Final Math Blog

Throughout this quarter I’ve been given a very unique and inspiring view on teaching and mathematics. The inspiration is continually growing. The tools you’ve given us are things and ideas we can apply in any subject while teaching. You’ve shown us ways to continue growth in ourselves and our students. These are incredibly valuable skills. I aspire to always be learning and as a teacher, I believe that’s something we must always be willing and seeking to do. Throughout the quarter I’ve been learning tools for myself and my future students.

Ideas and thoughts that I’m taking away are:

I’m thankful for the more emphasis and ideas about creating opportunities for integrated learning, specifically creating opportunities for connecting abstract concepts with practical application. I love the idea of having multistep problems that benefit the cohesive understanding of math concepts.

 

The missing and lack of use of manipulatives in the classroom has definitely stayed on my mind. I’m brainstorming how I can bring manipulatives into the class to strengthen the concrete understandings my students will have of mathematics. They deepen and strengthen my own understanding; I know they will help my students too. 

The need for alternative explanations is great! We as teachers need to be searching for ways to help students understand things in any way that we can. It is our responsibility to learn to teach other ways. It is a goal of mine to immerse myself in as much math as possible and in all different ways, even the forgotten ways such as the Mira!

I am experimenting planning my lessons backwards in creative ways. I’m still thinking about what I want them to learn and how I am going to get them there. How can we do this and use confidence as a motivator in math? We need to have “open ended work that can be assessed in different ways and taken in different directions.” We can do this in multiple ways, one way is by embracing and utilizing integrated lessons to build up students’ strengths and let it transfer over to math.  This even lets us get a whole different way to assess our students. It can be more cohesive for us and our students if we bring writing into math, or any other way of bringing other subjects to show students strengths.

Technology lets us access both math and education in a totally new and dynamic ways. I’m looking forward to finding electronic manipulatives with both the computer, applications and any other ways I can find for my students.  This is another tool to help create interest for our students.

Overall creating interest and confidence in our students is at the upmost importance and should be what governs our decisions so we are always making the best decisions for our students.

It doesn't hurt to ask...

Today, in math we learned...so many things...but what's sticking in my mind is how important it is to know what you need and want for your classroom. Just as important, know how you might use it in the classroom, and why it would make you a better teacher/ help students learn. If you don't ask for the things that will help your career and help students, then how on earth are you going to get them?? You have to ask! And if they say no...No big deal! At least you can reroute and know how to ask again later if needed or if you get the opportunity.


I need to apply this element of preparedness into my life, into my career, into my classroom, because I want to be prepared to help my students and colleagues. Really, it's just a part of being prepared...prepared with ways to grow, learn, and teach. I need to apply this by quite literally having a list of the things I could use and need. So I will be making my list...both in  my mind and physically on a handy piece of paper...My need list!

I'm still wondering how to do we create interest in math? Some students find relevance in school or subjects very easily compared to others. How can we help students find interest to do the work and to do it well?
 For that matter, how do we encourage a passion for education that will continue throughout their lives so they can use it to create opportunities in life?
Yeah..lots of questions..that's just how I think.

Acorns take a long time to grow...

Thank you for the acorns today. I do love those trees...but man do they grow slowly!

I'm thinking about the many ways we learned to be active and interactive while teaching math. Today was full of wonderful tips, ideas, inspiration! I'm letting it all setting in and looking forward to how these ideas will grow with me and become a rooted part of my teaching.

The manipulatives that we worked with today were helpful in numerous ways. The geometric shapes we were interacting with helped me in numerous ways. Being able to understand which shapes and rules apply to each other and can or cannot change in various ways, deepened my understanding of geometry. It helped my technology skills working! That's interdisciplinary (at least for me ;)!

Using the program and interaction with shapes on the "Can you make it" program helps build technology skills AND mathematics; it could be use with students of various ages. I work with second graders and I could see them benefiting from the interaction of these virtual manipulatives. It not only will sharpen their understanding of the quadrilaterals, or other shapes, but it helped them use their motor skills and technology skills at the same time. Sounds like a great way to keep kids of all ages (even in college) interacting with technology and math of all shapes, sizes, and styles....

