ostrovsky has been elected as a Foreign Member of Academia Europaea for the class of 2019. 001, MWF 02:30-03:20 pm, 115 Osmond Building; Welcome to Math 033: Course Description. beyond that of high school mathematics. Whether you are struggling with basic math functions in a course today, you are taking a new job that demands understanding of math, or you simply need to review or remember some part of basic math, this course will bring you up to speed. No textbook will be required for this section of Math 101. mathematics (including trigonometry - i. Emphasis will be placed on base 2 which is the most important for repre-sentation of numbers on. Phone: (609) 258-3361. Mathematics Department MAP 101 Thomas Rico Fall 2019 Syllabus Course Description: The goal of the course is to build a conceptual understanding of the fundamentals behind arithmetic and algebra. PY-101/ CY-101. Welcome! This is one of over 2,200 courses on OCW. All the applicants need to elect one desirable subject from their post-graduation, which will be advantageous to score high in NET, 2019. 2019-2020 Fall Semester (2019 – 1) MATH 119 – Calculus with Analytic Geometry. New math course starting in September 2019 for IB Class of 2021 Course description from IB Approximate current equivalent Recommended prior math background Mathematics: Applications and interpretation This course is designed for students who enjoy describing the real world and solving practical problems using mathematics, those who are. This is a mathematics pedagogy course in the Secondary Mathematics Education Program in the Department of Mathematics. There is no make-up for quizzes and homework. Mathematical foundations for all computational skills and concepts. Except by permission of the chair of the Department of Mathematics, a student may not receive credit for any of Math 101, 106, 107, 112, 114, 115, 118, 156 or 157 if that course is completed after completion of any higher numbered course in this list or after completion of a course in calculus for which college credit has been received. Objectives:. Long Island City, NY 11101 1-718-482-7200. All associate and bachelor degree-seeking students are required to complete the general. A correct submission to a problem by its deadline will result in 5 homework bonus points. MAT 593 Directed Study in Mathematics (1-3) MAT 594 Directed Study in Mathematics (1-3). CMPSC 101 - Intro to C++ Programming Course Description. This course provides an introduction to the basic concepts of information, information systems, information technology management, and the "Information Age. 3); HL syllabus (see syllabus section 1. MATHEMATICS N3 New Syllabus Module 0 contains revision ofbasic Mathematics and can be use as other quadratic 101 Exercise 3. Credit will be granted for only one of MATH 101 or MATH 142. The objective of this course is to master the materials in chapters 12-16 in the book which deals with the calculus of several variables. Its faculty, productive and research-oriented, is committed to the advancement of economic science. Topics (28 sections) 1 Feb. Little Known Facts about Math 101. Now check NDA 2019 mathematics syllabus details below. Department of. Please use this syllabus as a reference only until the professor opens the classroom and you have access to the updated course syllabus. 2016 Question papers and marking schemes. Rachelle R. He earned his bachelor's degree from the University of Alabama at Birmingham, master's degree from Princeton University, and Ph. The Course Descriptions catalog describes all undergraduate and graduate courses offered by Michigan State University. Class 2 maths plays a major role to make math basics strong. A student may receive credit for only one of the following courses: CMPSC 101, 200, 201, 202, 121. CHEM-101 is a prerequisite for CHEM-102. Officially, Applied Mathematics 21b or Mathematics 21b (or Math 23, 25, 55) and some knowledge of probability and statistics at the level of Statistics 110 or Applied Math 101. Math 101 Online Syllabus Introduction to Contemporary Mathematics Fall 2015 Instructor: Dr. And learn whether to add first or multiply first in a string of operations. Exam block #2: Math, Science, and Engineering Tools (20%) Objectives covered by the block (8 exam items). math class before 101 or plan to spend a lot of time practicing your math skills. Help with Math + Arithmetic & Algebra; Statistics; Precalculus; Calculus; Clubs & Activities + AMATYC Student League; Math Club; Sample Common Finals-Math 101/120 Sample Common Finals ; Math 141/146 Sample Common Finals; Temporary WebAssign Access; Faculty Resources + Math Faculty Training; Stats Faculty Training; Mathematics Division Forms. The make-up exam for the Final Exam takes place on the third day after the Final Exam. College Algebra Math 101 is a first-level course in the fulfillment of the mathematics requirement for graduation at the University of Kansas. STAT 101 is an introductory course in statistics intended for students in a wide variety of areas of study. MATH 101 SYLLABUS MEYER FALL 2019 you must earn a grade of C or higher in Math 101. Economy Schiller Chapter 2 Feb 11, 13, 18, 20 Supply & Demand Schiller Chapter 3 Feb 25, 27 Consumer Demand & Price Elasticity Schiller Chapter 4 Mar 4, 6 Supply Decisions and Production Schiller Chapter 5. Group actions. Typically run as a graduate course, and recommended only for those in the ADP program or that wish to pursue graduate studies in mathematics. Syllabus of Math 611 - Math 612: I. We write to communicate to others-whether they are colleagues, professionals in their fields, or friends. I can confirm that MATH 120/121 are noticeably different from AP BC Calc or A Level Further Maths (and I'd gander to also say IB HL Maths). 3 Credit Hours. Prior study of chemistry is not assumed. Click the "Important Syllabus Information" link to access more information that is relevant to your courses this semester. It contains a list of basic math formulas commonly used when doing basic math computation. Our faculty represent a broad array of disciplines within mathematics and also work on problems arising in physics, chemistry, biology, computer science and engineering. Success in College Algebra fulfills one unit of the Critical Thinking & Quantitative Literacy General Education Goal for the KU Core and prepares students for subsequent work in a second-level mathematics course (i. This question should have objective or short. Applications range across all areas of. in Mathematics Math Course Syllabi Class Schedule Mathematics News & Events Mathematics Undergraduate Research Dual Degree Engineering Program Math Colloquiums KME - AL Beta Chapter Mathematics Alumni Stories Summer STEM Camp Printable Brochures & Forms Resources and Facilities Statewide Math Contest. Each assign-ment will cover the material taught prior to the date it is posted on. MATH 115-Y Course Syllabus. Course Summary This Statistics 101 Syllabus Resource & Lesson Plans course is a fully developed resource to help you teach introductory statistics. This syllabus is proprietary material of APUS. Daily Syllabus, Math 101 Calculus I, Fall 2019. This means that. There are currently syllabi for. Three years of high school mathematics or equivalent. MS- 101 Topology and its Applications 04 40 60 100. By the end of Math 54, students are expected to be able to devise and clearly explain simple proofs on their own. The learning modules can be accessed using the password elearning. Whoops! There was a problem previewing MTM 101&102 SYLLABUS. Community College of Rhode Island is the largest community college in New England and has been a leader in education and training since 1964. The textbook can be purchased through the Louisiana Tech Bookstore. The syntax and semantics of a modern programming language. Sample syllabi for large-enrollment courses are available for download, as pdfs, listed below. Credit will not be given for both Math 1021 and Math 1023. Long Island City, NY 11101 1-718-482-7200. This syllabus outlines policies common to all sections of first-year English at Texas State University. Students should have a minimum Math ACT score of 19 to enroll in Math 1021. ASTR 101 is composed of nine lessons, two midterm exams, and a final exam. Reading Assignments All reading assignments will be from Astronomy Today. Descriptions of undergradaute liberal arts courses in the college of literature, science, and the arts at the university of Michigan. In differential calculus, we start with a function and try to understand its rate of change. Mathematics Department MAP 101 Julia Viro Fall 2018 Syllabus Course description: The goal of the course is to build a conceptual understanding of the fundamentals behind arithmetic and Algebra. Course Syllabus for MATH 101 (Spring 2009) Contemporary Mathematics Instructor Information Name: Dr. Typically run as a graduate course, and recommended only for those in the ADP program or that wish to pursue graduate studies in mathematics. 2015 Question papers and marking schemes. The office hours are held by the instructor and the two teaching assistants. 320 Armstrong Hall P. The other two courses are Elementary Algebra (MATD 0370) and Intermediate Algebra (MATD 0390). Help with MyMathLab assignments. Cutnell & K. You may seek help at the MLC during any of the hours that MTH 101 help is available. 2 The Tangent Problem: Example1. If you miss it due to incapacitating illness, severe domestic affliction or other compelling reasons you can apply for an excused absence. 001, MWF 02:30-03:20 pm, 115 Osmond Building; Welcome to Math 033: Course Description.


