Final Math Post

As I reflect on the quarter, both in my brain and in my blog, a few points jump out at me.

1.  Importance of student-led learning - we read articles about never saying anything a kid can say, about allowing students to participate in group-worthy tasks, etc.  A big idea for me as I go forward is to think about how I can incorporate more math talk and student conferencing in my teaching.
2. Manipulatives/software - I learned about tons of new manipulative and software tools: GeoSketch, Fathom, TinkerPlots, Wolframalpha, tangrams, miras, Gapminder, just to name a few.  Definitely more aware of some great resources for teaching math.
3. Trusting myself to take what I've learned and grow from it - some of my favorite lessons have been the ones that included a bit of a philosophy lecture.  It's nice to know that we won't be expected to be able to magically incorporate all of these tools at once.  I was reminded of the importance to take the time to breathe and think about how to incorporate one thing at a time.  
4. Thinking about myself and my own mathematical identity - I realized this quarter that I know much more math than I gave myself credit for.  I constrained my math thinking to a narrow focus, but our work has helped me broaden my thinking.  As I move forward, I will work to keep an open mind about my students' mathematical thinking and work to help them see themselves as mathematicians.

Thanks for a great quarter, Robin!

Lesson Planning Rules to Live By

Today in math I learned about TinkerPlot, an elementary level program similar to Fathom.  The short intro video we watched got me quite interested in thinking about how powerful manipulating data could be for students.  Still, the big takeaway for me today was the reiteration of the importance of the 4 main areas of lesson planning: 1) What do your students know? 2)What do you want them to know? 3) How will you get them there? 4) Did you get them there?  If not, how can you rework your lesson and try again?

As I move forward with my student teaching quarter and beyond, it will be important for me to remember that these 4 questions drive every lesson I plan, regardless of the format.  Also, our discussion about knowing our students today made me think back to Ayers and his argument that curriculum must be relevant to the students for it to be meaningful to them.  Another area of my teaching that I will pay particular attention to is making sure that my students see themselves reflected in the curriculum.

GeoSketch & Fathom

I enjoyed using the math software today.  I particularly liked the exercise where we had to use the shapes to cover the other shapes in the face.  It was also interesting to analyze teacher pay back in 1985.  I learned that Alaska is the highest paying state - who knew?

Still questioning the relevance to us.  I know we are getting a K-8 certificate, but this software seems quite advanced for elementary school.  I love learning about the software and knowing it's out there.  I just hope that I have the chance to use it again someday.

Implications - as digital manipulatives are just as helpful to students as tangible manipulatives, I need to think of ways to integrate more digital math technology into my teaching. Speaking of, I recently learned how to access math flip charts for the ActivBoard and hope to try it out during my lesson this week!

As we talked about the defining characteristics of teachers who make a difference, I was reminded of a favorite quote of mine: "I've learned that people will forget what you said, people will forget what you did, but people will never forget how you made them feel." - Maya Angelou

Jumping Frogs, Tangrams, & Math - Oh my!

I appreciate all the time in our math class that is dedicated to us exploring manipulatives that we could potentially introduce into our future classrooms.  I learned that I am not so good with tangrams, but I already knew that my spatial reasoning ability wasn't the strongest.  However, it was nice to double the giraffe as a group because I felt more confident trying to solve the puzzle, knowing that my group members were supporting me.

I am still wondering about applying all this stuff to elementary grades.  I understand that this is a middle level math class, but the majority of the people taking it won't be teaching middle school math - we'll be teaching elementary school.  How applicable are some of these manipulatives to younger students?

I plan on thinking about grouping students more carefully after our discussion on the math/lit article.  I liked hearing different takes on the article, particularly the idea about grouping students together that allows each of them to shine by showcasing their ability within the group.

Geometry? I got that!

Wow, another week has gone by already.  Eek!

I really enjoyed the activity we did today folding the paper over and over into various shapes before building a paper box.  1) My husband was impressed with the pretty purple paper box I presented him (say that 5 times fast!), and 2) I realized that I know a lot more geometry then I give myself credit for.  Going through and explaining how I knew a shape was a shape was a powerful experience. I feel that we're moving so fast these days that it's easy to say, "Well, it's a square because that's what it is."  It was refreshing to slow down a bit and actually think about the properties of what made it a square.  I also appreciated the piece about immersing yourself in the content you are teaching - the more knowledgeable you are, the more you are able to help your students.

