Using Modeling, Manupulatives, and Mnemonics with Eighth-Grade Math Students
Allsopp, David H., Teaching Exceptional Children
Usually we think of primary-grade students when we consider using manipulatives for teaching math, and we believe that learning algebra is a mostly abstract, higher level of learning. How wrong could we be? Research is showing that even older, secondary students can benefit from the planned, judicious use of manipulatives, mnemonics, and other learning strategies most often associated with elementary grades.
This article takes you step-by-step through a process for teaching secondary students in inclusive settings how to solve beginning algebra problems. Follow the figures and photos to a fun way to learn algebra.
Teaching One-Variable Division Equations
Recent research has found three approaches effective in teaching algebra to students with learning disabilities (see box on page 80, "What Does the Research Say?"). Teachers can use these approaches in combination for the best effect. They can use direct instruction to teach students specific learning strategies; and they can teach math problemsolving through a concrete-to-representational-to-abstract (C-R-A) sequence of instruction. Using Direc Insfrucion
Direct instruction-in a brief reminder-involves telling, linking, modeling, providing guiding practice with cues and prompts, giving feedback, providing independent practice, and evaluating. This type of instruction provides a systematic learning framework for the student-, as well, it ensures a high level of teacher-student interaction (see Figure 1). Although the figure describes direct instruction according to its critical components, this approach is not a "compartmentalized" teaching process. It does not have to be boring. You should implement direct instruction systematically, but with enthusiasm, with creativity, and in a fluid manner. Providing ample amounts of specific feedback, which includes both positive feedback and corrective feedback, is also a critical feature of direct instruction. You should provide feedback throughout the direct instruction process. Advance Organizers
An excellent way to "set the stage" for learning is by using an advance organizer. Tell students what they will be learning that day, link the present lesson to previous learning, and then provide a rationale for why learning the skill is important. Using an advance organizer at the beginning of a lesson helps students focus on the learning objective and helps them build connections between what they already know and what they will be learning. Helping students to develop personal meaning for learning the skill provides students incentive for learning (see Figure 1 for an example of an advance organizer). Think-Alouds
Next, explicitly describe and model how to solve the math problem several times, providing clear examples. You should provide both visual and auditory cues when modeling. An efficient way to do this is to "think aloud" as you visually demonstrate each step of solving the problem. Thinking, or talking, aloud provides students a chance to hear what the teacher is thinking as they solve the problem. You will be most helpful to students with learning disabilities if you do not assume that the students know what they are doing or why they are doing it. Solving math problems is often done abstractly, or "in the head." It is vital that students with learning disabilities concretely see and hear what it is that the teacher is doing as they model solving each problem (see Figure 1 for an example of a "think aloud"). Positive and Corrective Feedback After you describe and model how to solve several problems, provide guided practice. Specific teacher feedback is crucial during this phase of the direct instruction process. At this point, you take the students through each step of the problem-solving process while students work the problem also. Begin by providing a great deal of direction, giving many cues and prompts (e.g., asking students, "What do we do next?").
As students demonstrate their increasing ability to solve the problems, begin to fade your direction, allowing students to solve succeeding problems with more and more independence. …