I'm still wondering about...  How on earth did you get that "Buzz Light Year" to show you exactly the motion and   bounce that you wanted to demonstrate!! That is some serious corduroy, jumper, teacher skill!!

Tangram! Just make a square...how hard can it be?

Today I learned a new way of using writing in math as a method of interdisciplinary instruction and as a tool to better understand mathematics. In our discussion about creative writing in mathematics, my mind was opened to endless opportunities of mathematical writing. (This discussion  was based off the fun and enlightening article we read, Using Creative Writing and Literature in Mathematics Classes). This interdisciplinary idea is using math as a tool in so many different ways: creativity, assessment in their understanding of mathematical concepts, expression, etc. This isn't a way to assess grammar and fluency, this is a way to understand the mathematical ideas and concepts that they are grasping and/or struggling with.

This would be so great to use in the classroom. It opens the door for students who struggle in math. They are able to use their writing, drawing, and/or story telling skills to express themselves in math in a better way. They no longer have to feel as if they are not "good at anything" in math. Their "strengths" in other  subjects will let them do well in math too. It could help them feel more confident and secure with their work in math. Because after all, math is connected to everything else right? Well lets show the students how, and maybe ourselves! This is useful to both the teacher and the students! Beautiful!

I am still wondering if this lesson can be used often in our "scheduled curriculum" that I'm being more immersed in? I'm picturing teachers struggling with implementing this, because it is a little more time consuming than just asking a student questions via worksheet to find out what they know about concepts and ideas etc. But it is such a valuable resource, isn't it worth the time for both us and our students? If we (as teachers) only resort to the worksheet questions for evaluating how are students understand the material, then we will miss so much that they have to offer. They have much more to offer us in their understanding if we expect them to express it, and if creative writing is the way to get them there, then let's do it! Plus it's fun, refreshing, and supportive of their varying strengths! So how can we get more teachers to take the time to use this lovely interdisciplinary lesson?

Also, I'm still wondering if I'll EVER solve a Tangram puzzle on my own!!!??? It's been slowly eating at my ego my whole life! 

Learning to be prepared...is it possible?

Today I learned, to be much more specific with my objectives. I had it drilled into my head again, that they HAVE TO BE MEASURABLE! Indeed...this is why I love math; I can learn how to measure things, even objectives!! Okay seriously, ensuring that the concepts and ideas that are taught, are done so in a measurable way. I'm thinking more concretely...which is good, because I like having my feet on the ground...preferably grass but I'll settle with concrete.
Anyway, I also learned the more math I can immerse myself in the better prepared I will be for my students. I have to have the experience that will enable me to be able to teach math better to students. It is my responsibility to be prepared to offer students different ways solving and understanding problems.
My favorite take away message, is to start with the end in mind! Plan our lessons backwards.

I'm still wondering, about the idea of modeling. Well, when we model we have to be sure to model how to handle failure, struggle, and humility. More on this to come after some heavy percolation...
Confidence is the most intrinsic motivation for math. How do I use this as  a tool and/or power to help them learn, enjoy, and do well in math?

To use these ideas in the classroom...in order to establish confidence and interest in math.... (and this is another favorite quote and thought from today)...use "Open ended work that can be assessed in different ways and taken in different directions...." I'm learning more about this every week. Heck! Every day!

Good timing on the "pep talk"  we have all been being burnt out and beat up with the massive lesson plans and observations....You give us a realistic balance to be "prepared" for teaching. 

Gap Find the Mira

In math I learned and found fun ways to do lessons and activities with the ultimate graphing resource Gapminder. As I've said before, this tool has endless possibilities with students of various ages! And it's pretty fun to just play with for kicks. I really enjoyed the gallery walk...specifically I thought it was unique that we got to leave questions and comments on the graphs and posters. Thinking about how others organized their data forced us all out of our comfort zones. When I came back to my own graph and poster, I loved seeing the comments that everyone left for us. I had to think of alternative ways to represent my data, findings, and conclusion. This can be hard as a teacher..presenting students with alternative explanations of material...

I'm still pondering the Mira that we got to experiment with during class. It was such a simple device...with manipulatives like that it makes me wonder if we really need the virtual manipulatives on my ITouch...Then I play with the fancy apps and ponder the seemingly endless opportunities it brings.
How can we use the Mira in other ways than just for Congruence?
In my school we have a very specific math curriculum, how can I fit these creative math activities into the curriculum? Am I allowed to venture into my own ideas?

I can picture classrooms using the Mira to work with patterns, especially when the patterns are geometric. Patterns are accessible for all ages...I can still remember working with patterns in the second grade. If I'd have a Mira to work with I would have been able to make and understand complex geometric patterns even at such a young age.

Man-Manip-Manipulate!

Today we spent our day working through math problems using different manipulates. At first, I, like many, was reluctant to see how they could possibly strength my understanding of math facts and rules, on problems that I have long since "mastered"...or so I thought.

By using the various beans and algebraic blocks I was able to represent my thinking in a way that thoroughly strengthened my understanding AND my ability to teach or explain the idea to others. However, I will not try to explain these mathematical concepts in the same way I learned them long ago...No no no, what purely simple strategy to keep with math... to start with concrete examples and explanations THEN move to the abstract ideas, concepts, theories, and rules that math is so full of. The over used expression, "But where will I ever use this rule?" does not hold the same power as before...Still yes, I'll give it to us all...I'm not sure where the heck you'd be forced to use a quadratic equation...but now I can at least show you with real objects what exactly it is and/or what it at least represents. Awwww it feels good to have a picture for it...not just a rule.


I used to accept that math was full of rules, facts, and theories that you simply follow, just because...they are what they are...you are either right or wrong. In fact I used to like it for that reason... I loved that it was like a book of rules that I could follow...but I found myself at dead ends when I couldn't grasp concepts fully in calculus. Instead, I just plugged and chugged along...jumping through the hoops, thinking it would eventually make sense. With the understanding of math that I'm growing now, I look back shocked that I used to like thinking math were that way. My growing understandings of math are now seemingly endless, and I look forward to the knew ways of thinking that I will learn from other teachers, students, and people! Seeing different solutions as equals and learning from them all to strengthen my own tools to solve.


...So in all...
I learned to use manipulatives for quadratic and algebraic expressions!
This a great tool to use in class when teaching students math in a concrete to abstract method.
I'm wondering how to dig concrete examples deeper with higher level math. I won't be teaching higher level math but just out of wonder....how do manipulatives connect to calculus?
How do uphold our expectations of participation in class, but move onto another student if one student is struggling with an answer??

Inquiry

Today in math I learned that it can take a lot of warm up to get back into the groove of things... this does not just for running, but for math thought processes and inquiry.
Of course I always "knew" this, but today I truly felt this. It was the first day back from winter break and my first time trying to complex and layered solve quadratic problems and sequences in ... longer than I can remember.

I am still looking forward to finding out other ways that people think and how some people are so much quicker at recognizing math problems than others. Practice? Maybe.
Using the complex problems like we did today with the Gardens and Snakes, we covered a lot of standards...all seemingly in "one" problem. This was exciting. The many steps of the problem were rewarding at the end. What other ways can we use overlapping problems like this in our younger classrooms? How much stamina will the students have to do this and how far do I push them? Indeed that will be different for each class, but these thoughts are floating around in my mind.

I think it's exciting to use such an overlapping problem or scenario to get all standards connected and used. It makes me and the students see that the requirements we have to learn in math are not random and separate but useful and connected to each other.

It was fun to reflect on my own thinking processes through these math snakes and gardens!