Khan Academy now have on the order of 2,200 videos covering everything from basic arithmetic all the way to vector calculus . They have a million students a month using the site, watching on the order of 100 to 200,000 videos a day.
These resources can be very effective as revision or reinforcement tasks, a backup for students who miss a lesson or for students who need further input to fully understand certain concepts.
Salman Khan: Let's use video to reinvent education | Video on TED.com
See what is available:Browse the library
Start at the very beginning. The software will build your streak. It builds profiency with unlimited problems until you get 10 in a row, in a game like framework. Students can earn badges to encourage and motivate them.There are hint facilities available and the software allows students to work at their own pace. There is plenty of feedback for teachers and parents to view. These resources should be used as part of a balanced course.


As a teenager, I sat in the cold unpersonalized classroom listening to the obese man in the front of the room. He sat at a raised podium-like desk, spouting strange phrases focused on numbers and angles and how they all connect. A blackboard in the background was littered with figures and symbols, but none of it made any sense to me. Mr. High School Math Teacher broke from his monologue and pointed a question at me, grimacing as I shot back an answer that indicated I was clueless and didn't much care about what he was talking about. His face contorted as if in pain, and he held up and shook a large textbook as if to say, "This is important to your life and you should care, Mr. Hoskins."
But food labels confuse me. And EVERY bite of food carbs means you face a Stowaway Math Problem (see George and Scott's awesome YouTube video on this!). For example: measuring out 1/3 cup that costs 13g for each serving, and I'm eating 3.5 servings. Plug that into the equation with an insulin-to-carb ratio of 10g (which I refuse to change because that's a simple number that offers HOPE for easier calculations.) Then factor in a correction bolus for a 202 mg/dL, and adjust for the snack or correction bolus taken a couple hours ago that hasn't yet worn off completely...
Ugh. Seriously. Even though I typed that above graf, my mind tuned out right after the spot about measuring a 1/3 cup portion. Had you been here watching me type, you likely would have observed my eyes glazing over. There's numbers, symbols, lines, graphs, angles, and weird herioglyphics floating across my sightline... Ugh. But this is such a regular part of life, and food-makers don't ease the difficulties, either. Like when you order a pizza, and the pizza-makers own website says one slice out of 8 costs so many carbs... Yet the pizza you've received is cut into 10 slices! WTF?! C'mon! It's like they're trying to make my D-Math more difficult!
Luckily, I'm not totally lost to the Dark Mysteries of the Math World. Thanks to my wife Suzi, who's a banker and math guru. She's got the skill.
This means that while Suz is the calculator, I'm left to say what I want to eat, possibly help in cooking and preparing it, and letting her fill me in on what it all costs (in the Hoskins Household, that's our lingo for carb counting: How much does this "cost?"). It's a great partnership. Admittedly, though, I'm the weaker link as I'm just lost without her.
That's it exactly, Jim! At least some of us PWD are math teachers, have math-inclined spouses and family members, or simply can rely on insulin pumps for some math help. It does us well, even if we didn't capture the pride of our High School Math Teachers. We should form a D-Math Club, with Mr. Huck leading the way!
As far as the math goes, I'll look forward to returning to my pump in a month or two. Then I won't need to be a Human Calculator as much. Maybe then, 2+2 won't equal 5. Well, maybe it won't. I'll never be the person who could have answered that question posed so many years ago by Mr. High School Math Teacher, but at least I can look back and know that he had a point. Consider this my semi-public apology: Mr. H.S. Math Teacher. you were right. I should have paid more attention to you, because math is important to my life. Especially my D-Life. Wish I would have known it then.


