What knowledge have you gained about how children learn mathematics from this course?

1. I have gained a lot of knowledge about learning math in this course. Children all learn differently, we all already knew that, but what was unknown was different ways to teach how to solve a problem so that many different children can find the correct answer based on what they already know. Children can come to the same conclusion, same answer, even if they start at a different spot of the problem because it depends on where they are at and how they are attacking the problem. It is important to let students know that they can make mistakes and that's ok, it is also important to let children explore a problem before you give them too many limitations, the "correct" way to solve the problem or the answer. It is also valuable to let children discuss and verbalize what it is they are thinking, how they are getting to their solution.

What knowledge have you gained about how children learn mathematics from this course?

What knowledge have you gained about how children learn mathematics from this course? I have learned that children truly learn in different ways and those ways have to be met the best way possible. There is more to mathematics than showing students "this is how to do it" and then hand them a worksheet to work out similar problems. This procedure or way of teaching makes future math teachers to underestimate their students abilities because they only know how to think of a problem one way. Teachers need to become aware of what their kids know and then go further indepth on the topics that need to be. Children are really curious at different ages and I think teachers need to take that into consideration as well. When using manipulatives, question the students about them and about how they are thinking. Who knows how many ways will turn up to solve one problem.

How has this course changed or not changed your perceptions of teaching math?

I originally thought that math was as basic as introducing a basic formula to students and building on that. I never thought much about using manipulatives past the younger ages of students. I liked how the class forced me to look at problems the way my students would and break them down in order to be able to teach them to my students. This class frustrated me several times because it took me so long to understand the importance of breaking problems down the way Dr. Rein's did. Students need to be challenged and given opportunities to approach problems in different styles. Each student learns a different way and at a different rate, which means that my instruction should cater to the differences of my students. In order to teach a problem, it is important to start with the basics and work my way up.

Last two Questions--Kendra Lundeby

1. What knowledge have you gained about how children learn mathematics from this course?

• While being in this class I have learned many important aspects on how to teach math. I learned that is important to teach students the strategies and steps to reach the understanding and solution rather than just stating a formula. Explain why the formulas are set up the away they are and plan many activities to learn the stages of the problem. Teach students the foundation of the math so they create a strong foundation of the material before they need to use it in their worksheets and activities. I have gained a better ideas on how to properly teach math so that more students are understanding the material. In this course I have gained an understanding on how the teach math better while being in this course.
  

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How has this course changed or not changed your perceptions of teaching math?

This course has changed everything I have thought about math and doing math. I now know that helping students to reach inside to help themselves build on prior knowledge is a great way to learn math. Once given a problem, students are able to figure out a problem with out equations that they would have memorized in the old way of teaching math. Often students, if given time to think and struggle, will find a way to solve a problem.In the same classroom, with the same problem, there will often be many different ways that will be shared for solving the problem. Students will then learn that with the different ways to solve a problem, they can use other strategies to check their work. One of the things that really stuck out to me was that students should be praised, even if their answer is wrong. I think this is a great concept, because if a student is afraid of making a mistake, they will not try very hard. Overall, I think this class was great because it helped me see a whole different outlook on teaching math.

Knowledge gained

What knowledge have you gained about how children learn mathematics from this course? I have learned that some educators underestimate the abilities of children to solve mathematical problems. Teachers do this by sticking to the material in the book and only assigning worksheets instead of creating a classroom where students are able to really show what they know and the processes they take. To truly learn mathematics, children need to be presented with real life problems and allowed to discover the answers on their own or with classmates or at least attempt them. Too often we are just taught the rule but are not informed of why the rule is the way it is when knowing the reason would have students understand mathematics much more. Every child has the ability to learn, but it is up to the teacher to create material that is pulls students in and has them interacting with the material.