Final Math Post - What Have I Learned?

The most important thing I have learned is that math doesn’t have to be a word that evokes anxiety; it can actually be fun, engaging, and even entertaining.  I will be able to model the excitement I now have for learning math, which will be contagious to my students. 

What makes math fun?  One thing that makes it fun for me is using manipulatives to help with concepts that were only taught to me in the abstract.  Manipulatives do not have to be fancy gadgets; they can be ordinary everyday objects (like colored beans or folding paper).  You can use your whole body as a manipulative (ex. moving yourself up and down a life-size number line), or use good old-fashioned items such as miras.  The most important thing about manipulatives is that using them helps get kids (and adults) to move from the concrete to the abstract.  Setting a solid foundation helps students learn more, more quickly, as well as helping them move on to different types of problems beginning with the abstract.  In addition, students will feel more comfortable pushing themselves further when learning feels fun rather than boring or risky. 

Another way to make math fun is to make it interactive. (Rather than giving students a boring worksheet assignment- they should be given a fun and interactive group learning activity).  As social beings, group work is a natural way to figure out how to solve problems.  Having students take on roles (such as facilitator, etc.) keeps them engaged and accountable for their own learning.  Students need to make sure that everyone at their table understands, and can explain, the material.  This helps them learn how to care for others’ learning, as well as their own.  Also, changing up the projects and rotating their roles, which is important in terms of giving the students different points of entry.

Giving students an interactive math project also allows them to put a little of their own flair into the assignment, making it mean more to them, while helping them understand an abstract concept.  Students who wonder how or why would they need to know a certain math concept in "real life" will benefit by physically doing an activity like this.  Interactive projects also spark students' curiosity and creativity as well as their desire to learn - without making them feel anxious.  Removing the anxiety helps kids feel safe allowing them to take risks with their learning.

Having individuals take turns sharing out and rephrasing what others have shared keeps them invested in, and accountable for, their own learning.  Having students make sure that everyone at their table understands and can explain the material keeps them accountable for others’ learning. 

When planning group activities it is important to help your students see how and why the assignments are connected to real life, and why they need to be able to understand the concepts, etc.  Connecting the assignments and activities to things that matter to the students gets them interested in solving the problem and keeps them engaged in the activity as well.  

The last thing I would like to mention in regards to what I will take away from this class- is that a new teacher should not expect herself to have the all the wisdom of a seasoned teacher, and that she should focus on improving her instruction by 10% each year.  I plan on doing that!  I have really enjoyed this class.  I think I would have taken higher-level math classes if math had been taught to me in this manner.  Thank you for opening my eyes to the endless possibilities of teaching math in fun and interactive ways.

It All Comes Down to Knowing Your Students

What did I learn and what are the implications for classroom practice?

This week I learned another reason why it is so important to get to know your students - and - why group work is such a beneficial "tool" for teachers and students alike.  I was introduced to Wolfram Alpha, which is an answer engine (rather than a search engine), that students can use to find answers to math problems (and just about everything else!).  Wolfram also displays the work involved to solve the problems.  Students who are using the engine simply to copy down the answers (and the steps involved), aren't "learning" HOW to solve the problems.   In this instance, an answer engine would be working against what a teacher is trying to do.  However, if a student is using the engine to study how the problem is solved in order to LEARN how to do it on their own, then the answer engine would be a positive learning tool.  Can we tell without an assessment which student is which?   If we know our students well, we should be able to have a pretty accurate educated guess.    

Why is this a concern?  Because more and more students have possession of technology with them in class capable of using answer engines, such as Wolfram Alpha.  Since we will not know whether a student is using it to copy down answers or to learn how to solve the problems on their own, group work (designed like Robin's) rather than having students do worksheets with multiple problems - avoids the temptation/possibility for students to copy answers, and encourages all students to be engaged and "forces" all students to understand WHAT is being learned during the process.  (I do not think that technology in the classroom is a negative tool - it all depends on how and why it is being used.  Many teachers are creating powerful lessons using technology in the classroom!).