Fascinating facts, figures, and pictures highlight informative text about some of the most interesting and extreme jobs that use math. Young readers will learn what kind of training it takes to be a stunt coordinator, how much money a cryptologist makes, and what exactly a fluid mechanics engineer does, all while discovering how math is involved in each of these exciting jobs.
Unusual and Awesome Jobs Using Math: Stunt Coordinator, Cryptologist, and More
Tuesday, March 14, 2017
Pi Day is the celebration of the mathematical constant π (pi). Pi Day is observed on March 14, since 3, 1, and 4 are the first three digits of π.
Pages 32 pages
Reading level 3-4
Interest level 3-9


My little boy has really started to get into counting recently. He also loves fish (any water based creatures actually) and enjoys playing with playdough. So I thought, what better way to help him develop his early math skills than some cute and functional fish counting playdough mats!
He’s only 2 so he’s not ready to use the writing part of these mats yet, but he loves counting the fish and trying to make sure that there’s the right amount swimming in the fish bowl.
Just playing with playdough can have so many amazing benefits for your kids, but these mats will help you take some of that creativity and focus it towards learning and developing their math skills.
What Skills Can Your Children Learn And Practice?
When playing with these fish counting playdough mats, your children will have the chance to practice and develop some early math skills such as:
- Counting skills – they’ll have to count the fish carefully to ensure they are making the right amount for the fish bowl and ten grid
- Number recognition – these mats can help them to improve their number recognition as they associate the amount of fish with the written form of the number
- Number formation – shaping the dough into the correct shapes for the numbers can be a wonderful, hands-on way to reinforce number formation, especially for those not ready to write them yet
- One to one correspondence – this important skill (trickier than you may think) is the ability to only touch and count an object of a set once.
They will also have the chance to improve some non-math skills such as:
- Fine motor skills and hand-eye coordination – when they are molding the playdough into fish, balls or numbers they will have to use these skills to ensure they make the correct shapes
- Hand strength and dexterity – playing with playdough can be a great way to improve these important pre-writing skills
- Pencil grip – if your child is ready to have a go at the writing part
I’ve created these fish counting playdough mats for the numbers 1-10.
How To Prepare These Fish Counting Playdough Mats
What you’ll need:
- The printable fish counting playdough mats
- Playdough (if you fancy making your own with your little ones, you can find a cheap and very easy no-cook recipe here)
First you’re going to want to download the mats by clicking on the download box at the bottom of the page.
There’s no cutting involved here unless you want to trim around the edges of the mats.
Once you’ve downloaded them, you’ll need to print them off onto paper or card.
Then you’ll probably want to laminate them to ensure they don’t get ruined by the dough.
After that you’re all done!
Let your kids practice their math skills in a fun, fishy way!
I hope your children enjoy practicing counting with these mats – be sure to check back in for more awesome educational printables.
If you want to make sure you don’t miss any, you can turn on notifications by clicking on the little bell in the bottom right corner.


I have a degree from the University of Wisconsin Madison. I am autistic. I am very intelligent but my thoughts get scrambled and talking to people makes me nervous.
About origami: I create Origami because it is beautiful and the repetitive motion of paper folding has a calming effect for me. I like the geometric models best because of their mathematical and visual components. I taught myself origami when I was 9. I graduated from cranes to more difficult figures and can now make the most complex and difficult designs. A few of my Origami designs I created myself, but I mostly use designs by others. I like the large geometric models best because of their mathematical and visual components and the need to plan color schemes.
About Fractal Graphics: Fractals graphics involve the computerized generation of pictures based on mathematical chaos theory. I have software on my computer that is designed to manipulate and/or solve mathematical equations and then translate the results into computer graphics. These graphics are "chaotic" in the mathematical sense in both form and color. I sometimes make up complex equations of my own and plug the results into the software. I have been fascinated by fractal graphics ever since I first saw the “Mandelbrot Set” in a magazine when I was a teenager.
About My artwork: I am fascinated by mythical beings; some of which I made up myself. I have made up an imaginary world where people, animals, Burmecians, Cynopians, and many other beings (both real and mythical) live together. Much of my artwork is based on characters in my imaginary world.


