Math Identity Blog Entry 4 - Invented Math Strategies

In the problem-solving interview, my student N used a mix of counting strategies and direct modeling strategies to solve the problems. I particularly remember her strategy for the measurement division with a reminder problem that reads, “Abby has 23 little toys. If she puts 10 toys into each bag, how many bags of toys will she be able to make?” N used direct modeling and began by counting out 23 unifix cubes and connecting them together. She continued by counting out 10 cubes and breaking the chunk off. N then checked to make sure she had counted out 10 correctly as she counted each cube of the chunk one-by-one. That group represented her first bag and she counted out 10 more cubes to serve as her second bag. Eventually, she determined that Abby still had 3 toys leftover, which could not be put in a bag on their own.

    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!

Math Identity Blog Entry 3 - Math Talk Moves

I have really enjoyed learning about Chapin’s Five Productive Talk Moves. Although I have unknowingly used these strategies while teaching in past years, I have never really thought about them in depth. Using revoicing, students really have a chance to process their own thinking while the teacher or other individual voices their steps in proper terms. Asking students to restate someone else’s reasoning and to apply their own reasoning requires that students understand a strategy, perhaps one different from their own. Finally, prompting a student for further participation and using wait time allows a student the opportunity to respond on his or her own. It is important that we respect the child’s thought process and encourage the child to share their opinions, proving that we value their skills. While I am aware of these techniques, I still find it somewhat difficult to use them in the midst of teaching under time restraints and other pressures. I hope to become more comfortable using these strategies over the semester and into future years of teaching.

I did not teach or observe math this week, as I was in a Data Analysis Meeting for the 5th grade team on Tuesday and the 4th grade team on Wednesday. Last week, I remember observing a lesson on operations and key words that provide hints to which operation should be used in word problems. I noticed my teacher is excellent at providing sufficient wait time with students. She will call on students but if they are hesitant to answer, she will tell the student to think about his answer, as she probes other students. If the student is still stuck, he may ask for the help of a friend. At times, the silence is almost uncomfortable. The students realize, however, that their teacher is expecting an answer and that she is willing to give them ample time to respond. I will certainly be looking to my teacher as a model for this “talk move.” One other strategy she demonstrates particularly well is revoicing. Since my students are ELLs, it is critcal that my teacher models appropriate math language and vocabulary (and English language too) to aid their instruction.

If I could redo the lesson, I would also have students restate their friend’s reasoning. I think, in this way, students would be attentive to all problems rather than only the ones that are designated to one student by name. Students could also gain better insights to problem-solving strategies that could potentially be easier or more efficient. I would integrate this talk move into the teaching practice with simple prompts, like, “Student ___ can you tell me in your own words how Student ___ solved the problem?” I find this method would get students more involved in the lesson and foster a positive classroom culture.

*** NO pictures this week because I was in the Data Analysis Meetings mentioned in paragraph 2