I also learned, partly from my own personal experience in class, that it is very important to assess your students before beginning a new unit.  Knowing where they are at now will help in planning your unit, and all the lessons that go into it. The first lesson you plan may need to include review of (or introduce new material) to some students. This can be done in a group project when you know where your students are at. 

My question is, how do we continue forward with the move toward using technology in the classroom (when appropriate) when there are so many students who do not have the access to the devices?  And when some schools (and districts) are in the same boat?

Math is Scary?

1.  What did I learn?

This week I learned that math (and math tools) aren't scary just because there are a lot of numbers (or buttons, or gadgets) involved.  I learned that you can show kids that math can take them to INFINITY and BEYOND!  Math can be.... COOL.

I never had to use a graphing calculator.  I was one of those high school students who only took the math classes required for graduation, period.  Just the thought of having to learn about something I heard other kids say was hard was enough to keep me from signing up for the class.  Where was the teacher in her special jumper standing on tables and animating toys when I was in high school?  I bet if kids talked about stuff like that I would have more intrigued and less anxious... I may have even signed up for the class, who knows?

2.  What do I have questions about?

How would I teach students about graphing calculators when I know nothing about them?  I guess the better question is, when will I have time to LEARN all there is to know about them before I have to teach students how to use one.  Honestly, that is one of the reasons I have decided to teach K-5...

3.  What are the implications for classroom practice?

I can see how using a tool, like the graphing calculator, in the way that was presented for us in class, can spark students' curiosity, creativity as well as their desire to learn.  All without making them feel anxious.  Removing the anxiety, and helping kids feel safe will allow them to take risks with their learning.  What a great way to get students actively involved in their learning.

Spit Wads in the Classroom?

1. What did I learn? 

This week I learned how to turn spit wads into a constructive learning activity.  We learned how to turn what could have a boring worksheet assignment into a fun and interactive group learning activity.  One of my group members turned her cotton ball "frog" into a nicely weighted flying machine using her very own spit- how's that for ingenuity and creativity?  Giving students an interactive math project allows them to put a little of their own flair into the assignment, making it mean more to them, while helping them understand an abstract concept.  Students who wonder how or why would they would ever need to know a certain math concept in "real life" will benefit by physically doing an activity like this.  

I also learned about how to use tangrams to give students additional points of entry.  Although everyone at my table had trouble figuring out how to make the giraffe until it was done for us under the doc cam, we did feel successful when we figured out how to make a giraffe that was twice the size of the first one.  It was fun to learn with my group members.  We did a great job listening to each other, and solving the problem together.

2. What do I have questions about? 

I wonder how long it will take me to be creative and comfortable enough to incorporate interactive learning projects into my classroom.

3. What are the implications for classroom practice?

Students will be able to use the information they have gained from doing these types of projects/activities by applying them to abstract concepts and understanding how math is used in their everyday lives.  All students benefit from activities like this for the reasons stated above, and because different points of entry are offered for the students who need them.  (I think all students benefit in one way or another when exposed to many points of entry - you can never tell what will spark a students love for learning - or when a certain concept idea will "click" with a student).  

We have learned that students won't take risks with their learning if they do not feel safe.  I think the group projects and activities that we have been exposed to allow students to take risk with their learning in a safe and fun environment.  Students will feel more comfortable pushing themselves further when learning feels fun rather than boring or risky.   

Week Four

1.  What did I learn?

I learned how much fun geometry can be.  Learning something (geometry terms, etc.), while creating something (the box), was fun for me.  However, the assignment we did made me realize just how much review I am going to need before I start teaching.  I couldn't remember what congruent meant, and I couldn't prove/justify why or how I knew my line segments were parallel, etc.  I need some serious vocabulary refresher courses!

2.  What do I have questions about?

How can I bring fun and interesting things into my teaching, when I am not very creative and haven't learned many tips yet?  I do not want to wait three years to "improve" my lessons, especially in math.  