Schools in Brighton and Hove show GCSE improvement
GCSE results in Brighton and Hove have shown an improvement on last year, despite tougher exams.
Brighton and Hove City Council said the ‘Attainment 8’ measurement, which shows average attainment at individual schools across eight subjects, has improved in the city.
Last year the city’s overall Attainment 8 score was 46.8, while the figure for this year is 48.0.
Related stories: GCSE results for Brighton and Hove – our live round-up
Most GCSEs are now being graded from 9 to 1, with 9 being the top grade. Government guidance advises that a grade 4 is considered a ‘standard’ pass.
This new system was introduced last year for maths and English, but this year nearly 20 other subjects are being graded in this way.
City-wide figures in the key maths and English accountability measures are as follows: grades 9 to 4 in maths, 73 per cent (up from 72 per cent last year); grades 9 to 4 in English, 78 per cent (down from 79 per cent last year); and grades 9 to 4 in English and maths combined, 68 per cent (the same as last year).
Cllr Dan Chapman, chair of Brighton and Hove City Council’s children, young people and skills committee, said: “The new Attainment 8 system is widely recognised as an effective way of measuring overall school performance across their wider curriculum.
“This year-on-year improvement is above all due to the sheer hard work and dedication of our students.
“It also comes on the back of improved results city-wide at both A-level and primary level.
“I would like to congratulate all of our young people, as well as the secondary schools, teachers and support staff who have supported them.
“I would say to any students who did not get the results they wished for to remain positive.
“As well as A and AS levels there is a fantastic range of vocational and other opportunities in our city, including apprenticeships, to match any skills you wish to develop.
“Congratulations to the council’s schools team and the city’s Education Partnership for their continued collaboration to raise standards.
“Today’s results show that this approach is working well.”


Home » Posts tagged 'Math Tutoring Programs'
Tag Archives: Math Tutoring Programs
Every student is not the same and some need extra attention when it comes to improving grades. Mathematics is a very crucial subject to get better grades and some of the students need tutors to help them get better grades. It is very important to carry out research before you enter into a contract with any tutor to ensure if he is suitable for your child or not. You need to ask several important questions from the tutor like If the tutor is well qualified or not? Is the tutor specialized in math?
Nowadays, there are rich sources to seek math tutoring services. You can look up for newspapers, check online. Also, there are many websites that help with math homework. There are many websites that search for professional math tutors in your area. You can contact https://www.get-ahead.org/ for assisting your child with math homework.
Image Source: Google
There are various advantages of hiring a private math tutor:
Firstly, Your traveling time is saved as the tutor is in your locality and you can utilize that time in fun activities.
Secondly, You can ask as many questions as you want from your private tutor comfortably.
The tuition classes are completely different from classroom teachings as there is no dedicated time for a lesson or topic and you can revise any topic a number of times.
Private tutoring is best if you are having trouble understanding complex topics or you are preparing for the entrance tests. They will provide you in-depth knowledge and short tips or tricks to solve problems and help you perform better in exams.


