The Elusive Search for Balance - National Council of Teachers of Mathematics By Matt Larson, NCTM PresidentFebruary 20, 2017 In a recent President’s blog post on the need to make homework comprehensible, I referred to the Fordham Institute Report, Common Core Math in the K–8 Classroom: Results from a National Survey. The report offers another interesting finding: “The math wars aren’t over.” The authors of the report observe, “The Common Core math standards seek to bring a peaceful end to the ‘math wars’ of recent years by requiring equal attention to conceptual understanding, procedural fluency, and application (applying math to real-world problems).
Subtraction: More Than Just Taking Away - Well-Trained Mind Can you tell what these three word problems have in common? I had 8 cookies, and then I ate 5. How many cookies did I have left?I have 8 cookies. 5 are chocolate, and the rest are oatmeal raisin. How many are oatmeal raisin? There are 8 chocolate cookies and 5 sugar cookies in the cookie jar. Technology and the CRA Sequence of Instruction - Math Coach's Corner I got an email from a reader last week asking about the impact of technology on the CRA sequence of instruction, so I thought I’d blog about it. First, let me remind you that CRA stands for concrete, representational, and abstract. From Van de Walle (pg 99):
commoncoretools You may have noticed that I am back to publishing regular blog posts! My goal for now is a blog post every second Wednesday. I am now also trying to answer forum questions promptly. I want to thank the readers who took up the slack for the last year and a half in answering questions in the forums. Search Results From my own experience teaching 5th grade and a lot of conversations with teachers in grades 1-4, subtraction always seems to be such an area of concern with students. After the introduction of subtraction as take-away, students tend to live in that land forever. This idea was spinning in my head the entire time I […]
Concrete Representational Abstract (CRA) in mathematics In response to a Twitter inquiry, I decided to write up some longstanding thoughts on the Concrete Representational Abstract (CRA) sequence that is popular particularly in designing instruction for learners with disabilities. First, what is CRA? Here, from a researcher who done several studies on CRA with students with disabilities in mathematics: First, manipulative objects are used to promote conceptual understanding. Concrete-level instruction proceeds as follows: The instructor demonstrates the mathematical skill/process with manipulatives; the instructor then guides the students by participating in the use of manipulatives with the students, providing prompts and cues; and the students independently use manipulatives to demonstrate the skill/process.
Levels of Convincing - Robert Kaplinsky If you think others need to see this, share it on one of the sites below by clicking on the button. I recently attended a full day workshop with Jo Boaler where she shared a different way of thinking about convincing someone from Thinking Mathematically by J. Mason, L.
How Many More? - Math Coach's Corner Comparison subtraction is really tricky for kids. Part of that is lack of exposure. We typically teach subtraction as take away, and that is certainly one of the subtraction structures. But we need to move beyond that and help students understand that comparing also involves subtraction.