How could I transform the lesson we did in class to a group lesson?  I would love to learn more about doing that.  (I just ordered Designing Groupwork), so maybe that will help:)

3.  What are the implications for classroom practice?

I can see how having students explain their "proofs' out loud can help others learn.  I had a hard time following what my cohort members were saying, but I think part of that was due to my struggle in recalling geometry terminology- and because I am couldn't see what they were referring to/doing.  If students are currently learning the concepts/vocabulary etc., I think it would be pretty easy for them to follow along.  I know that kids are very good at describing things in a way that their peers can understand them, so I think exercises like this can be very beneficial for all students - but especially those who may not "get it" from reading straight out of their math book.  The more they learn, the more confidence they will have to attempt risks in their learning.  I like that!

MIras!

1.  What did I learn?

Today I learned the value of making something old new again.  I learned that a new teacher should not expect herself to have the all the wisdom of a seasoned teacher, and that she should focus on improving her instruction by 10% each year - keeping herself sane, while fixing the world 10% at a time! 

I learned why we should have kids take a close look at graphs, etc. when we have them make their own. Funny how we thought our graph was "finished" and that the information was on the poster was "perfectly clear"... It was because we had researched all the data and we knew what our poster was representing, but didn't necessarily come across that way to those who had not seen the research.  We need to make sure our students understand that piece of the puzzle.

I learned how much I enjoy playing with miras - what closet where they in when I was in school?  Pencil and paper was all I had....

I learned how to put math symbols into a Word document on a PC.  How cool is that?  I have been Googling the symbols I needed and copying and pasting them into the document!

2.  What do I have questions about?

Where are the math symbols located on my mac? 

3.  What are the implications for classroom practice?

Regarding the graphs, etc. our students will have a more solid foundation processing data and problem solving when they are taught how to look at data from the perspective of someone who needs to understand the graph, without having seen the data.  

Connecting assignments/activities to things that matter to the students gets them interested in solving the problem and keeps them engaged in the activity as well.  

Algebra Manipulatives

1.  What did I learn?

I learned how algebra manipulatives can be FUN!  Before Mondays class I couldn't picture how manipulatives could be used with abstract concepts like algebra.  I remember learning how to memorize the steps involved with algebra. Last year I tried helping my daughter learn how to use the FOIL method.  She was very confused and had trouble doing the problems without my help.  I have a feeling that the manipulatives would have made more sense to her - and would have saved both a few headaches.

I also learned how to use colored beans to help kids grasp the concept of adding and subtracting negative and positive numbers.  I also learned how using a life size number line helps kids see what is happening, making more sense to them than just doing the problems on paper.

2.  What do I have questions about?  

I would like to know more about how and when to introduce which types of problems to students (abstract first vs. concrete first).  If you know a particular student learns best in the "concrete,"  why wouldn't you always use that as a starting point for him/her?

3.  What are the implications for classroom practice?

I can see a lot more students "getting it" when being able to use manipulatives in addition to other forms of problem solving.  I loved the algebra tiles and would have loved to spend more time working with them - doing different types of problems because I think I (and students in general) would have a much easier time grasping what what is "happening" within the problem while manipulating the tiles/beans.  I think that students would benefit from using manipulatives in many ways.  Students would be able to have additional ways of looking at, and solving, problems (more entry points).  I also think physically moving the manipulatives around help us (our brains) move the information over from the concrete to the abstract - making a huge difference in what teachers are able to do within the classroom (students would learn more, more quickly, and would be able to move on to different types of problems beginning with the abstract as they would already have the foundation set for those types of problems, etc).

Week # 1

1.  What did I learn?

I learned that it is very important to have students share their thinking with one another.  Shared thinking gives students the opportunity to share what they know (teach) to other students.  Explaining their thinking to other students will help them solidify the process in their own minds as well - they will be learning as they teach others.  Students also need to be paying attention to their classmates and be able to rephrase what they hear - which makes them accountable for their own learning.  Students need to make sure that everyone at their table understands, and can explain, the material.  They are in a sense, learning how to care for others.

2.  What do I have questions about?

What would the cons be to using co-operative games?

3.  What are the implications for classroom practice?

Providing students with the opportunity to voice their own way of thinking/strategizing puts them in control of their learning.  Knowing that they are helping to lead the discussion makes them pay closer attention to what is going on, so they are more accountable, confident, and invested in their own learning and their classmates as well.