Math Reflections

Reflecting on my learning this last quarter, two themes have continued to come up: students learning through manipulatives and technology and knowing my students.

Using what I know and am learning about my students can help me pick the right kind of technology and manipulatives to optimally engage students in learning.  Students will learn much more when they are able to take their learning into their own hands and it is my job to give the tools to think, not just the tools to complete a task.  We have access to so much technology that can open doors for students and we need to take advantage of it.   The more I know about my students, the more selective I can be about the technology I pick to optimize their learning.

Know Your Students

What I Learned
This isn't necessarily new learning.  But it really does affect me differently each time I hear it.   It doesn't matter how much technology I know or can use if I don't know how to adapt it to my students.  It's interesting to think about shifts in technology and how that is going to affect how we look at a school day.  I love the idea of assigning a lecture as homework and collaborating in class the next day to elaborate on concepts from the previous night's learning.  This will give students a more equal playing field (if they choose to take advantage of it) in class the next day.  It would also allow students to take the time to think about what they don't know and give them the chance to come up with relevant questions.  Hopefully, this would better engage students in the learning the day after they do their "homework."  For me, there is a huge different in my level of engagement when I have some sort of background knowledge rather than feeling completely lost.  In terms of knowing our students, it is important to know what kind of access students have to outside technology can help us create assignments that .  We need to teach students to advocate for themselves in order to have access to the resources they need to be successful.  It's true that not all students have the same access to technology at home, but they will need to learn to take advantage of the resources that are potentially available to them outside of their homes.




Implications for Instruction
Knowing our students is the most important thing to remember no matter what subject we teach.  We need to be aware of what kind of background (academically, culturally etc).  In our science class this morning, we talked a lot about knowing our students in terms of how their cultural practices affect how they view themselves as learners.   If we ignore the connections between cultural practices and areas of expertise, we could be ignoring some of the main ways to connect the curriculum to their students’ lives. In terms of what this means for instruction, I want to be able to connect students' lives to all aspects of my curriculum.  Whether this means incorporating their favorite things into their math problems or constructing a curriculum around what you know about their scientific interests, students need to know that we notice things about them and that those things matter to us too.

Geometry Sketchpad

Something I've noticed recently in my own learning is that I've had a hard time paying attention to class lectures (Robin, this isn't specific to your class by any means).  I know that part of it is definitely related to the fact that we only have a few weeks left to go in the quarter, and I'm a little antsy to finish.  However, in reflecting on that, it's becoming increasingly evident that if I want my students to be engaged in their learning, my talking is not what's going to do it.  It was great working in the computer lab with Geometry sketchpad.  Each of us got the chance to complete the task and had to think about why certain shapes worked with other shapes in order to complete the task correctly. It was fun to be able to engage in a thinking task without being lectured about the properties of different quadrilaterals etc.

In terms of bringing these strategies into my classroom.  I'm excited to try different technologies that can help students engage more deeply into task oriented learning.  While it has been difficult to do this within the context of the materials available to me in my main placement, I'm excited to see the difference that task oriented learning and/or group work will have on my students.

Tangrams

This week, continues to reinforce the idea of differentiated instruction for me- not only in terms of struggling students, but also in terms of multiple intelligences.  Working with the tangrams supports the idea that there should be multiple entry points for students to be successful.  One of the main reason people have such a strong opinion about the subject of math is because they’re used to only having one way to correctly solve a problem.  Likely, they are also used to only being presented with one type of problem to solve.  It’s important to emphasize that there is a variety of ways to be smart at math other than just getting the right answer from plugging numbers into an equation.  Allowing students to be successful in multiple areas can give them the encouragement they need to work at math in areas where they aren’t as successful.

Implications for instruction

These principles are important to remember in math and all other subjects as well.  It is important for students to have entry points of success without resorting to remediated instruction.  This kind of work makes me think that I want to focus the differentiation in my classroom as more than just ability level.  Whether the subject is math, reading, writing, science or social studies, at least some of the differentiation should ideally be by interest or learning style.  Differentiation by ability just reinforces ideas that students already have about how smart they are and how successful they can be.  Differentiating in multiple ways allows students to find ways to be successful on their own.

Math Manipulatives

After getting bogged down in teaching standards and worrying about covering tested materials, I sometimes forget that math can be fun....and I like math.  I can imagine that as teachers, the way we feel about math really affects the way our students will feel about math.  If we project the image that teaching math is stressful, we project that stress on to our students.  When we were using the miras in class on Monday, many of us were having so much fun, we forgot we were doing math.  It was interesting to learn that many teachers don't take advantage of the manipulatives available to them at their schools. This seems strange considering how helpful they can be in getting students to move their thinking from concrete to abstract.  Also of interest to me was the fact that today's students don't differentiate greatly between virtual and tangible manipulatives.  This fact increase teacher access to many different ways to help students learn.

In terms of classroom application, I'm encouraged to have the access of so many materials online, even if I end up in a school or district that does not place much emphasis on learning with manipulatives.  It was encouraging as well to see that teachers who had your students in later years, could pick out which students were yours because they had a much deeper grasp of math concepts.  

Concrete to Abstract

It's interesting to me how at first it seemed so counterintuitive to go from concrete to abstract in math. It's a method we use to learn and teach most everything else, and it seems strange that we would choose to learn or teach math differently. We're often looking for someone to tell us a formula and give us the quickest way to find an answer. While there's nothing wrong with efficiency, we lose a lot of understanding by not thinking about why the algorithm we use works. Our brains are constantly looking to make connections from the patterns we see, and we can make generalizations about those patterns when we connect our concrete learning to our abstract thinking.

In terms of classroom practice, I'm seeing manipulatives in use much more often than I experienced in my own education. In my dyad 7th grade math placement, we used chip boards to teach the students the difference between the adding and subtracting of negative and positive numbers. I did notice that the teacher's comfort with a particular manipulative had a big effect on the students choice to use that particular strategy. For me there's still a question of how to know when to use them, and how long should we allow students to rely on them before we encourage them to use a more efficient algorithm?

First of all, algebra tiles are probably one of the coolest math manipulatives I've seen so far. It

I'll be the first to admit, I've always liked math. Growing up, I was what you would call a "math person.' I was very good at plugging numbers into an equation to get a right answer. Throughout this program I am continuing to learn that this is not necessarily what that is about. I'm learning about the excitement that comes with working collaboratively on a problem and then coming up with an answer in a way that means something to me. Not only do I have a better understanding of why I'm doing what I'm doing on certain problems, but I also get to share this with others and see the many different and very cool ways that others go about solving the same problem.

In terms of translating this into classroom practice, the idea of group work and collaborative problem solving seems great--in theory. It's not that I don't see the value in these types of problems or their ability to cover multiple standards at a time. In fact, it's clear that the type of learning that occurs through this type of work goes much deeper than plugging numbers into formulas and memorizing how to solve specific types of problems. It was clear both in class and from the videos that this type of teaching engages students much more than other methods I've seen. I guess what I'm wondering is how to incorporate this when working in one of many districts that adheres very strictly to a scripted math curriculum.

The Wonder Years

I saw this episode of the Wonder Years the other day and had to laugh. It's the first day of 8th grade and everything is going well...until math class. When I watched this, I laughed at how ridiculous the teaching of math appeared. The episode was set about 50 years ago and I'd like to think we'd come a ways in math education since then. And certainly we have, in many ways. But I have to wonder why it is that math has a reputation for being the class that nobody understands and many students hate. What can we do to change this?