Teaching Practicesfor the 21st Century
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Whether you work with Common Core Standards, or your own state standards, students are being required to communicate mathematical ideas using appropriate language to justify and defend mathematical solutions. Some of the "tips and tricks" we have taught in elementary mathematics are now coming back to bite us because the "tips and tricks" are not rooted in sound mathematical practices or concepts. We must be so very careful teaching absolute truths in elementary math. If we teach an absolute truth in 2nd grade, that absolute truth should still hold true in 6th or 7th grade as well.
How many of us ask students to solve a problem and then stop when the student produces a correct answer? Give students a good rich task but don’t ask how they arrived at the answer or how they know it is correct? This is where reasoning and proof comes in.
What do we teach math for if it is not to have students use their mathematical knowledge and understanding to solve problems? I used to tell my students that their employer was not going to ask them to do a straight computational problem such as, 346,328 - 132,004. No, they were going to ask them how many widgets were available to ship after the Acme Company’s order of 132,004 widgets was filled.
Deborah Schifter is a principal research scientist at the Education Development Center in Newton, Massachusetts.
In the book, Adding It Up: Helping Children Learn Mathematics, (National Research Council, 2001) (beginning in chapter 4, page 137) researchers talk about the components or strands of mathematical proficiency. They identify these strands as: