CGI Blog

Before I read the first three chapers of CGI I had never really stopped to think about how children learn math. I have always just thought of math as something you get or you don't. It was very informative to read about the different ways in which students learn math such as; join, separate, part-part whole, and compare (graph page 12). I thought it was neat how the book stated how strategies such as counting come naturally to young children. Children do not have to be taught that a particular strategy goes with a particular type of problem. I thought this little fact was so cool and it got me thinking about the students I work with and how each of them use different strategies for the same problem. One student isn't more right than the other, it just shows how children learn things in different ways. Another thing that I found particularly interesting was the effort that goes into creating story problems for students. I had never stopped to think about how the wording in word problems can make a problem harder or easier for a student. Problems are easier if their wording corresponds to the action sequence. For example:
Janice had 9 cookies. She ate 3 of them. How many cookies does Janice have left?
VS
Janice just ate 3 cookies. She started with 9 cookies. How many cookies does Janice have not?

Clearly the first one is easier because the starting quanity is given first. All in all I really enjoyed these three chapters and learned a lot about math, however I do have one question and that is at what age do you try to get students to stop counting up or down and just doing the math? How do you teach students to SOLVE a math problem, rather than just counting up or down?

More on Cognitively Guided Instruction

When reading the first three chapters of Cognitively Guided Instruction it was refreshing to review the different ways to construct addition problems (as well as subtraction). I found it particularly helpful to have the chart (page 12) that explains the different types of problems (Join, Separate, Part-Part-Whole, and Compare). I was also helpful to include the result unknown, change unknown, and the start unknown sections. These ideas are new to me. I think that understanding how to construct math problems using a variety of these methods is beneficial to students because it allows them to use critical thinking skills even if they are solving the same problem. In my field placement, my students struggle with word problems so I think it is important to introduce all of the problem types and to give them practice in completing such problems.
Another thing I noticed that in my students' math workbooks, the students always skip the story problems. I think they really struggle with the language which may be detrimental to their learning. I found the Chapin and Snock article to have many interesting points about how the language of word problems can negatively influence student understanding. Having these two readings in mind, I hope to make sure my future students are well versed in the language of math as well as well practiced in the many problem types.

Cognitively Guided Instruction

In many college level courses students find the reading to be useless, unneeded, or boring. For me, this was not the case when reading about Cognitively Guided Instruction. When reading the first three chapters of the book I became excited know that I could use some of this information in my future classrooms. The author of the book states, “Over time, direct modeling strategies give way to more efficient counting strategies, which are generally more abstract ways of modeling a problem” (Carpenter, 3). I was struck by this quote, not because I did not realize that children moved from direct modeling to more abstract thinking of mathematical concepts, but because I questioned if all students do this on their own time or if some need more direct instruction on how to begin to think abstractly (for example: doing mental math). This quote also reminded me of the subtle things teachers need to be looking for during mathematical thinking. An observer may think a child who gets the answer right by using direct modeling has a better understanding of mathematics than a child who uses mental math and gets the answer incorrect. In reality the teacher needs to think about the student’s mathematical thinking and where they need to grow from there.

In the book the authors state, “Variations in the wording of the problems and the situations they depict can make the problem more or less difficult for children to solve” (Carpenter, 10). I found this extremely interesting. I had never thought about how a word problem can be manipulated to change its difficulty. In the book the example the authors gave (in case you do not remember) was:

Janice had 9 cookies. She at 3 of them. How many cookies did Janice have left?

Janice just ate 3 cookies. She started with 9 cookies. How many cookies does Janice have now?

The problems are the exact same, just worded a little differently. This information visually showed me how a teacher needs to be careful when writing his or her own word problems, or when picking word problems from a book. This is because the ways the word problems are written affect the way a person perceives the problem. Another way a teacher can use these two word problems are by using one or the other for an extension or simplification. Depending on the needs of the child the same word problem can be written in a harder or easier way.

I also really enjoyed learning about the different types of word problems. I had never thought of word problems as having so many different types. I am not sure if I have completely memorized what each of the word problem types are called, but I know have an idea that when teaching a classroom a teacher can not just pick a word problem arbitrarily. A good teacher has to plan ahead!