Scientists, engineers, students, and others are programming with Omikron Basic since 1985. Read about the benefits of this easy to learn programming language.Omikron Basic was originally developed in the 80s to be used on ATARI computers. After that, it was mainly used by scientists and engineers...
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A version of the classic worm game, played in non-Euclidean space - that is to say, on the surface of various three-dimensional shapes. It features retro-style vector graphics, exciting differential geometry and almost guaranteed nausea!
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smib is a mosaic of FORTH and LISP, C Sauce and an experimental programming language close to mathematical language. In this version : law of large numbers, central limit theorem, hyperbolic trigonometry, warnings are cleaned . Features . Number theory : infinite size integers, arithmetic...
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Geometry Master 3.0 is a Geometry Tutor that enhances Geometrical, Spatial and Drawing skills. The program comes with many excellent drawing tools. The Software runs on all Windows systems and has multiple Drawing Tools, Color Fill Options and Custom Shape Tools. It also can save the images in...
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Custom Geometry is an extension which resizes and positions the window according to your settings. Custom Geometry adds a button to the Firefox status bar that will resize the Firefox window to your specifications. Many other extensions will resize the window, but only to preset dimensions,...
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Modest Ordinary Differential Equation Library is a C++ library to model rate equations. MODEL is a numeric simulation library written during my PhD to simulate systems of rate equations describing Vertical Cavity Surface Emitting Lasers (VCSELs). I decided to write one myself after looking at...
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Geometry Description Markup Language (GDML) workpackage is primarly ment to provide geometry data exchange format for the LCG applications. The workpackage consists of the GDML Schema part, which is a fully self-consistent definition of the GDML syntax and the GDML I/O part which provides means...
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Geometry Solver 3D is an accessible and handy application that will resolve analytic geometry problems with ease.
The program will also provide tools for calculations in 3D as well as graphic OpenGL demonstrations. Now you can use this handy software to solve math problems.
Platforms: Windows, Windows Vista, 7
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Circles Geometry has 9 graphic calculators to solve line and circle problems. All possible solutions are calculated in your coordinates and units. The picture, drawn from the calculated values, witnesses that the computations are correct. Use thie step-by-step help information to code your...
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ceometric provides efficient math libraries for object-oriented spatial geometry programming in a .NET language. Our libraries enable very intuitive and CAD-like working on geometric objects in space in C#, VB.NET or J#. All methods are highly efficient and suitable for large scale computations....
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Geometry Express is the newest addition to Praeter Software's award-winning line of educational mathematic calculation and teaching software for students and teachers.
Designed to help students and teachers visualize and demonstrate various calculations for different geometrical shapes,...
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Basic Differential Encoding/Decoding of input vector of numeric valuesdiffencodeve.m : Differential Encoding functiondiffdecodevec.m : Differential Decoding functiondiffencodevecTest.m : Test Program for Differential Encoding/Decoding.
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Graphical user interface (GUI) is used to solve up to two ordinary differential equations (ODEs). Results can be plotted easily. Choose between MATLAB's ode45 (non-stiff solver) or ode15s (stiffer solver).This is primarily a teaching tool.
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A differential equation can be solved by several methods. I have presented the simulink method to solve the differential equ. The que is showed in the screenshot.Queries and Comments are dearly invited.
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This function solves the linear fractional-order differential equations (FODE) with constant coefficients. The short memory principle has not neen used here, so the length of input signal is limited to few hundred samples. The parameters of the FODE (in its standard form) are the inputs of this...
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First-order-degree linear differential and non-homogeneous equation's solution possible the unknown integration multipler technique. Also, this simple technique's depend both sides of original homogeneous differential equation. The solution is slightly and more complicated if this integration...
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Polar Parallel Coordinate Geometry (PPCG) plots standardardised time series data. Colour is used to demonstrate data through time; black being the oldest to white being the newest. 2 - 3 Std deviation warning/action limits are also highlighted by yellow/red respectively.
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[D]=Diff_Quad(N);Differential Quadrature Matrix for 1st derivative based on Lobatto grid.It calculates for N grid points.Higher derivatives can be easily calculated by using D matrix.
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Math::Geometry is a Perl module that implements classic geometry methods. It should be considered alpha software and any feedback at all is greatly appreciated. The following methods are available: vector_product. Also known as the cross product, given two vectors in Geometry space, the...
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Interactive geometry software for performing interactive calculations, visualization and modeling in math, science and engineering. The construction concept and the interactive visualization are the basis of the program. Designed to be easy-to-use, it provides a powerful mathematical platform...
Platforms: Windows, Windows 7, Windows Server
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MATTHEW SCAIFE - WIN/LOSS ANALYSIS
Win/Loss Rate percentages are calculated by dividing the number of tasks won by the total number of tasks flow against another competitor. For example, if Competitor A has 8 task wins over 10 tasks flown against Competitor B, then Competitor A will have a Win/Loss Rate of 80% and Competitor B will have a Win/Loss Rate of 20%. Two equally matched pilots will have a Win/Loss Rate of 50%.
The Average (AVG) Win/Loss Rate percentage for a competitor is calculated based on the average number of tasks won and/or lost against all other competitors that they have competed against. For example, if Competitor A has 40 task wins and 10 losses against 5 competitors, then Competitor A will have an AVG Win/Loss Percentage of 80%.


Some people are natural-born MVPs.
They pick up the slack that we all leave behind without anybody asking them to in the first place. Gracie Cunningham is just one of those people.
The high schooler created a TikTok questioning the existence of math – and the internet nearly exploded. What’s even more amazing is that a real mathematician actually responded to her questions.
Talk about a statistically significant TikTok.
In the original TikTok, Cunningham asks:
“I get, like, addition. Like hey, if you take two apples and add three, it’s five.
But how would you come up with the concept of, like, algebra? What would you need it for?”
this video makes sense in my head but like WHY DID WE CREATE THIS STUFF
Critics of the video came out in droves – so Cunningham released an additional video clarifying what exactly she meant.
Haters still inevitably piled on, but Cunningham actually raises an excellent point. It’s a question that we’ve all undoubtedly wondered at some point.
Just where does the idea of math come from? Who made it up? How is the way that we understand math different today from the way we understood it when it first began?
That’s where Dr. Eugenia Cheng comes in.
The Chicago-based mathematician came across Cunningham’s viral TikTok and responded with an extensive, two-page reply explaining the concepts that Cunningham had called into question.
Cheng, the author of x+y: A Mathematicians Manifesto for Rethinking Gender, shared her thoughts on Cunningham’s questions:
Her thoughts and questions are the kinds of things that research mathematicians think about all the time, and I believe it’s what drives us to do research: we are not satisfied with basic answers and we keep wanting to ask why, more and more, to get deeper and deeper into the root of a question.”
Moments like this give me hope for the rest of us. We could all use some more internet wholesomeness in our lives.
What are some questions about math that you’ve always wondered?
Let us know in the comments below!


