4 responses with 60 words each (No plag) don't forget to put the initial thanks.

  #1:     B H CAT Question

In a way I am giving you one strategy for the discussion question.  In my classroom, I loved the think-aloud strategy for math.  I would solve a math problem out loud overexagerating my thought process.  Why is the think aloud a great math strategy? 

#2:    S J

“Teaching through problem-solving” means that the students learn mathematics through inquiry. In this type of teaching, students use exploration to learning mathematics including exploring real contexts, problem, situations, and models. In this type of teaching approach students are given a problem, then discussion is facilitated to share their ideas and ask questions to help build and connect conceptual and procedural knowledge, rather than, these concepts being taught before problem-solving. A strategy that could be used for this would be to start a lesson or unit with presenting a mathematical problem to sole. The students do not yet know exactly what to do for this problem but instead use their prior knowledge to make informed decisions about the math problem. Once finished, the teacher asks the students to do the problem on the board. While they are explaining their findings, the teacher is writing the steps the student took to answer the question on the board for the rest of the class. This provides the students with a summarization of the lesson’s new mathematical ideas (Van de Walle, Karp, & Bay-Williams, 2017).

References

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2017). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Boston, MA: Pearson Education, Inc. ISBN-13: 9780134802084

#3:    C D

"Teaching through Problem Solving is an effective way to teach mathematics 'for' understanding. It also provides students with a way to learn mathematics 'with' understanding" (Degner, 2012). Not to be confused with teaching problem solving,  the goal for teaching through problem solving is for students to learn the mathematical idea that the curriculum requires that they learn next. A “teaching through problem solving” lesson would begin with the teacher setting up the context and introducing the problem. Students then work on the problem for about 10 minutes while the teacher monitors their progress and notes which students are using which approaches. Then the teacher begins a whole-class discussion. In other words, instead of the teachers "teaching" students the lesson, they are given the opportunity to determine the how-to of the lesson on their own or in pairs. 

Degner, K., 2012., Teaching through problem solving., Retrieved from https://eric.ed.gov/?id=EJ981840 

#4:       C H

To “teach through problem-solving” means to basically learn through trial and error. When teaching this way students will hold discussions before attempting to solve the problem instead of a lesson being taught first. The students will not fully know what to do but will work through what they can on their own. The best way to teach this in the classroom is to have the students work out the problem but after, when reviewing, write out the steps the students took to get the answer and explain why these steps are right or wrong.