Happy Summer Everyone!
I was just reading an article from NCTM titled, Discovering the Greatest Area of Need in a Mathematics Classroom by Derek Pipkorn. This article focuses on a middle school classroom, while I teach a fifth grade classroom, but good teaching practices are good teaching practices regardless of age or grade. Here is a link to the article: NCTM Article
I love this article because it reminds us that good teachers do not lecture or give formulas, instead we provide experiences so that the students can derive their own formulas or approaches to solving a problem. Towards the end of the year my fifth graders learned about Volume of a Rectangular Prism. In Texas, this concept and math formula is new to fifth graders. This was one of the last concepts I taught before the STAAR test (our state wide high stakes test). I could have shoved the formula down their throats and then done drill and kill until they “mastered” the concept. I chose not to take the easy way out (and really is it that easy?) and instead provided opportunities for students to derive their own thinking and explanations and subsequently the students found the formulas V=Bh and V=lwh, all on their own. When students take ownership of their own learning, the learning becomes significant and put into long term memory.
Unlike Mr. Pipkorn, I have a longer class periods and I work in a school where 57% of the students are economically disadvantaged and 50% of the students are considered At Risk. Despite these differences the theory behind the article rings true. Students who DO MATH are more successful then the students who passively learn math.
Mr. Pipkorn refers to students learning through the struggle, for which he and NCTM refers to as Productive Struggle. I couldn’t agree more with the concept of Productive Struggle. The article provides a chart about what teachers and students should be doing while learning through the struggle. Here is a copy of that chart below: