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TransMath® Third Edition is a comprehensive math intervention curriculum that targets middle and high school students who lack the foundational skills necessary for entry into algebra and/or who are two or more years below grade level in
A targeted math intervention program for struggling students in grades 2–8 that provides additional opportunities to master critical math concepts and skills.
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by John Woodward on Nov 30, 2017
In part one of this blog, I outlined many of the factors that underlie the shortage of qualified teachers for secondary students who are struggling in math or have learning disabilities.
Many commonly proposed solutions to this shortage include significant pay increases, better working conditions, reduced class sizes, and an overall change in national sentiment about the importance of teachers to our society and the economy. These solutions are expensive, complex, and they will take considerable time to implement. Many of them have been with us for years and have yet to be seriously implemented. So, what can be done in the short term?
During my recent talk at the National Science Foundation conference on STEM and learning disabilities, I proposed three near-term solutions:
The promise of newer, more all-encompassing educational technologies has been with us since the early 1980s. At that time, the claims were overblown, and most certainly, a good deal of the hyperbole remains today. The background messages still seem to be that technology “will do all of the work.” In other words, turn students over to computers and all teachers have to do is occasionally monitor performance.
A more careful integration of technology into the academic needs of all students is one where educational software complements what a teacher does naturally. In some cases, that means software—which is markedly more sophisticated than even a decade ago—can provide limited, structured practice in developing automaticity, practice on procedures and concepts, and even problem solving. The emphasis is on limited. There are appropriate occasions where students may engage with a software program for an entire period, but it is the teacher’s job to monitor, motivate, and assist when students make repeated mistakes or when they encounter problems that are too challenging. It also is increasingly clear that Internet-based programs can offer structured practice away from the classroom, thus allowing a teacher valuable time for focused instruction on chronically difficult topics for struggling and special education students. The permutations in how software can be used on a limited, but effective basis are many. The key idea is teachers need to carefully select what instructional needs a software program can address, and what their role is while students are on computers. Is it to monitor performance, motivate students to do their best, and/or provide timely assistance?
A growing use of technology in the classroom and online is the use of narrated, as well as animated explanations of concepts. Teachers with limited content knowledge can often misstate or even avoid these kinds of critical explanations. Brief technology-based explanations can be played and replayed by teachers, students, and others who assist students struggling in mathematics. Again, this is a limited use of technology, but consistent, clear explanations of concepts along with animated graphics can go a long way to help struggling students understand a wide array of math concepts.
The No Child Left Behind Act gave us the mandate that curricula materials should be research based. That was an important first step in improving the materials used in all classrooms. Admittedly, not all materials can comply with this requirement, and conducting research to find the best, research-based, high school chemistry textbook is hardly a high priority. However, this mandate makes considerable sense in critical areas such as beginning reading, elementary mathematics, and intervention materials for struggling and special education students.
The next step in research-based curricula is to make them educative. That is, materials need to go beyond the teacher’s guide in making the big ideas, cognitive strategies, and other key information transparent to teachers, students, and those assisting students (e.g., tutors, parents). And this needs to occur on a daily basis. When my co-author and I wrote TransMath®, our intervention math curriculum for middle school students, this was foremost in our thinking. Far too many math curricula at the time—and even today—don’t afford space in their texts to explain clearly the concepts and strategies students are trying to learn. The benefit of just doing this is manifold.
Clear explanations in the text (vs. one or two model problems) along with visual representations in the lesson provide critical supports for students and those assisting them outside the classroom. But, most importantly, they are a source of ongoing learning for teachers who have a weak understanding of the concepts and strategies that underlie standards-based mathematics today. Finally, a textbook design that draws attention to key ideas or vocabulary through features such as call-out boxes and highlighting is essential. These design techniques, along with the elimination of irrelevant pictures and tedious “fun facts,” can signal to readers what is in a lesson is carefully selected and important.
Mathematics educators have argued for decades about the importance of content and teaching or “pedagogical” content knowledge. While this certainly is a necessary underpinning for effective math instruction today, the question “How much do teachers need to know?” is elusive. In today’s world of teacher shortages, the difference between optimal and practical knowledge makes all the difference. Given the shortage of qualified teachers for secondary students who are struggling or have learning disabilities, it simply may not be feasible for many of these educators to have robust content and pedagogical knowledge typically expected of those certified in math education. Also, it may not be necessary for middle school intervention teachers to know the pedagogy around primary-grade topics. Instead, a concentrated blend of content and pedagogical content knowledge in rational numbers, ratios and proportions, and algebraic thinking may be the core of professional development for these educators.
Certainly, these are not the most optimal solutions to our critical shortage of math teachers today. However, educator David Berliner observed decades ago, the world of education and the classroom is typically bound up in solutions that suffice. This does not mean they are inferior. Rather, it suggests immediate, practical solutions guide our work more often than not.
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