Self-identies, encouragement and failure

I learned that students' opinions of their own math abilities differed from others' opinions of their math abilities. I found this so interesting and helpful to know because it reminds me that students need constant encouragement in the classroom to develop and grow in learning mathematics. 
I was also reminded that students have the right to fail. Teachers deprive them of valuable learning opportunities by not allowing them to fail.
I still wonder how to strike the right balance between letting students fail enough to learn, but not so much that they become discouraged.

Virtual Manipulatives

I really enjoyed using virtual manipulatives at school and it was a great way to reinforce rules of geometry. Once I got the hang of the game, it was fun and  I wanted to keep playing, even when class ended. I realized how educational this could be in my placement where we teach fifth grade math and we just finished a unit on geometric shapes and rules.
We use "Envision" math curriculum and it has many similar games for students to play to learn and reinforce math concepts. We have not played them in class before until yesterday and I have never seen so many hands raised at once for students to come up to the board and show what they know!  It was unbelievable! They could not contain themselves and were out of their seats hoping to be the next one called on, they were talking over each other, etc. They loved it and it was obvious that many of the students play these games at home and I'll bet the rest will be from now on. They were even fighting over who got to go up to the board and show each other how to log on to the website!
Applications for virtual manipulatives in the classroom are endless. When I saw how excited students were to use them, I immediatly thought about how they could help with classroom management. They provide a great incentive for getting students to stay on task and do their work during class time. Teachers could give students a chance to use the computer at the end of class or the end of the week or something like that when they finish their work.
I wonder how, logistically, using math games as incentives for desired behavior could be managed well. I will ponder this and try it out next quarter. I see problems if  only some students (e.g. who were done with their work) got to play the games while others still had to finish work, particularly with the noise level and the distractions created by the players.

Lessons are about concepts, not checklists.

Lesson planning is one of the most challenging and important part of teaching. This week I learned that thinking of a lesson plan as s concept rather than a checklist is a great, simple idea that helps me keep the objective in mind while planning and teaching.

We have spent a great deal of time in school learning how to create lesson plans using specific templates and formats. I think this is helpful to make sure nothing is left out and has given me the tools to think and work through the process of planning lessons. However, upon reflection, I have been presenting lessons as if they were checklists and they lacked excitement and engagement and probably learning. I was so concerned about checking off everything on my lesson plan, that my students' quality learning took a back seat.

Using unit tests to plan lessons from is great for keeping the end in mind and developing a concept. It is helping me simplify planning and I feel this will bring more life into future lessons. I do still wonder though, how to figure out what it is that students of various ages will relate to. One way of figure this out is by watching movies that my students watch and reading their books.

Confidence and Learning

It has been enlightening and comforting to learn about how math and emotions are tied together. I have always liked math and done fine with it in school so it is not something I learned about through personal experience. Well, not exactly. Robin said that whenever she tells people she is a math teacher she gets one of two responses every time. I hadn't noticed that before, but once that seed was planted, I started thinking about it and it is totally true. It is the only (almost, and I will get to that later) subject where people always either like it or dislike it.

I see the importance of finding out how students feel about math when you are trying to figure out how you can help them.  Especially students who seem to have given up. If they have negative, hopeless and incompetent feelings about their ability to succeed, they really are doomed. Lack of confidence is absolutely detrimental to learning. I can relate this to my ongoing and worsening feelings about my ability to succeed in the technical part of this program. The lack of confidence has somehow crept in and I almost think that I will never figure it all out. The problem becomes even bigger when students keep slipping further and further behind. It is this level or type of stress that I believe Robin is talking about when she says students need to have some confidence in order to allow their brains work to learn what is necessary to move forward. They need encouragement and help from their classmates, which seems like quite a challenge for teachers to motivate teenagers to do.

We also discussed the "learning tension" that forces students to think in ways that facilitate real learning. It is a disservice to children to not let them struggle at all. This applies to everything, not just math. They need to have some learning tension, but not so much that the stress turns off their brains to new information. Groupworthy tasks can build confidence in learners. They are difficult and time-consuming to plan. They take a lot of time to do well, but I believe the benefits to students are worth it. 

We discussed several ways to plan and execute groupworthy tasks in math, but I still have questions about how to do this successfully on an ongoing basis with all children

Brains & Patterns

One thing I learned on the first day of class is that our brains automatically try to make sense of things we see by grouping things into patterns.
I still have a question about why this is and why we see different patterns when looking at the same thing. Are there certain types of thinkers (e.g. right/left brain) who view things differently.
The implications for classroom practice for this are that if we knew which types of thinkers/students looked at things in similar ways, we would have a common place to start when teaching.
(Robin, FYI - I posted this blog on the first week of class, Jan 10 then I accidentally deleted it when I was trying to organize my labels on Jan 28, so I just re-posted it today, Jan 30, from a printed copy I saved, KB)

Orchestrating Discussions - 5 Practices

This article helped focus my thinking about teaching mathematics to middle level students. It still seems overwhelming, however, the Five Practices Model provides specific ways for managing whole-class discussions. I am learning the importance of planning every minute of classroom time. Quality lessons must be carefully constructed in advance to make good use of the limited time available for teaching math. Anticipating student responses, monitoring their work, selecting and sequencing particular students' responses to move the lesson forward and connecting this all together is a huge task. I wonder how I will be able to all of this at once. Knowing this is quite different than applying in the classroom. It will take a lot of practice and reflection to bring it all together. I guess that is why it is called the practice of teaching.

Gapminder Website

On January 10, I learned how to use the Gapminder website. I had only seen it used in lessons in biology and geography classes last year. I loved it then and was so excited to see it again and to begin to learn how to use it.

I still have questions about how to use it to show historical population growth and estimations for future population growth in various places. I saw this in a class in the past, but it was shown as sort of pyramid and hourglass shapes that moved over time, but I can't remember if this was on Gapminder or something else.

The implications of Gapminder in classrooms is that since it is visually stimulating, I think students will be easily drawn to it and will be motivated and able to learn how to use it fairly quickly. For me, just watching the colored bubbles bounce around brought many questions to mind and it was fun to find the answers....they kept leading to new questions. Great for inquiry lessons.

Quick Images in Math

I've always loved math, but what is math? There are so many ways that it comes into our lives. I find it challenging to describe my thinking about it in terms of solving problems. Now that I need to relflect on it and its relevance in education, I am beginning to understand how to relate to elementary school math learners. In order to better understand how elementary students think about math, we participated in a few math games in class. It was enlightening to see how ohers think about math. I have been suprised at the differences I have seen in all of our thought processes.
During the "Quick Images" activity in our own class, I discovered new ways and strategies for solving math problems. I agree with math teachers who say that understanding students' approaches to solving problems is key in helping them move forward in understanding math. Learning how to ask the right questions in order to elicit valuable responses from students about their thinking is tricky. It takes practice and reflection. It has been helpful to watch students' for learning new methods come from situations where they need to become more efficient thinkers.When we did Quick Images in our own class , as well as with elementary studends in their classes, I ovserved how the pressure of time has a positive impact on my own and students' problem solving thinking because of the need for efficiency. In Quick Images, we only had three seconds in which to count the number of objects in an image.  This required us to "group" items, rather than count each one to come up with more accurate answers. Necessity, as is often the case, seems to be the mother of invention.