How To Calculate Finance Charges
Having some intelligence of how to calculate finance charges is constantly a good thing. Most lenders, as you know, will do this for you, but it can helpful to be able to check the math yourself. It is imperative, however, to comprehend that what is presented here is a elemental procedure for calculating finance charges and your lender may be using a more complicated method. There may as well be other problems attached with your loan which may affect the charges. The first thing to comprehend is that there are two elemental parts to a loan.
The first problem is called the principal. This is the amount of money that is borrowed. The lender wants to make a profit for his services (lending you the money) and this is called interest. There are a myriad of types of interest from simple to variable. This article will examine simple interest calculations. In simple interest deals, the amount of the interest (expressed as a percentage) does not difference over the life of the loan. This is many times called flat rate or fixed interest.
The simple interest formula is as follows: Interest = Principal × Rate × Time
Interest is the total amount of interest paid. Principal is the amount lent or borrowed. Rate is the percentage of the principal charged as interest each year. To do your math, the rate have got to be expressed as a decimal, so percentages have got to be divided by 100. For example, if the rate is 18%, then use 18/100 or 0.18 in the formula. Time is the time in years of the loan.
The simple interest formula is many times abbreviated: I = P R T
Simple interest math issues can be used for borrowing or for lending. The same formulas are used in both cases. When money is borrowed, the total amount to be paid back equals the principal borrowed plus the interest charge: Total repayments = principal + interest Usually the money is paid back in traditional installments, either monthly or weekly. To calculate the traditional payment amount, you divide the total amount to be repaid by the number of months (or weeks) of the loan. To convert the loan period, ‘T’, from years to months, you multiply it by 12. To convert ‘T’ to weeks, you multiply by 52, since there are 52 weeks in a year. Here is an example issue to illustrate how this works.
A single mother purchases a used car by obtaining a simple interest loan. The car costs $1500, and the interest rate that she is being charged on the loan is 12%. The car loan is to be paid back in weekly installments over a period of 2 years. Here is how you answer these questions:
1. What is the amount of interest paid over the 2 years?
2. What is the total amount to be paid back?
3. What is the weekly payment amount?
You were given: principal: ‘P’ = $1500, interest rate: ‘R’ = 12% = 0.12, repayment time: ‘T’ = 2 years.
Step 1: Find the amount of interest paid. Interest: ‘I’ = PRT = 1500 × 0.12 × 2 = $360
Step 2: Find the total amount to be paid back. Total repayments = principal + interest = $1500 + $360 = $1860
Step 3: Calculate the weekly payment amount. Weekly payment amount = total repayments divided by loan period, T, in weeks. In this case, $1860 divided by 104 weeks equals $17.88 per week.
Calculating simple finance charges is easy once you have done some practice with the formulas.


I was excited to facilitate this workshop at RME 4 in Boulder on September 29, 2013. Even thought the title, abstract, and slide design is very similar to the ICME talk, a lot has changed in my thinking around our study of slope in 2012. In this workshop we looked deeply at a couple of tasks and explored how the context and representations used in the tasks mediated the reinvention process.
Below the abstract, there are links to the complete unit in editable form for teachers and others to use. Please download, modify, and use the tasks with your students!
Despite its foundational nature in secondary and post-secondary mathematics, student understanding of slope is often formulaic and underdeveloped. To explore how students learn slope in a more robust way, we designed a curriculum for slope in which students mathematize situations involving rates of change. We designed the curriculum using RME principles, and tested and refined it in a design experiment. In this workshop, participants will engage in activities from the curriculum and I will discuss our design process. I will also discuss key findings, including how contexts and representations mediated student learning of slope.


round(exp(uniform(min_value, max_value) / q) * q
Specify a uniform distribution of the form
round(exp(uniform(min_value, max_value) / q) * q.
This is suitable for a discrete variable with respect to which the objective is "smooth", and gets smoother with the size of the value, but which should be bounded both above and below.
qloguniform(min_value, max_value, q)
A double of the minimum value in the range (inclusive).
A double of the maximum value in the range (inclusive).
An integer of the smoothing factor.
A list of the stochastic expression.


Monday, September 7, 2009
Back to School! Here's a mathematical formula (courtesy of Dine Out and Lose Weight - The French Guide to Healthy Eating) to help you calculate your ideal weight (height in cm, weight in Kg).
For the ladies: Weight = (Height - 100) - 1/2(Height - 150)
And for the men: Weight = (Height - 100) - 1/4(Height - 150)
If only losing weight was as simple as calculating it!


We define a ribbon knot as a knot that can be embedded into three-dimensional space such that it bounds a ribbon disk, that is, a surface that can be deformed in any topologically valid way, as well as passing any one section of the disc through another completely, with the line of intersection that forming a slit that does not touch the edges of the disc. Let K be a knot, not necessarily a ribbon knot, with crossing number k. We define an algorithm to create a ribbon knot from K which has crossing number at most 4k such that, which we call "ribbon doubling." We also investigate the number of potential ribbon doubles for a knot, and potential restrictions on its crossing number. We propose a partial inverse operation for ribbon doubles, and show that it is not unique. Lastly, we propose a potential lower bound for the crossing number of the ribbon double of a knot. We then relate the concept of a ribbon double to that of a partial knot for symmetric union presentations, and propose a potential technique for selecting a unique ribbon double.
University / Institution: University of Utah
Format: In Person
SESSION C (1:45-3:15PM)
Area of Research: Science & Technology
Faculty Mentor: Edmund Karasiewicz
Location: Union Building, PARLOR A (2:45pm)


