Week 15 blog posting

I read the Barody and Bartel article. I picked this one because I thought that the idea of connections was interesting and something worth discussing. The author makes a very clear argument in the first section of the article. He states that "Research suggests that understanding can be viewed as a connection between two pieces of information (Ginsburg 1977), and an understanding of elementary concepts is essential for mathematical power, for example, applying school mathematics to everyday tasks, inventing mathematical procedures, understanding and solving genuine problems, and comprehending more advanced mathematical ideas." This sentence totally convinced me of his idea and drew me to want to read more. The author then goes on to talk about the use of concept maps to achieve this goal. While this was something that I had never thought of before, the author makes sense. That using this model allows students to draw their own connections on the concepts of math. This will also give information to the teacher about what connections the students are making versus those that we want them to make. As well as showing students how everything that they learn builds upon itself and is all interconnected. I believe that this is an interesting way to show students a new technique and grasp their knowledge.

Week 14 post

To our group: I am very sorry this post is late. There was quite a bit of confusion on my own part of whether we had to post or not this week.

When it comes to how the equal sign article relates to the activity that we did in class, I feel that it can be very confusing for children at an early grade level when it comes down to it. As we figured out from 2 weeks ago, the equal sign can cause many many confusions when looking at the way that students write it. Having students express the equals sign as "the same as" instead of "equals" causes many confusions as well. As we saw in our class it comes with a lot of debate about what and how it should be used. I feel that we need to make a standard for not only our classrooms but for how our students can best understand it. The equals sign is obviously a very basic thing that is used in mathematics everyday. I think that if we don't get a good basis down for our students at an early age of appropriate ways to use it then a lot of debate will still come about, just like in our classroom.

Week 12 Post

I really enjoyed reading the Whitenack and Yackel piece. I believe that it simply presented a lot of good information that could be really useful to us. In my experience it is rare for students to challenge one another by asking questions about their process, although I believe that if this were happening more it would only benefit the children more. In the scene on the second page where Casey's logic is challenged by Teri, it allows us to see the very clear distinction between people who are looking for explanation versus those who are looking for a justification. Students who are looking for an explanation do not understand the problem, while those who are searching for justification believe that they know the answer and that the one they are questioning is incorrect. This distinction is key to understanding when teaching math because it will allow you to properly answer the questions that the students are asking. The article also states that this discussion is a learning opportunity for all students because it will help them develop the ability to form mathematical arguments and will in turn advance their mathematical thinking. This is something that every educator should want for their students, and through methods such as these, I believe that it is possible.