19 Ways to Teach Learners to Understand Abstract Math Ideas

Are you looking for ways to teach students to understand abstract math ideas? If so, keep reading.

1. Teach the student ideas such as “square” and “cube” separately. It may be confusing to introduce both ideas at the same time.

2. Present abstract symbols and terms after the student has worked with concrete manipulatives and learned the concept (e.g., ounce, oz.; cup, c.; pint, pt.).

3. Use physical objects to teach math ideas (e.g., give the student a yardstick when referring to a yard, etc.).

4. Give repeated physical demonstrations of abstract ideas (e.g., find things far away and near the student, a tiny box in a large room, etc.).

5. Give the student clock stamps to use when practicing the concept of telling time.

6. Give the student apps that uses graphics associated with math problems.

7. Utilize a scale, ruler, measuring cups, etc., to teach math ideas using measurement.

8. Complete the first problem or two with the student explaining how to associate concrete examples with each issue (e.g., 9 minus 7 becomes 9 apples minus 7 apples).

9. Examine previously introduced abstract ideas. Present new abstract ideas only after the student has mastery of those ideas already presented.

10. Teach shapes using ordinary objects in their surroundings (e.g., round clocks, rectangular desks, square tiles on the floor, etc.).

11. Teach the student abstract ideas (e.g., dimensionality, size, space, shape, etc.) one at a time before pairing the ideas.

12. Utilize actual coins and dollar bills, clocks, etc., to teach ideas of money, telling time, etc.

13. Utilize concrete examples when teaching abstract ideas (e.g., objects to express more than, less than; rulers and yardsticks to express height, width, etc.).

14. Get the student to follow a recipe to make a treat for the class using measuring cups, teaspoons, etc.

15. Utilize the following steps when introducing an abstract concept: • concrete—cups and liquid, • practice—use cups to solve problems, • abstract—word problems with cups, • practice—prepare a recipe, • review, • test.

16. Give the student money stamps to solve money problems (e.g., penny, nickel, dime, etc.).

17. Consider using Alexa for the Math Classroom.

18. Try gamifying your math lessons.

19. Consider using one of the apps and tools from our many math app lists:

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