Student-centered math instruction. That’s what we all want, right? If only we didn’t have this hectic race to “cover” so many topics, now exacerbated by snow days (at least in our neck of the woods). Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 by de Walle et al. is a terrific guide for teachers who want to get it right. It’s not light reading, but I would highly recommend it and its partner volume for Pre-K -2.
Teaching Student-Centered Mathematics focuses on teaching math through problem-solving. The authors recommend using authentic contexts for instruction instead of what they refer to as “naked” numbers. They address the intricacies of teaching content from number sense through fractions, decimals, measurement, geometry, and data. They also describe common misconceptions as students learn math and strategies for addressing those problems.
What makes this volume so effective?
- The authors reference the latest neuroscience and math research
- They focus on the diversity of learners, including those with math disabilities
- They deal specifically with how to incorporate parents in the learning process
- Technology is incorporated throughout
- Specific activities are provided
- There are ample opportunities/suggestions for reflection
- Multiple visuals provide explanations of how to present math concepts and the ways students might solve problems
- The authors clarify common teacher mistakes in math instruction for each topic
- Purchase of the book provides online access to black line masters for downloading and printing
I do find it ironic that this excellent book is published by Pearson, a giant in the educational publishing world and responsible for enVisionMATH, one of my least favorite math programs! EnVisionMATH, often introducing new topics every 10 days or less, seems to be the antithesis of what de Walle et al. are recommending. Perhaps enVision was written for snow days.
In my previous post, I shared some of David Sousa’s findings related to elementary students struggling in math. These kids find themselves in a tangle of partially and incorrectly learned skills and procedures. They are uncertain about how to begin problem solving and which operations are appropriate. They are not fluent in math facts. These kids often become highly anxious about math, describing themselves as incapable of learning. They may act out in school or withdraw; either way, they define their situation as hopeless. When they attempt homework, they valiantly try to recall the procedures, but are mostly unsuccessful. These are the kids who cannot tell me what topic they are learning in math.
As in all areas of special education, the first step is gradually leading kids to an understanding of where they are, while building confidence and hope that relearning is within their ability. This is a difficult undertaking for both me and my student. Struggling math learners have a hodgepodge of knowledge. If they are identified in upper elementary grades, that tangle is enormous. I have found that the smartest students have the greatest tangles. Some of these students are twice exceptional, gifted with a disability. They have been able to stuff many partial facts and procedures into their memory and may have camouflaged their disability for a few years. Students with weaker memory may be easier to “retrain” because they have less to unlearn.
I described this process as “tricky” because of the emotional aspects associated with relearning. These smart kiddos have been told, “You can do it!” because their working memory gives them the appearance of deeper understanding. These bright kids often have strong metacognitive skills: they are aware that something is wrong and may have interpreted that as “stupidity.” Anxiety has now begun to seriously impact every math lesson. They become hyper-vigilant about their performance, expecting to make a mistake at every juncture and dreading tests.
Depending upon the student, I disclose enough information about their weaknesses to provide motivation but not so much that they want to run away! My goal is to infuse hope by demonstrating how much they HAVE learned. Systematic assessment is crucial to this process. Providing external motivation is often necessary, especially if they are phobic about math. They have not yet experienced the value and joy of truly learning math skills, so they need something to get them started.
Brain-based research gives us a clearer picture of the optimal times for learning new content. According to Sousa in his book, How The Brain Learns Mathematics, there are two “best” times for learning: at the beginning of a lesson and and the end. Using a 40 minute lesson as a model, he explains that the brain’s capacity to download and retain new information declines in the middle of that lesson. This model of learning also makes plain sense. Kids’ brains (like that of adults) have a limited capacity to maintain attention and absorb and apply new information. After a “high” point of acquiring information and a relative period of reduced retention, there is another maximum learning opportunity in the last portion of the lesson (these times are approximate, of course).
How does this affect special needs kids who are struggling in math? The initial explanation of skills and procedures was not clear to them. It may not have meshed with previous learning (often because the previous topic was not not learned adequately or correctly). It may have triggered anxiety about past math failures. It may not have included visual cues or manipulatives. It may have had too much information presented too quickly. Guided practice may be completely embedded into the initial instruction, so that student were overwhelmed by both new vocabulary and new procedures. When these kids are “released” into independent practice at this point in a lesson, the teacher may not be available to provide corrective feedback, so the kids practice incorrectly. And practice makes permanent. Kids are also hitting that learning slump in the lesson, along with increased anxiety and perhaps task avoidance. Special needs kids may be heading down a dead-end road. When the teacher concludes the lesson with opportunities for students to apply this newly learned information to real problems, our special needs kids have partially memorized procedures, partial understanding of underlying concepts, and inadequate practice without corrective feedback. Yikes. Then they have homework on the topic, where they continue to practice incorrectly.
As Sousa points out, “unlearning and relearning that process correctly is very difficult…. (B)oth teacher and student have a difficult road ahead to unlearn the incorrect method and relearn it correctly.” (page 63) Obviously, the earlier the math intervention, the better the outcome. Younger learners relearn more easily and have had less time to practice incorrectly. Motivation to relearn is also a big factor.
There is hope. Stay tuned for how to navigate that “difficult road.”