The Panel's final report was issued today and contains 45 findings and recommendations on numerous topics including instructional practices, materials, professional development, and assessments. Here are some of the highlights. My comments are in red.
Core Principles of Math Instruction
The areas to be studied in mathematics from pre-kindergarten through eighth grade should be streamlined and a well-defined set of the most important topics should be emphasized in the early grades. Any approach that revisits topics year after year without bringing them to closure should be avoided. YES! We do have a spiral curriculum, and it is important to revisit certain concepts each year, but we should always be pushing to move students forward in their understanding. This can't happen if 60% of the material "taught" each year is review.
Proficiency with whole numbers, fractions, and certain aspects of geometry and measurement are the foundations for algebra. Of these, knowledge of fractions is the most important foundational skill not developed among American students. Yes, it is. The problem here stems from learning rules about fractions and not really understanding what they mean and why they are of value. For example, do you know why fractions were invented? Just thinking about this makes them vastly more understandable.
Conceptual understanding, computational and procedural fluency, and problem solving skills are equally important and mutually reinforce each other. Debates regarding the relative importance of each of these components of mathematics are misguided. AMEN. We can't keep focus on procedures devoid of meaning. We must teach the how and the why.
Students should develop immediate recall of arithmetic facts to free the "working memory" for solving more complex problems. Learning basic facts is a must. However, flashcards and rote memorization techniques are not enough. We need to teach fact families, underlying patterns, and relationships of operations to one another if we want kids to remember facts automatically.
Much of the public's "resignation" about mathematics education is based on the erroneous idea that success comes from inherent talent or ability in mathematics, not effort. A focus on the importance of effort in mathematics learning will improve outcomes. If children believe that their efforts to learn make them "smarter," they show greater persistence in mathematics learning. Amen, again. However, we also need to make sure that ALL children get this message. Even if it's unconsciously done, many young women still get the message that math is not for them. Math can be done by young and old, male and female, white and non-white. ANYONE can be a math whiz.
Importance of Knowledgeable Teachers
Teachers' mathematical knowledge is important for students' achievement. The preparation of elementary and middle school teachers in mathematics should be strengthened. Teachers cannot be expected to teach what they do not know. We absolutely must focus on content and pedagogy. Teachers also need to understand how children learn mathematics, what misconceptions they may hold, and how best to overcome them.
The use of teachers who have specialized in elementary mathematics teaching could be an alternative to increasing all elementary teachers' mathematics content knowledge by focusing the need for expertise on fewer teachers. NO! I absolutely, positively do not agree with this one. Every elementary teacher needs to know and understand the mathematics children learn. Period! By allowing elementary teachers to specialize, we lose the ability to integrate the curriculum. We also begin to adopt a middle school mentality when it comes to teaching, with "each to their own" area of expertise. Taught the right way, every elementary teacher can have a deep and broad understanding of the math content taught at this level. If they don't, we need to work harder.
- Teachers' regular use of formative assessments can improve student learning in mathematics. Yes, it can. But keep in mind that formative assessment means more than paper and pencil tests each week. It could take the form of journal entries, observation, interviews, performance assessments, class participation, etc. This type of ongoing assessment is what teachers do well. Assessment of this kind is an integral part of good instruction.
Instructional practice should be informed by high-quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers. Well, yes, we should be looking at what the research says. We should also be looking closely at those classrooms where teaching is a challenge, and despite this, teachers are helping children to grow mathematically.
The belief that children of particular ages cannot learn certain content because they are "too young" or "not ready" has consistently been shown to be false. I tell my students all the time that we teach algebra in kindergarten and first grade. Don't believe me? Well, remember those "box" problems you solved as a kid? They looked like this.
Now, I wouldn't teach the use of the variable x to first grade students, but that doesn't mean they're not capable of thinking algebraically. What matters here is the delivery. Teachers need to work to make the content meaningful for kids, and teach it in a way that makes sense.
Explicit instruction for students who struggle with math is effective in increasing student learning. Teachers should understand how to provide clear models for solving a problem type using an array of examples, offer opportunities for extensive practice, encourage students to "think aloud," and give specific feedback. I am all for using multiple models to help students learn a concept, and believe that "think alouds" are one of the best tools we can use to really see how students are thinking about concepts.
Mathematically gifted students should be allowed to accelerate their learning. Of course, but I worry a bit about who will teach them. This is where I can see the use of math specialists.
Publishers should produce shorter, more focused and mathematically accurate mathematics textbooks. The excessive length of some U.S. mathematics textbooks is not necessary for high achievement. AMEN, AMEN, AMEN!