16_Rapp_CH16.indd

Teaching Everyone

scales, and recipes is one idea. A quilting station, where students measure fabric and patch together patterns of cloth, is another idea.

Choice

The third category of engagement strategies is choice. Any time that a student can make his or her own choice about learning, engagement is increased. The homework menus presented in Chapter 7 are a great example. Figure 16.2 shows a menu for math. In addition to menus, tiered math problems provide choices with just the right amount of challenge for individual students. For any math problem, provide options of increasing difficulty from an introductory level to a more sophisticated level. Wormeli (2007) provided an example for finding the surface area of three-dimensional solids. From least to most sophisticated, the tiers could be: determine the surface area of a cube; determine the surface area of a rectangular prism; determine the amount of wrapping paper needed to cover a rectangular box; determine how many cans of paint you’ll need to buy to paint a house with given dimensions, if one can of paint covers 46 square feet (p. 84). Once students choose a starting point, the teacher can guide them through increasing levels of mastery.

Collaboration

Fitzell (2005) offered some examples of ways to collaborate on math problems:

Math Strategies for All Students

Choose and complete three activities in a row.
There are 25 students in the Your teacher is correcting math Solve the problem 48 × 4 two
class. To complete a craft proj- homework. A student multiplied different ways
ect, each student needs 3 pipe 32 × 5 and wrote the answer
cleaners. Write an equation to as 150. If you were the teacher,
show how many pipe cleaners how would you explain to the
are needed in all. Draw a picture student how to correctly solve
model to go with it. the problem?
Create a “caterpillar” that has Which product do you think will Your brother has 15 stuffed
seven body parts: be greater? Why? animals. Your friend has twice
v as many as your brother. You have a third as many as your
Place prime numbers in each 38 × 9 = friend. Write an equation to
body part so that the sum of the 3 × 89 = show how you figured out how
numbers equals 58. many you have.
Make a collage of items that can Interview a classmate about You are bringing a birthday treat
be divided into equal parts or ways that multiplication and to school. There are 24 people
fractions. division are used in daily life. including yourself and the teacher. You buy a bag of 72 candies. Write an equation to show how each person received equal amounts and how many are left over.
Figure 16.2. Math menu. (Adapted from Westphal, L.E. [2007]. Differentiating with menus: Math.
Waco, TX: Prufrock Press, Inc. http://www.prufrock.com.)

Self-Regulation Strategies

The last category of engagement strategies is ways to help students regulate and monitor their own understanding and work. The first part of this is to make sure that students are working in a setting that is free of as many distractions and threats as possible. By threats, we mean anything that might make the student feel uncomfortable—physically or emotionally—frustrated, or insecure. The case of Beth’s fourth-grade classroom in Chapter 8 included many strategies for keeping discomfort and distraction to a minimum. The quiet area where students can choose between various seating options or use a clipboard under softer lighting is just one example. Allowing students the opportunity to share their thinking can be engaging, but demanding that they present orally to the class unexpectedly can be threatening.

Gargiulo & Metcalf (2010) shared examples of strategies that increase engagement graphic organizers because they help students regulate their own learning. Teachers can provide graphic Visual representations organizers to fill out, mnemonics to rehearse, and strategy posters to review. Silverman of knowledge, ideas, or (2002) also encouraged the use of mnemonics. OnlineMathLearning.Com at http://www.onlinemathlearning.com/math-mnemonics.html includes several mnemonics for many different math concepts. LINCS is a research-based mnemonic strategy to assist in including webs or charts. remembering new vocabulary: list the parts; imagine a picture; note a reminding word; mnemonic A memory construct a story; and self-test your memory. aid. An example of a mne- monic is the acronym ROY

Input

G. BIV to denote the colors in a rainbow—red, orange, yellow, green, blue, indigo, and violet. There are many different ways that you can represent math concepts to students to increase their understanding. This section covers multiple representations of math concepts in three categories: visual, auditory, and tactile input; teaching math language; and anchoring activities.

Visual, Auditory, and Tactile Input

The first category of representation or input strategies includes ways that make math visual, auditory, and tactile so that different.

$$ 32\times5 $$

$$ 3\times89= $$