Overall, I really thought this book had a lot of helpful information. I am interested to see what others thought about the book and the information they found important. The only thing I am worried about is being able to spend enough time to pick the correct word problems for my students. I am also questioning myself on how I will be able to remember all the different types of word problems and recognize them by sight. Hopefully this will come from experience and time, but as of now I feel that this task may take a lot of time and effort for beginners.

There are many learning goals that I would like to accomplish throughout this semester. I have always been pretty average when it comes to math and I have always enjoyed it, however I did not always feel safe in the enviroment in which I was learning math. I was always scared to raise my hand and give an answer because I was too scared of being wrong and being made fun of. I want to create an environment much like the one described in the Lester article. I want my classroom environment to allow the students to be curious, question things, explore and most importantly feel respected. I believe that when you create an environment such as this, that all students have a better opportunity to succeed. Another goal that I have is I want to walk away from this class and be able to explain how something is done. For example, I know that 4+4=8, but when a student asks me "why?" I want to be able to provide them with a confident explanation. I am very good at solving math problems, but I have not yet mastered WHY math problems work out. I would also like to walk away from this class knowing different methods and strategies to teach math. I can remember from my own math experience that I didn't always learn math the same way as my classmates and therefore I think that it is important to provide students with different ways to learn math. The most important goal that I would like to learn from this class is how to help my students appreciate math. I do not think that many students appreciate math or think that it is important, and therefore I want to make math fun, and engaging for my students.

Learning Goals

After reading the syllabus and the readings for this week, I developed some learning goals for this semester. I was really interested in the article that discussed how to gradually create a learning community for math. One of my goals is to learn how to create a safe environment such as the one in the article. I want my students to feel that they can take a "risk" in the classroom to express new ideas. I also want to learn more about how to get parents involved in their child's learning, if possible, pertaining to math. Another goal that I think is important is learning about different strategies to teach the many methods of solving a math problem. In the article where the teacher used the unifix cubes, I learned a strategy for teaching addition and subtraction that is hands on and engaging. Although it is impossible to learn every strategy for teaching every type of problem, I feel that individual examples in case studies add up and can help me to develop my own strategies for in the classroom.

A last learning goal, is that I want to be able to see math problems from many different perspectives. Before taking Math 201, I only solved math problems in one way that was comfortable to me. I want to be able to look at a math problem and imagine the many ways students can solve it. I want to be skilled in looking for patterns in solutions and seeing if that method will work every time.

Welcome!

Hello!
I look forward to discussing with all of you over the course of the semester about issues relating to education. I feel that this blog is a way for all of us to get to know one another and also talk to each other in a professional manner. I hope we can learn from each others ideas and work together as a team to push our thinking beyond the surface. With that said, I would like to begin by discussing my ideal classroom and goals for this semester in TE 402.

Throughout my experience as an undergraduate in at Michigan State University I have had some good experiences and some that could have been better. This is also true when thinking about my experiences in Elementary School, Middle School, and High School. I believe that most, if not all, students come to school with expectations for themselves and their teachers. Students want their time in the classroom to be worthwhile and memorable. The content that is taught may change from year to year but these expectations for the teacher do not. I believe that the things that I am stating here deal with my ideal classroom for TE 402 and in the field. As a student and a teacher I want my classroom to be welcoming and hands-on. I also believe that the academic content which is taught during class should be molded by the interests of the students. This makes the learning process more authentic.

Students come into the classroom with prior experiences that have molded who they are as a person. Some students may be quiet while others may choose to talk a lot in class. Other students may struggle with certain academic content and become quickly frustrated with themselves or their peers. As a teacher you have to take all these different learning styles and create a learning community where all students can excel. This is not always easy, but through TE 402 and our field placement this semester we can hopefully learn how to create lessons and activities for children with a variety of learning styles.

Overall, I am confident that TE 402 will meet my expectations and that we, as a class, will benefit from open discussions that connect class content with what is going on in our field placement.

Have a wonderful week!

Kathryn