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:
Source of the chart: http://www.nctm.org/Publications/Mathematics-Teaching-in-Middle-School/Blog/Discovering-the-Greatest-Area-of-Need-in-a-Mathematics-Classroom/
In my experience students often times rely on the teacher to "spoon feed" the solutions or formulas to be successful. This year was my first year to have an inclusion classroom. This means I had regular ed students in with special needs students. To say I was scared would be an understatement. I was terrified until I realized that a student is a student regardless of ability. What I noticed was that the special needs students were just as scared as I was to be in the regular class. At first I felt compelled to hold their hand throughout each lesson. Around October it hit me that they were not progressing like the others. I self evaluated and knew that the spoon feeding had to stop! The learning is in the struggle! This was a rough transition, moving from constant support to very little. One student in particular really had a tough time and often times refused to work. I kept encouraging her and she eventually came around. Last year (2014) she didn't pass the modified version of the fourth grade STAAR Math test, however this year (2015) there was not a modified test so she took the regular fifth grade STAAR Math test. She received a 64% on this test! This is miles from where she started! In fact I had 8 special needs students who I taught and all of them except for one did substantially better than the year before. Even the one student who did not officially pass made huge gains in his ability.
As teachers, our role is to provide activity based lessons in which students can construct their own meaning through productive struggle. When students take ownership of their own learning students will retain more and become more successful. I love when articles hit home and remind you that you are on the right track! Thank you Mr. Pipkorn and NCTM!
Peace, Love, Math- Jennifer