Last year I had the amazing opportunity of being a filming teacher in a partnership with the Digital Library and Illustrative Mathematics . Through this process, I was filmed by The Teaching Channel, and they produced this video of introducing ratios.
Today was take 2 of Perfect Purple Paint (the 6th grade entry version). I wanted to see how student’s thinking would compare to last year and if the launch would be as successful. Today though, I wanted to apply a formative assessment. I wanted to give the task without blocks first and then with blocks, second, to compare the success rate and level of understanding.
- I gave students about 7 minutes of private think time (without blocks).
Note: No directions were given as to how a student could show thinking. At this point, about ¼ of the students had a correct answer based on prior knowledge.
- I asked students to return to their seats and begin building models, in their table group, to show the ratio and solution (below are different examples from the same group). .
Above are some of the students’ creations:
- We came back together as a group (we sat in a circle) and laid out all of our models in front of us. Students were asked to identify similar models. (below are models the students connected to one another). Students were asked to explain how they connected to one another.
Students were asked how these models showed the 2 to 3 ratio and to physically point out the initial ratio.
- After a series of sharing the ideas, the groups returned to their seats to draw models and past into their notebooks. (Note: By this point, 80% of students could successfully build and explain the number of cups needed that kept the original ratio in place).
I am always reminded of how the blocks really help to distinguish the different parts of the ratio. In addition, it is very apparent how the manipulatives themselves, help students make sense of math. I am also reminded of how this will help us build into a tape diagram. (We will begin looking for shortcuts on our models tomorrow.)
I am left thinking how I can improve asking equal questions to students who both appear to have correct models and those that do not. It is apparent that students still feel generating an incorrect model is punitive and thus, begin to shut down when they realize that their model needs changes made to it. Changing the mindset of these students, is going to take some real time and effort. At times, I question my abilities in this arena.
My wondering to all of you (whom may be reading) is how do you help change mindset to one of fixed to growth? What strategies do you use when students sit almost paralyzed when they think they can’t do something?