As my colleague and I learn to teach effectively using a problem-based, constructivist approach in math, we want to be cognizant of the many powerful strategies that exist to complement such instructional methodology. The explicit teaching and use of manipulatives, for example, and the incorporation of graphic organizers into ones’ teaching are two well-documented strategies for effective teaching and learning.
Today was one of those rare days when everything just seemed to click, and every student seemed really engaged with the task, and was easily able to show understanding (or lack thereof) as I wandered around the room with my trusty clipboard…
The task involved students sorting 2D attribute blocks using two or more different attributes. Using the IWB, we reviewed the concepts of shape, size, colour and thickness. Students were able to come up and manipulate the “infinite cloners” I had created on the board, and move them into a VENN diagram slide I had prepared in advance. (During this whole-class time, one boy called exclaimed, “OH! I get it now!” It was very exciting for both of us!)
Today was one of those rare days when everything just seemed to click, and every student seemed really engaged with the task, and was easily able to show understanding (or lack thereof) as I wandered around the room with my trusty clipboard…
The task involved students sorting 2D attribute blocks using two or more different attributes. Using the IWB, we reviewed the concepts of shape, size, colour and thickness. Students were able to come up and manipulate the “infinite cloners” I had created on the board, and move them into a VENN diagram slide I had prepared in advance. (During this whole-class time, one boy called exclaimed, “OH! I get it now!” It was very exciting for both of us!)
After the introductory review and mini-lesson, students went off to work with either a whiteboard or a prepared VENN, and sorted the blocks into two or three circles.
The fact that I had a special ed. teacher in the room to support some of the needier learners allowed me to gather some formative assessment data.
As I circulated throughout the room with my clipboard and a class list, I did as I have been told in the GEIM and other resources we’ve been reading, and asked questions to find out more when I wasn’t sure how deep a student’s understanding was. For example, I asked one boy who had made two circles, “red” and “square”, if there was anything on his mat that could go in the middle, where the circles intersected. It took him a while, but he eventually realised that the red square he had in his “red” circle could go in the middle. Another student had piled blue shapes in one circle, red shapes in another, and yellow in the middle. She clearly did not have the concept of the overlapping attributes. I asked her to tell me about her sorting rule, and was soon able to glean a deeper understanding of her misconception and guide her to see where she had gone wrong. She happily resorted her blocks, choosing two attributes (size and colour this time). Several students challenged themselves to fill in a 3-circle VENN; many of them did it correctly the first time, or after only minimal guidance from me.
As I circulated throughout the room with my clipboard and a class list, I did as I have been told in the GEIM and other resources we’ve been reading, and asked questions to find out more when I wasn’t sure how deep a student’s understanding was. For example, I asked one boy who had made two circles, “red” and “square”, if there was anything on his mat that could go in the middle, where the circles intersected. It took him a while, but he eventually realised that the red square he had in his “red” circle could go in the middle. Another student had piled blue shapes in one circle, red shapes in another, and yellow in the middle. She clearly did not have the concept of the overlapping attributes. I asked her to tell me about her sorting rule, and was soon able to glean a deeper understanding of her misconception and guide her to see where she had gone wrong. She happily resorted her blocks, choosing two attributes (size and colour this time). Several students challenged themselves to fill in a 3-circle VENN; many of them did it correctly the first time, or after only minimal guidance from me.
Using the IWB to demonstrate the concept at first, and have students model it was definitely a motivating factor for the class, and the use of manipulatives and graphic organizers consolidated their understanding of the concept of attributes and sorting. Although this lesson was not presented as a “problem” in the true sense, it nevertheless constituted a valuable mathematical experience for all.