The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples.
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This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. Multi-parameter Singular Integrals will interest graduate students and researchers working in singular integrals and related fields.
AM 62 by Eugene R. By addressing this in a quantitative way we obtain a holomorphic analog of the quantitative theory of sub-Riemannian geometry initiated by Nagel, Stein, and Wainger. We call this sub-Hermitian geometry.
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Moreover, we proceed more generally and obtain similar results for manifolds which have an associated formally integrable elliptic structure. This allows us to introduce a setting which generalizes both the real and complex theories. In this paper, we give optimal regularity for the coordinate charts which achieve this realization. We do this by generalizing Malgrange's proof of the Newlander-Nirenberg Theorem to this setting.ccomesacmenwilch.ml
Multi-parameter Singular Integrals. (AM-189), Volume I
Given a finite collection of C 1 vector fields on a C 2 manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector fields have a higher level of smoothness. We give necessary and sufficient conditions for when there is a coordinate system in which the vector fields are smooth, or real analytic, or have Zygmund regularity of some finite order.
Furthermore, we provide a diffeomorphism invariant version of these theories. In the first paper, we study a particular coordinate system adapted to a collection of vector fields sometimes called canonical coordinates and present results related to the above questions which are not quite sharp; these results from the backbone of the series. The methods of the first paper are based on techniques from ODEs.
Analysis seminar: L^2 theory for a class of multi-parameter singular Radon transforms
In the second paper, we use additional methods from PDEs to obtain the sharp results. In the third paper, we prove results concerning real analyticity and use methods from ODEs. We establish optimal Lebesgue estimates for a class of generalized Radon transforms defined by averaging functions along polynomial-like curves. Here at Walmart.
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Celebratio Mathematica — Zygmund — Singular Integrals
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Family Math Day
We have enjoyed the Family Math day this week. The children were so happy and proud to have their parents attend their classrooms and see their Math learning in class
World Teachers Day
On the occasion of World Teachers Day , Qatar Academy in collaboration with the QF Community Development Team organized “Teacher’s Appreciation Corner” and distributed some souvenirs to all ...
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No streaming of mathematics students success at Horowhenua College
Non-streaming of mathematics in NCEA Level 1 has achieved a marked increase in the number of Māori and Pacific students studying and achieving in the subject at Horowhenua College in Levin.
When head of mathematics Misbah Sadat arrived at the school in 2017, the NCEA Level 1 programme was spread over three types of classes: MATH1 (which includes algebra and graphing) and the lower level MAAP1 (applied mathematics) and MATC1 (third tier) classes.
"In 2017, Year 11 mathematics had 47 European students, 32 Māori students and eight Pacific students," says Misbah.
Due to streaming, she says, the school had no Pacific students in the MATH1 class, and only 11 Māori students, compared with 33 European MATH1 students. In contrast, there were only three Europeans in the MATC1 class and 11 in the MAAP1 class.
MATH1 is the class that leads to algebra and graphing, and Misbah says that essentially all Pacific and 21 Māori students were unable to go on to enroll in STEM (science, technology, engineering and mathematics) courses.
"Denying these students access to STEM courses means you have divided society into 'haves' and 'have nots'," she says.
“Everybody needs to be given opportunities to succeed. I am not saying that everyone has to go towards STEM courses to succeed, but everyone should be given the opportunity to make that choice for themselves. My problem with streaming is that, unfortunately, many Māori and Pacific students end up in the bottom classes.
“If you decide that at 14 or 15, someone is incapable of doing algebra, you are saying they can’t have careers in engineering, medicine, computer science and other STEM professions, and I think that’s too early.
Misbah says that New Zealand has a crisis in that there aren’t enough people in STEM courses and yet we are still streaming in mathematics and science. She says there isn’t a ‘shred of evidence’ that says streaming works for students at the bottom or the top.
Removing barriers to achievement
At the end of 2017, the college decided not to stream Year 11 mathematics and English.
“Instead we used differentiation in our classrooms and proved that it is possible to teach different standards in the same class,” says Misbah. “Yes, it was hard work, but totally possible.
“I was very lucky I had a senior leadership team who took the risk to do this and I had a team of incredible teachers who were behind this 100 per cent. We had multiple standards happening in the class at the same time. We taught everyone but we offered an additional standard for those who didn’t want to sit externals,” she explains.
At the end of 2017, instead of streaming, all students were put in mixed classes for 2018.
“We were quite prepared that we may not get stellar results but, in actuality, students surprised us,” says Misbah. “Previously, because they had been placed in those lower classes, we had put a glass ceiling on their achievement.”
It has been hard work getting students to feel confident, Misbah says.
“It didn’t matter what we said to our students in MATC or MAAP classes. This is what we heard over and over – ‘Nah we can’t get merit or excellence, Miss’. It broke our hearts because even though the data and the placement of these students told us these students were not capable, we found no evidence of that in our teaching.”
Misbah and her team are particularly proud of one bright Māori student who, despite being in MATC1 in Year 11, carried on in mathematics and is now taking STAM3 (Level 3 Statistics).
Motivation is catchy
One of the most noticeable benefits of abolishing streaming was that there are now fewer behavioural issues in the Year 11 mathematics classes.
“The level of engagement went through the roof. When students see other students motivated, they follow. The whole atmosphere is now towards learning and what the students can, and will do.”
