N could also have solved this problem using direct modeling with pencil and paper. She could easily have drawn 23 squares or shapes to represent toys. N would then have counted 10 “toys” and drawn a circle around the items, grouping them into a bag and then another bag.
Student N may have also been able to use a counting strategy. Able to count by tens, N could have simply stated, “10, 20,” drawing a bag on her paper at each counting interval and then counting “21, 22, 23” as she drew individual toys remaining. Yet another way to use counting by tens would have been to provide N with a multiplication chart and counters. If she placed a counter at the end of each complete row, N would know that only 2 complete rows, or 2 “bags,” were filled and 3 leftovers remained. Regardless of the particular strategy, the student would still be able to reach the same answer. N really enjoyed visually representing the problems with manipulatives and her explanations were excellent, with added detail to tell a true story in her explanation of the problem. I think it’s wonderful to see the variety of strategies students use and I look forward to learning new ones from my students over the years!
My child also used a mixture of counting and direct modeling strategies. These two are very close to the same thing and I have to pay careful attention to tell which one is actually being used. I also like the problem that you chose because it is not a cut and dry problem and leaves the student with a remainder. These problems show the students ability to think critically about what the remainder means and what to do or don't do with it. Direct modeling with the manipulatives is a great way for the student to visualize and make sense of a problem like this.
ReplyDeleteEric
Christi,
ReplyDeleteThroughout my interview, my student decided to use multiple strategies as well. She never used derived facts, everything was either a counting strategy or a direct modeling strategy. It makes sense to me that these would be the two most commonly used strategy, because that is what I use when I am "acting" like a student. Derived facts simply confuse me, to be quite honest. I too get excited when I think about the many strategies we will see in our careers. Even throughout my placement, I have one student who solves everything mentally, one who draws a picture for everything, and another who solves using a traditional algorithm. It is so interesting to watch each student solve the problem their own way and yet all students reach the same answer majority of the time. It is really cool to allow the students to solve the problem their way and respect that strategy.
My student also did a lot of direct modeling. I had to keep asking (on a few of the problems) for her to try and think of another way to solve the problem (probing her to try an invented strategy). It was interesting to see how my student wanted to solve the problems in her head. I had to keep asking her if she could *show* me how she solved it rather then if she could tell me.
ReplyDelete_laurenfritz
I like your idea of another way she could've solved the problem being to count by tens and then count up. If the student knows how to count by tens, it's interesting that she didn't seem to use that ability. My student used direct modeling to first solve this problem - I think because i'd been encouraging him to use the blocks as a possible way to show his thinking. When I asked him to solve this problem a different way, he drew what looked to be three grocery bags and two the numbers "10, 10, 3" in the bags. I'm wondering if your student went for the Unifix cubes to solve problems in general or if she started to use them after encouragement.
ReplyDelete~Claudia