6 responses (don't forget to put the initial)

#1:      B H  CAT Question

What would be a good strategy to explain mathematical thinking for students?  Explain your thinking/rationale.

#2:     S J

Educators can help students feel more comfortable when asking them to explain how they arrived at the correct answer of a math problem by explaining the importance of mathematical discourse and effectively encouraging it in their classrooms. Teachers can explain to students that they will be asked to provide rationales or explanations of how they obtained their answers by letting them know that this is a way teachers can help students build bridges between what they know and what they still need to learn, as well as, that it gives the students the means to explore with math. Educators can use mathematical discourse by establishing it as a classroom culture. This can be done with setting expectations on students justifying their answers, contributing to the discussion, active listening including commenting or redescribing another students contribution or having student pose more clarifying questions to each other, and having students explain why they do not accept someone else’s explanation. Teachers can encourage calculational and conceptual explanations by using questions that pose a range of responses to facilitate discussion further.

#3:    T D

I know how it is to get frustrated when it comes to math. I struggled so hard and thought I was so dumb but ONE teacher sat down and explained to me that everyone is different. Once it clicks... math will be easy. It just takes practice.

In my future classroom I will tell students to show work so it will allow me to see how they came up with the answer. Work is so important because it allows you to jump into that students problem solving process and you can see where they messed up. The work can be half of the answer and the actual answer could be the other. This way if they get the answer wrong they can still get some points for doing the work.

Teachers should encourage students to show their process so they can get some points for an answer.

#4:       M J

Encouraging students to reflect on their mathematical course of completion and understanding is important because it allows the students to walk through their own train of thought and allows them to see a pattern in which they are completing the given assignments. In some situations, students may get a correct answer and solve the problem wrong ( a lucky guess ). Discussing the walk-through of a problem is important because if the student gets a wrong answer, the teacher can walk through the steps with the student and explain what they can do to prevent making what could be just a small potential mistake in the future. Although, many students do become frustrated when they are asked to walk through the steps that they took to get their answer, we must encourage the students to think out loud and express how they solved a specific problem. Tone and manner will come into play with this, you do not want the student to feel as if you are questioning the fact that they got the answer right.   

#5: N J  CAT Question 

Why should we use manipulatives in math at any grade level? 

#6:      S J 2

Manipulatives are a great way to explain math processes to very young students. Educators can use almost anything at their disposal as a manipulative to get students interested in learning the concepts of math. My son is four years old and loves math. He started with counting anything we could find to count (legos, candies, movies on the shelf, cousins at a family gathering, anything). Once he mastered the concepts of counting, he began using those same hands-on manipulatives to start learning the concepts of adding or subtracting. We would take a small bag of skittle or m&m’s and I would place 2 on one side of a piece of paper, write the addition sign, then place 2 more on the other side with an equal sign at the end of the page. At first, he was counting them out loud to get his answer of 4. Now, he internally thinks of the problem in his head and answers out loud 4. Subtraction was a little harder at the beginning. I started this by explaining that subtraction always means taking something away and through the candy exercise of me taking away 2 of his 8 skittles he started to understand. Later, we did other activities like we would be playing dinosaurs and I would have 4 and he would have 8. He would say “my t-rex has ate your triceratops”. I would them ask him how many I have left to continue battling with. I have found this to be a great way to teach and encourage math to young children as he is now wanting to learn simple multiplication problems, now.