Promoting math learning for ALL students is important! The National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics recommends that teachers focus on math processes, such as problemsolving and making connections between math and the real world in their instruction (National Council of Teachers of Mathematics, 2000). In the last section of this module we reviewed the intent of the Common Core State Standards in Mathematics. Think about the CCSSM and the Mathematical Practices reviewed in the earlier part of this module. Those practices are important to all learners, but for those who struggle with math, the practices may be the missing link between “doing math” and “problemsolving”. Students with learning disabilities or mild intellectual disability are often missing some of the skills needed to dig deep into the content. The skills may be the actual mathematical skills missed or misunderstood at an earlier grade level, OR the ability to:
Improving students’ computation and problemsolving skills should be the most important goal in teaching mathematical learning for all students, especially those with disabilities. For math educators, a strong foundational understanding in mathematical learning and math learning progressions is essential is helping all students make progress. However, it may be necessary to embed additional supports to math learning for students with disabilities. These supports can come in many shapes and sizes. Click on the link to visit the module on UNIVERSAL DESIGN FOR LEARNING to learn more about designing instruction to meet the needs of all learners in the classroom based on multiple modes of representation, expression, and engagement.
While many students with specific learning disabilities have trouble with computation and problem solving (Miller, Butler, & Lee, 1998), number processing and number sense (Mazzocco, 2007), or solving word problems (Fuchs & Fuchs, 2002), these difficulties are not unique to those with “identified” disabilities. Many students struggle with math learning! As noted in the beginning of this module the learning progressions within the math content are essential, students ability to access the standards and demonstrate their understanding is key in their continued success throughout their school years.
Teachers need to use a variety of strategies to help students with disabilities learn new content, including math. Recent literature reviews of the research (Gersten, Baker, & Chard, 2006) have found specific strategies to be successful to support math learning of students with disabilities. Take a moment to review the 5 strategies and visit the websites for more information about what each of these are.
In the next section of this module we will review three ResearchBased Strategies to support learners with disabilities and other learning challenges access the CCSSM, make progress within the learning progressions, and demonstrate understanding to promote deepened problemsolving skills.
A graphic organizer is an instructional tool students can use to visualize, organize, and structure information and concepts. When building math understanding all students can benefit from graphic organizers. To learn more about what a graphic organizer is, visit the link below to read the Current Practice Alert, supporting the use of graphic organizers in academic learning to support students with learning disabilities. Current Practice AlertGraphic Organizers and link to http://teachingld.org/alerts#graphicorganizers
Now, let’s look at some examples of graphic organizers that can be used to support math learning together. Click on the link below.
ResearchToPractice: Graphic Representation Technique (Jitendra, 2002) This approach uses semantic diagrams that allow students to organize information in the problem to help them “translate” and find “solutions”. The Graphic Representation Technique helps to lessen the cognitive load of solving complex problems, but still allows students to engage in problem analysis and solutions. Problemsolving strategies that emphasize conceptual understanding can help students with learning difficulties access general curriculum mathematics. It is important to focus problemsolving on “big ideas”, the three types of problems outlined by Jitendra (2002) are: CHANGE, GROUP, & COMPARE (characterized by most addition/subtraction problems). Within the two steps outlined below, students focus their attention on the schema of the problem at hand. For example, when presented with a “compare” story in which Mitch has 43 CDs and Anne has 70. Anne has 27 more CDs than Mitch. The student would focus their attention on 2 sets, more and less than values, comparisons between sets. After several examples have been given, students will then begin to make comparisons on their own. 


A concreterepresentationalabstract (CRA) sequence is a form of instruction that begins with concrete lessons that involve the use of manipulatives (i.e., 3D objects). The use of these manipulatives is to promote conceptual understanding. See the link below for a list of possible familiar manipulatives and how they can be used to support learning in the CCSSM.
STEP 1: The teacher will demonstrate how to use the manipulatives to represent and solve the math problem. The teacher may also use “thinkalouds” to help the students learn how to solve the problem or to explain why and how the teacher is using the manipulatives. Think about some of the examples of the graphic organizers, it would also be possible to use the graphic organizer to help support some of the “think aloud”. Once the teacher has demonstrated how to use the manipulatives the students may begin practice activities with teacher feedback.
STEP 2: Once students have begun to use the manipulatives with success, the sequence of instruction moved to the representational level. This level of instruction utilizes drawings and/or tallies to solve the same type of problems. Remember the graphic organizers, it is possible to use them with the manipulatives (e.g., graphing sample), but many of the examples provided earlier in this module used representations of the information. Similar to the concrete level of instruction, the teacher will provide explicit instruction by modeling and allowing students to begin to practice solving problems with feedback.
STEP 3: Once mastery is achieved at the representational level, instruction moves to the abstract level. This level of instruction involved the teacher providing opportunities to solve problems without the use of additional graphic supports. Only numerical symbols are used. This may be a struggle for many students who have learned to depend on the additional supports. While not all students will need to fade all of the supports built into Steps 1 and 2, it should be the goal for all students to eventually master the “numerical” understanding of the math learning. to abstractlevel lessons that involve solving problems without the use of manipulative devices or drawings.
The main idea to remember is that the emphasis of all math learning should be the difference between showing a student exactly what to do VS. helping them model and remodel to illustrate their thinking!
For some additional videos and supports on explicit instruction and using a CRA sequence, visit the MathVIDS website, an interactive website for teachers who are teaching mathematics to struggling learners made possible through funding by the Virginia Department of Education.
http://fcit.usf.edu/mathvids/strategies/cra.html
Before we finish our module journey into math support for struggling learners, let’s take a look at a video (link below) that outlines a math lesson in which students with and without disabilities are supported in the same lesson/classroom. After you watch the video, we will talk more about what you see and how this links with the research base on supporting students similar to James.
http://www.cast.org/library/video/gr1_math/
(Transcript is available at the URL.)
In this video you saw a classroom teacher support all of her students in a way that supports much of the research based ways to support learners who struggle to learn math. You probably noticed the use of graphic organizers, manipulatives, and a “structured” lesson. This structure with a “modelleadtest” approach is an example of the explicit instruction mentioned earlier in this module. Did you notice that all of the students were working with each other to support learning? This is also an example of peersupports (also outlined as a practice supported by research).