Tags: Deloitte Case Studies ConsultingThesis Statement For Self Evaluation EssayChoices For Accounting MajorsDay Essay LawAffordable DissertationFood Research PaperStructuring A Research PaperHomework-Help.OrgCrucible Critical Essays
I'm sure we've all seen it happen at one time or another in math class.We give a student a story problem to solve and after a quick skim, the student pulls the numbers from the problem, computes with them, and writes down an answer.I chose the problem below and thought about what I would learn about a student’s mathematical understandings and sense-making after they answered the questions.
They had just finished their multiplication and division unit and would soon be starting work on fractions.
In order for their teacher and I to see and hear how students apply the operations, make sense of contexts, and currently think about fractions, I thought it would be interesting to take a story problem from their Student Activity Book and take out the question and numbers.
I was curious how they would go about choosing their numbers! When I told them I was not giving them the information and that instead they were choosing their own numbers along with the question they wanted to answer, they were so excited!
Would they strategize about the numbers to make it easier for themselves? Some partners chose their numbers very strategically to make it easier for themselves.
I learned so much more about what each of the students know beyond simply multiplying five and six.
Taking out the numbers and the question allowed every student to think about the meaning of the sentence, the implied mathematical connections, and to plan a solution pathway before jumping into a solution attempt.This was a great way to formatively assess students' thinking related to fractions before they began that unit. Who would have thought 3rd graders would reason about the leftovers in terms of percentages?Reflecting on the difference between what students would have done with the original problem versus the reasoning work they did related to the one simple sentence, I'm amazed at the outcomes.Most importantly, we ask ourselves, how can I help students make sense of what they're reading and to think about the logic of their answer in the context of the problem?If we're lucky, we can identify the student's mathematical misconception and work with that.They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.The best way I've found to help students make sense of a problem is, ironically, to take the question out altogether.If the answer is correct, we assume the student has a grasp of the concept.However, if it's incorrect, we're left with a laundry list of questions: Do they realize their answer doesn't make sense? Did they simply pull the numbers and operate in order simply to finish or did they truly not know what to do with them?I asked them what questions they could answer if I gave them those pieces of information, and they responded: At this point, I could have given them the information they wanted.However, I thought it would be so much cooler to allow them to choose that information for themselves.