I'm a Mathematician

As I looked at my first version of my math autobiography, I enjoyed looking at my previous thinking from “a distance”. It was encouraging to see how my thinking of myself as a mathematician and my thinking about teaching math have both changed. I even think my own understanding of math has been changed for the greater.

One area that I think is of greatest importance is the change in my view of myself as a mathematician. Prior to this quarter I saw myself as a mediocre student of math who had some pretty big holes in my own understanding. Now, I am mathematizing the world around me! My enthusiastic math professor (that’s you Allison) has me seeing math all around me. Never before did I care to count and solve the world around me. Now, my husband gives me funny looks when he finds me starting at items around our house in new and prolonged ways. With this, I see myself as a mathematician now. Despite the fact that I still have more to learn about math as a subject (who doesn’t?), I have now recognized my own math strengths. Additionally, my math weakness, number facts, is coming along now that I understand the idea of derived facts and grouping of numbers. With practice using these strategies I know I have been able to move some number facts into my own recall. Success! A few years late but I am ok with that. Altogether I see myself as a mathematician now, I enjoy math more and I know that I will be a great math teacher. Very exciting!!

Math Expressions v.s. Envision Math

Yesterday I had a mock interview with a principal and he asked me, "What are you still learning how to do?" After some thought, I told him that I was still learning how to take curriculum straight from a box and go beyond the curriculum to create a learning opportunities that provided for the needs of all students. The curriculum I was thinking about specifically was Envision Math. I have been meaning to blog about this for a while now because I feel as though I am really struggling with this curriculum.

At my Dyad placement I was fortunate to work with Math Expressions. This curriculum has been in the school for a few years, therefore the teacher was able to manipulate it as necessary, and it seemed to me to be very exploratory. From what I observed, students were engaged, their thinking was being heard and they often worked collaboratively and with manipulatives. In my main placement we use Envision Math. This is the first year this curriculum is being used in this district and so most teachers are teaching it “straight from the box”. From my observations, this math is very paper driven, has little to no group work, does not allow for students to discuss math or be involved in math talk, and rarely uses manipulatives. When I watch this math being taught from the back of the room I see students struggling. This math is totally teacher centered and teacher paced. Students know by now that the lesson is over once they have filled in the whole worksheet. Therefore, some students work ahead of the teacher, others copy those who work ahead to finish early and the rest of the class just waits for the teacher to give them the answer. Test scores in math are low and students are not able to perform math outside of specific math lessons.

Because of what is going on in my classroom around this math curriculum I am scared to teach math. I felt successful in teaching math in my dyad placement because of how well Math Expressions was working for the students. With all this in mind, this is what I am learning how to do; to make curriculum better fit the needs of the teacher. If anyone has any suggestions or experience with either curriculum, feel free to chime in!

Facilitating Small Group Discussion

Facilitating a small group discussion with Arynne and Kristin!

Learning from students

This past week when I spent time having math discussions with third grade students, I came to the conclusion that we sometimes do not realize how our students understand more than we give them credit for. During our math discussion, I had one little boy who looked at a series of dots and grouped them in such an advanced way in order to count them. It was more advanced grouping than I would have thought of in the three seconds he was able to see them and count. When I remove myself from the situation and think about that little boy, I see him as a third grader, as a student who still has so much to learn. Although, when I think about his thinking he shared with us I realize that he is older in a way that we are not able to see.

This situation made me think about how children have more to offer teachers and classrooms than we usually allow. It was interesting to me to watch a video recently, a TEDtalk on YouTube titled "What adults can learn from kids" in the video Adora said that teachers should be learning from their students. This is an interesting point of view. I know in previous classes in our program we have talked about being students of our students, studying them to get to know all we can about them. But, this perspective is different. This video and our recent math discussion has caused me to think more about listening to what my students have to offer and to not underestimate my students' thinking.

Division

This last week in class we discussed varying aspects of division. From our Fosnot reading I was most interested in the concept of partative and quotative division problems. At first, I seemed confused as to why this would be important for us to know as teachers. After our time in class I have a greater understanding of the difference between the two division contexts and the importance of knowing these as a teacher.

First, it is my understanding that partative division includes the action of “dealing out”. It is in this situation that students generally use trial and error in order to find the answer. One example problem includes: There are 21 cartons of milk and there are three helpers. How many cartons does each helper get? Partative division is often the most challenging for students. In the example above students know that they have three helpers to “deal out” the milk to. Often times the count, “1, 2, 3” to deal out to the three helpers and then start over with the first person and continue the dealing out until all of the items are distributed out.

Quotative division, on the other hand, includes the action of scooping things together in groupings of a certain number with the number of groupings unknown. One example problem includes: If you have 21 cartons of milk and you want each person to get seven, how many people can you give them to? With this quotative division problem, students will start by putting the total into groups of seven.

I have come to realize that understanding the difference between partative and quotative division context is important in order to provide students with varying division problems in the classroom. This will ensure that students know that division is not just sorting into even groups (or dealing out) or the other way around. Additionally, since students often have a harder time with one of the contexts more than the other, it is good to be able to recognize which type of division problems your students need more practice in.

Finally, when working with division in the classroom I think it is important to make math tangible and accessible by using real life numbers. For example, using food such as candy bars or drinks can become a great entry point for students, which in turn makes division more engaging. 

What Mathematics Education should be

I have heard people say that math plays no role in the world besides its presence in the school classroom. While I very much disagree with this statement, as I am sure many people do, I think the main problem is not with the person but with their experience of mathematics education. Mathematics education, like all other education, is a part of a swinging pendulum where reform and new theories take teaching in one direction and then later in another. In the past, I believe the focus of elementary mathematics education was simply for students to learn the steps necessary to solve given problems and memorize a set of math facts. This type of education allowed little freedom in thinking and exploration. This type of education has misled many people to think that math is separate from the real world and has planted within them the idea that you will rarely use any math you learn in school.

Today, the pendulum has swung the opposite way. Now the idea is to enable students to mathematize their worlds, to find meaning and understanding from a mathematical approach. Teachers are encouraged to  allowing students to discover math, much like they discover science, and then share their ideas and their thinking with the rest of the class.  No longer is there a goal to open children's brains and plant the necessary information, instead there should be freedom in allowing students to make their own discoveries. Through this type of exploration, and according to Fosnot and Dolk, teachers must give students context in their exploration. In addition, the context of the assignments must be open enough to allow for individual development. It is all very exciting to read about "new" ideas for mathematics education. I am eager to learn more and incorporate these ideas in my own class.