Another side-effect of removing streaming was that all mathematics classes could be scheduled across the timetable so that students were in more evenly sized classes.
What success looks like
Horowhenua College has found itself punching well above its weight in terms of the achievement of Māori and Pacific students nationwide.
In 2017, the national average for these students getting excellence in mathematics standards was 8–9 per cent, but Horowhenua College’s average was 4.6 per cent. In 2018, the national average for excellence for Māori students remained the same; however, on average, 24 per cent to 33 per cent of Horowhenua’s Māori students achieved excellence in different mathematics standards.
Non-streaming had no impact on grades for Pakeha students, but the gain in achievement for Māori and Pacific students was ‘astounding’, Misbah says.
Originally a journalist in Pakistan, her country of birth, Misbah came to mathematics later in her career. She says she has seen no evidence that streaming in the subject works.
“In 2017, we did heavy streaming, but only 10 students ended up in the MATH2 programme in 2018, which is the class that those students are supposed to go into. This means that in 2019, we only have six students overall doing Level 3 calculus.
“By contrast, with no streaming in Year 11 in 2018, we currently have 24 students in MATH2 who opted in, compared to 10 the previous year. Hopefully this will lead to a higher number of students studying Level 3 calculus next year.
“This is a total team effort,” says Misbah. “I am incredibly proud of what my team was able to achieve last year.”
Horowhenua College Principal Grant Congdon says, “After taking the brave step to not stream Level 1 mathematics students, Misbah and her team have then worked extremely hard to develop the mathematics potential in our students.
“The results speak for themselves and we are very pleased with the gains our students have made – especially our Māori and Pacific students. As such, we will continue to non-stream our Level 1 mathematics classes.”
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Though it is permuting notes, the function Train() is not ‘permutational’ because it does not compose permutations but only iterate through the notes of some series in order to modify the corresponding values in another one. This could certainly be done ‘permutationally’ but with much more computation and it’d be useless in this context, since the goal of this set of functions is precisely to obtain sequences different from typical permutational ones. With Trainsposition() we had an already interesting example since each modifying note was given two parameters (in addition to its index): an integer value and a sign. The amount of strictly permutational manipulations needed to perform such a computation would be fairly large.
Now instead of applying one modification to each note in a series and take a picture of the result after each step in the process, we want to have a sequence of intervals (they can be represented by a series too) that will run through our original series and stop at some stage. Each interval will be applied to a gradually decreasing number of notes in the original row. Let’s name ‘origin’ the series to be modified. The number of concerned notes in the origin is decreasing because each time an interval has reached the last available note, is remains as a permanent modification. So for a twelve-tone origin, as soon as the first interval has reached the last note, it remains there and this note index is not available anymore for further modification. Then the second interval only touches eleven notes in the origin, and so on till the last change which only concerns one note. This is a train of static intervals.
These schoenbergian examples are taken from a 2008 Etude for clarinet.
Series S: 05814B62793A Reverse R: A39726B41850 Inverse I: 074B816A5392 0pposite O: 2935A618B470
*** DESCR: seq_obj: Seq_2 after Build_tree: object tree: 25814B62793A 65814162793A B5814562993A 27814A62193A 1B816162693A 5481A0629930 278134828934 A6A161020939 AA2159549930 677199885B3B 73A365715333 A39726B41850 funt: Static(A=05814B62793A,oct,B=A39726B41850,oct,ord=05814B62793A) ready: 1 *** *** seq_proc : Tkrow_2 Sequence object: recorded
In this sequence we reach at step 12 the schoenbergian Reverse of Series S. The notes are modified following the order given by the same Series S. Now we could be interessed by the series of intervals that is applied in this case. To acquire this knowledge, Csgrouper provides – on the ‘Series’ tab – an analytic function called Statana(). Putting our origin (05814B62793A) into fields A and ord and our target (A39726B41850) into field B and applying function Statana() we obtain the resulting series (261215A2265A) and a sequence of signs (++-+++—–+) that have to be applied to S in order to get R under the static intervals sequential method. You can verify that the first value (2) has to be added (+) to note index (A=10, i.e. the eleventh note in S = 3) in order to get (5) which is the eleventh note in R. To get there, (2) had first to change the value of each other note in S. This knowledge isn’t required to run Static() though, but the same sequence of values can then be devoted to another role somewhere else in a work for instance.
Now we can also have our origin modified permanently by each interval. Instead of falling back to the original value when a note has been modified, we keep the modified value. Then next time the interval changes this note, it is no more the value that was shown in the origin. This is a train of dynamic intervals, and it almost makes melodies sound like random sequences. However, the ultimate state of the series is completely determined too. Thus sequences of dynamic intervals are useful in music because from an original pattern they create complications leading to other defined musical patterns. The complication itself shows properties that the ear may perhaps sometimes apprehend or recognize, most of all when this form is used in several places in a piece. Again the internal parameters of Dynamic() can be known by feeding the same fields and appying Dynana() (checking the box ‘exp’ will further expand the results).
Now we start from where we left off in Static(), i.e. R (A39726B41850) and we want to reach O (2935A618B470) according to order (A39726B41850):
*** DESCR: seq_obj: Seq_2 after Build_tree: object tree: A39726B41890 A39B26B41850 A39726B41030 A39526B818B0 A31126B41610 A39326321250 A37726BA1474 A339669018B0 A75126541A9A A39B06765216 A1B38ABA1038 2935A618B470 funt: Dynamic(A=A39726B41850,oct,B=2935A618B470,oct,ord=A39726B41850) ready: 1 *** *** seq_proc : Tkrow_2 Sequence object: recorded