Articles throughout this issue both share strategies for helping students who struggle with math and explore broader policy questions about how math should be taught.
“Standards With Teeth”?
- Do you think math instruction would be more effective if the United States enforced a national math curriculum? Why or why not?
- What would be the advantages and disadvantages of aligning math curriculum and instruction?
Mostly for Math Teachers
- Leinwand believes that without alignment math teachers end up trying to please too many “masters” (state standards, textbooks, local needs, and so on). Do you ever feel torn between the demands of various masters in teaching math?
- Look at your state's standards for math for the age group you teach. How many topics per grade level are there? Compare this number with a colleague from another state—or better yet, another country. What do you notice?
A Teaching for Understanding Challenge
- Whatever discipline or grade you teach, challenge yourself to present to students one or two real-life scenarios related to your discipline that require an understanding of fractions or proportions. Include a visual element (such as a bar graph) or a hands-on component (such as having young students make a check mark next to the name of each student in their grade who is on a sports team). Discuss with students how understanding and manipulating fractions relates to this real-life situation.
Deepening Our Own Understanding
Why not try some of the hands-on explorations of abstract math concepts described by Nancy T. Goldman as part of the collection of attitude-changing math strategies on pp. 72 (“Attitude Adjustments.”)
Invite to your group teachers who would like to deepen their math understanding. Let each team find a way to build a model of the Pythagorean theorem or measure common objects to find circumference, diameter, and the true usefulness of π, as Goldman describes. To extend your understanding of π, brainstorm real-life situations in which it would help to approximate the circumference of an object by knowing its diameter.
- Did the concept in question become clearer because of this hands-on activity?
- How—if at all—were you taught the concept in school?
And Just for Fun. . .
Compare the mnemonic devices and tricks you learned to remember mathematics facts and algorithms (such as “yours is not to reason why; just invert and multiply”). Do you ever still use them? Is there a place for this kind of trick in helping children grasp mathematics?
