How to Learn Math for Students
by Jo Boaler, Stanford University Professor of Mathematics Education, has just opened for registration. The MOOC course is FREE and is designed for any learners of math, to give them a positive relationship with math.
The course has 3 goals:
- To instill a growth mindset, especially in math
- To teach a range of mathematical strategies, such as representing, and seeking big ideas
- To show math as a connected, living subject with videos of math in soccer, dance, art, nature and many more applications.
The MOOC was designed and is presented with my team of undergraduates, and offers a pedagogy of active engagement.
There are 6 course sessions, that take 15-20 minutes each. They combine short videos that teach ideas with questions for students to think about and help deepen learning. At the end of every session students are asked to summarise the ideas for someone of a similar age. This draws from the “saying is believing” approach of psychological research that shows that when students summarise ideas and explain them to someone else they are helped in believing them for themselves.
The course is designed for learners of all levels and all ages. I recommend that teachers judge the suitability of the materials for elementary age children. For those under 13 a parent or other person responsible for them will be required to register on the site, giving email and other details.
Ideally students can take the classes during lesson time and spend the rest of the lesson discussing them as a class. I recommend not taking the classes faster than once a week. The class is best taken individually, not as a class, as it involves deep, personal reflection on mindsets.
The class will open at the end of May/beginning of June and stay open until the end of December, so that students could take the course this school year, in the summer or in the fall. But register now, so that you can be sent more details and news when the course opens.
Why are fractions difficult?
There are several reasons fractions are extremely difficult for students with dyscalculia. Both the notation, using two numbers close to each other, and the different ways we show fractions can couse confusion.
- When using the fraction notation, students need to work with two numbers at the same time. Not only is seeing the two numbers so close to each other confusing, the words used to ‘read out’ a fraction leave the impression it is ‘one entity’, ‘one number’ and does not bring in mind the ‘whole’ that is being divided. In fact a fraction is built up from two really different numbers and the numbers actually have an opposite influence on the size of the fraction. A larger the top number makes the quantity of the fraction larger, but a larger bottom number makes the quantitiy of the fraction smaller. This is counter intuitive to students who have just learned that bigger numbers mean larger quantities! Students with dyscalculia usually do not understand and remember that these numbers have totally different meaning depending on the place they are written.
- Another reason students with dyscalulia often get confused with fractions is because they do not automatically see the similarity between different models (such as folded squares, fraction strips, fraction circles, or pizza pies) thta are used to illustrate fractions in their textbook or are used in class presentations. Moreover they are slower in copying from the board and prone to makig reversals in the numbers as well as in the top and bottom of the fractions in their written notes.
The fraction notation cards and the symbol and number tiles in this activity are designed to show the different meanings of the top and bottom number, focusing on one number at a time, instead of both. The words numerator and denominator are unfamiliar vocabulary and do not add to understanding, so they are not used in this lesson, we call it top and bottom number. The top number shows how many equal parts you count. A larger top number makes the amount of the fraction larger. The bottom number shows what type of parts you count. A larger bottom number makes the amount of the fraction smaller.
Go to FREE ACTIVITIES AND DOWNLOADS to see the full activity.
When you are shopping for school supplies, think about an extra package of three ring binder paper: quad lined paper is the first and most economical help for your struggling Math student.
Neatly lining up calculations prevents errors. Quad paper can also help illustrate many concepts that are more complicated to explain in words, ranging from area and perimeter to slides, flips, and transformations and many more.