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by Mary Stroh on Apr 5, 2018
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In the early days of research as a co-author of Voyager Sopris Learning’s TransMath®, I spent a lot of time observing struggling math students in the classroom. I soon discovered these students had much more than a deficit in math content knowledge. They also had lost all confidence in their ability to learn math.
Who could blame them? They had failed for many years to make any measurable progress and were performing several years below grade level. Their math class experience consisted of daily worksheets completed in isolation in a subject area they had grown to hate. They had “checked out” of math class.
This also was the case with seventh- and eighth-grade math students at the City School District of New Rochelle, New Rochelle, NY. Jeffrey Cole, assistant director of special education, said despite previous math intervention programs, these students were still performing below grade level. “Many had all but given up,” Cole said. They needed an intervention that would not only catch up their foundational skills but also provide a positive learning experience to boost their confidence and encourage them to be persistent in math. District leaders selected and implemented TransMath and their students have been experiencing significant improvement in mathematics achievement and confidence since. You can read the New Rochelle story here.
A strong commitment to building student confidence is evidenced by the entire first level of TransMath, Developing Number Sense. In creating this level of the program, we knew we had to meet students at their functioning level (quite often several years below grade level) without making it feel like “baby math.” We found something as simple as putting the material in textbook form rather than a series of random worksheets could make a huge difference in how these students perceived themselves. Further, TransMath’s emphasis on conceptual understanding and problem-solving proficiency gives students consistent strategies that are successful and dependable. For example, Patrice Kentner, special education instructor at New Rochelle, found student confidence and class participation have improved significantly since implementing TransMath. “As my students develop math skills, they grow in other areas,” Kentner said. “Since they now have strategies they can use consistently in the classroom and for their homework assignments, they are confident enough to come up to the smart board and ‘teach’ the skills to other students.”
Another key area where the confidence factor plays a role in math is in the classroom discussion. An important aspect of learning math has to do with communicating about one’s math thinking. It is difficult to engage students in classroom discussion, however, if they lack confidence. One of our earlier research studies for TransMath involved preparing students for critical thinking problems which have become quite common on high-stakes math assessments. Each week, the classroom teacher would present a challenging practice problem, which the students would solve and then discuss. I was assigned a small group of students who lacked confidence in this type of problem solving and, therefore, never participated in the class discussion. I started previewing the practice problems with these students prior to class in a small-group setting. They began opening up, asking questions, and discussing their thinking within the small group. Having a “head’s up” on the problem and a chance to try their ideas in a safe environment boosted their confidence level. Soon, they were participating in the larger classroom discussion, sharing their ideas and, even at times, assisting their higher-achieving peers. TransMath provides engagement strategies like this throughout the program to help facilitate classroom discussion and engage students who shy away from participation. At New Rochelle, Kentner experienced similar success. “I love when I overhear one student offering help to another student who may have made an error or is confused,” Kentner said. “It empowers them and also tells me that if you can teach the skill, then you have mastered the skill.”
Student confidence also can derail at the common “roadblock” areas that occur naturally as students move through the continuum of math topics. For example, once students have mastered whole number operations, the traditional next step is to introduce rational numbers; e.g., fractions. Even students who have had a high degree of success with whole numbers can lose confidence at this juncture. The rules seem to change and the math is no longer predictable. For instance, when you multiply two whole numbers, the product is always bigger. Example: 2x4 = 8. However, when you multiply by a fraction, the answer gets smaller. Example: ½x4 = 2. For this reason, we have dedicated an entire chapter in Level 2 of TransMath: Making Sense of Rational Numbers to conceptual understanding of fractions prior to any instruction about operations with fractions. Anticipating these common roadblocks and being prepared to address confusion is yet another way we can help students maintain confidence in their math skills. This is something we gave a tremendous amount of thought while writing TransMath.
Finally, one of the most rewarding aspects of helping students gain success and confidence in their math skills is seeing their attitudes change. As a regular part of our research for TransMath, we gave students a questionnaire before and after the intervention, and asked them to describe their attitudes about math. It was exciting to see students who once claimed to “hate” math now say they “love” math and declare math as their favorite subject when it was once their least favorite. As Kentner said, “When I hear a student tell another student that they are ‘good in math’ or that they find something ‘easy,’ it makes my day. With TransMath, my students are becoming truly prepared for success in their future coursework.”
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