Questions - What format are we using for our lesson plan?  Is there a specific format?  Are we borrowing from several formats? I am confused.

I'd like to take forward my experience of talking through my knowledge.  My ability to talk through my thinking and validate how I knew a square was a square demonstrated my understanding of the properties of a square.  When I allow my students to explain their thinking, I can assess their understanding, and they can reinforcement or clarify their understanding.

I also plan to spend more time learning about the curriculum I am teaching.  I was reminded of a conversation I recently had with my MT.  We've been working through a unit on nonfiction with our first graders.  Other educators believe that the work they've been doing is a bit much for first graders to handle.  I will admit to being one of those people before seeing this unit taught.  I have been continually impressed by both my MT and our students.  One of the key components of nonfiction text is the ability to give our students background knowledge.  Reading nonfiction text helps them as they continue to grow in their personal and academic lives (particularly in social studies and science).  Without background knowledge, much of the learning can be empty.  As teachers, we need background knowledge.

Today, in math class....

As a proud Longhorn, I have heard UT's slogan "What Starts Here Changes the World" many, many times.  Today, I learned that it will be a few more years.  First year teachers don't change the world.  They just try to survive so that one day, they can.

I am still skeptical about group work.  I recognize its benefits, but as someone who grew up loathing group work, I have my reservations.  I was always the person that ended up doing everything because I couldn't trust other people to pull through.  Granted, some of that was my fault for being willing to pull up the slack, but even now, I would probably choose to do an individual assignment over a group assignment if given the choice.

Implications...I need to be brave and try on some group work.  I work with small groups in my placement, but it is not necessarily group work (the students are not working together to solve a task).  Gotta push myself out of that comfort zone and see what can happen.

Concrete Examples

I learned about the importance of giving students concrete math examples.  It was interesting to think about the fact that math is taught from abstract to concrete, instead of the other way around.  Almost all other subjects are approached in this manner.  What a powerful point.  I plan to do more reflecting on introducing concreteness into my math lessons.

I am still wondering about the comment, "Subtraction is just addition in the opposite direction."  I understand the concept, but I think it might be difficult for kids to grasp.  They may realize they just go the other way on a number line, but I would probably argue that they aren't truly understanding what subtraction is.  I am also wondering about the process for bringing multiple strategies into a classroom. How do you determine which strategies to use?  How many do you introduce?  Which ones?  Why?

I feel that our work with manipulatives today translates directly into use of manipulatives in the classroom.  As I previously mentioned, I'm doing a lot of thinking around integrating concrete examples in my math lessons.  Knowing which manipulatives to use and how to use them to give children concrete experiences is key for an educator.  Guess I'd better start brushing up!

Border Tasks & Sneaky Snakes

First day back and straight into puzzling out complicated math problems.

I re-learned how wonderful it feels to finally make sense of a problem.  I understood the pattern with Sneaky Snakes, but struggled to create a rule.  When I finally saw the 1x3, 2x4, 3x5, etc. grids in the snake, there was an excitement as I saw a pattern that I could use to move forward with creating my rule.  I'm 24 years old, have two Bachelor degrees, have taken advanced calculus, and still got very excited over seeing a pattern!

I am still a bit apprehensive about the whole calling on people with cards idea.  I think it is imperative to mix us up because we do tend to gravitate to our same tables (I personally have a designated space & chair).  However, I feel a sick sense of dread as I wait for a card to be picked.  I am completely capable of sharing my thinking, and often do voluntarily, but the card thing is hard for me right now.  I did appreciate that people called up were willing to share their thinking and did not feel the need to necessarily "have the right answer."

I am reminded of the need to share the moments of accomplishment with my students more.  As they "see a pattern" and feel that sense of "Wow, I did it!," I need to take a second to revel in that with them.  They are making sense of their world and enriching the learning environment in our classroom.  These feelings help drive motivation and are an integral piece to the learning process.