What should we consider when teaching students with math difficulty?

Question: What should we consider when teaching students with math difficulty? 

Answer: Hi, I am Sarah Powell from the University of Texas at Austin. When we are teaching students with mathematics difficulties there are six things to consider. The first is incorporating systematic and explicit instruction and while we are doing that we want teachers to really focus on the vocabulary that they are using to explain mathematics as well as the symbols that are used in mathematics. We want teachers to be using the concrete-representational-abstract framework or the CRA framework which gives students opportunities to use hands-on materials as well as pictorial representations and those represent the abstract, the numerals and symbols of mathematics.We also want teachers to consider using fluency building activities. Those that build fluency with your basic math facts and also those that build fluency with computational algorithms. While all of this is going on, we want teachers to engage in effective questioning strategies and as students work we want teachers to conduct an error analysis of students’ work. So what are the errors that students are making in mathematics and then how can you use those errors to inform instruction.

First, let’s talk about systematic and explicit instruction. Systematic instruction means that easier skills build to more difficult math skills, so we have developed a sequential scope and sequence for students. Then when we think about explicit instruction; there are several components that go into explicit instruction. First, is always giving students an advanced organizer. Here is what we are doing in the lesson today and here is why this is important. Once students have that organizer, it is really important for teachers to review prior skills. So if you are working on subtraction you might want to review addition skills because addition relates to subtraction. Then teachers are going to do modeling. This is where teachers will actually maybe use hands-on materials or pictorial representations to model different concepts and procedures in mathematics. And then after that modeling, teachers need to have the students participate in guided practice. That is where the teacher and students are working on problems together; the teacher is providing immediate feedback to the students as they work those problems. And then finally students need to participate in independent practice to see if they can practice these problems on their own. Those are all of the tenants of explicit instruction and those should occur every time we are teaching mathematics to any student with a math difficulty.

Another important component of mathematics instruction is really focusing on the vocabulary that we use to introduce math concepts and procedures to students and also the symbols that we use in mathematics. So first about vocabulary, there are a lot of different ways that we can help students queue into mathematics vocabulary, but one of the most important things that teachers can do is just to be very precise with their vocabulary. So instead of saying bottom number, using the term denominator. And any time a new math vocabulary term is introduced, giving students lots of ample practice with that new vocabulary term. Also important in mathematics are the symbols that are used to explain mathematics. There’s a lot of different symbols. We have the plus sign, the multiplication symbol and the equal sign, the inequalities symbols, lots of different symbols, dollar signs, percentages, all of those types of things. Any time we use a symbol, just like vocabulary, we need to make sure that students understand the explicit meaning of that symbol and explain that symbol in a meaningful way to students.  

Another essential component to effective mathematics instruction for students with math difficulty is to use the concrete-representational-abstract framework. With the concrete, this is where students use hands-on materials and they touch these materials and move them around to demonstrate math concepts and procedures. With the representational these are pictures of the concrete materials, so they are two-dimensional flat images where students can actually see the different mathematics. These days we have two-dimensional representations images on paper but you also have two dimensional virtual manipulatives that students can also use to represent the representational. And we are using the concrete and representational to help students understand the abstract in mathematics. That is the numerals and symbols that students use to represent mathematics problems. Teachers also need to work with students to explicitly build fluency of math facts and procedural algorithms. Teachers can use a lot of different activities to build fluency. We can do timed activities we can use flashcards, cover-copy-compare, tape problems; there are quite a few different strategies that students can use to build their fluency. And when we are thinking about the procedural algorithm, it’s just practice.  Here is what you do first, second, third, fourth, and fifth. Teachers are modeling that students practice it with the teacher and then they have independent practice on their own. But building fluency makes everything in mathematics easier.

Teachers should ask questions that encourage reversibility. That is, the teaches give an answer and the students work backwards from that. We can also ask questions that encourage flexibility. That is, is there another way to solve the problem? Is there another way to solve the problem beyond that? We also need to ask questions that encourage generalizability, so how does this relate to other things we have learned in mathematics?  And all the time when teachers are asking questions we also need to think about the role of feedback. That is providing affirmative feedback and corrective feedback. The corrective feedback is especially important for students with math difficulty. Any time students make a mistake we need to pinpoint that mistake and help the students learn from that mistake. We also need to think about using error analysis to inform instruction. So for example, any times that students are solving computation problems or perhaps area and perimeter problems within geometry we can use any mistakes that the students make within those types of problems to inform instruction.

Remember, any time you are teaching mathematics we want to see the following going on in our classroom. Using systematic and explicit instruction. We want you to be paying attention to the vocabulary and symbols that you are using. We would like teachers to use the concrete representational abstract framework. All the time you should be building fluency and incorporating effective question strategies and also conducting an error analysis of students’ work

Developed By: 
National Center on Intensive Intervention