Quarter Wrap-Up

This quarter has taught me a lot about not only how to solve math but also how to approach math as a teacher. Math has always been one of my strengths and there were a few times this quarter where I found  the material challenging and new. I have taken my fair share of math classes and found this one unique in that it often pushed for further thinking and deeper understanding. I now realize that it is so important for students to not only understand how to complete math work, but also have strong number sense as well. Throughout this quarter, my own understanding of numbers and systems was questioned and I was having to think about the 'whys and hows' a lot more than I ever have had to before, especially regarding math.

One activity that really challenged me was the activity where we were asked to draw a line segment on a sheet of paper and then find a parallel line, perpendicular line, and a square where a side was the line. Although I know all of the vocabulary that was used in the activity and have a good understanding of how to create an accurate square, I found myself stumped on this one. What I realized from this activity, and other ones that made me think deeper, was that teaching math and learning math isn't about getting the right answer. It is more about process and understanding the concepts and characteristics of math elements. I have always been confident in math because I have been confident in my ability to get the right answer, and this class pushed me to think more about math in a larger context.

This is an area of math that seems to be lacking in schools. It is not secret that timed tests and 100 problem-ed worksheets are the norm for math curriculum. The videos we watched and reflected on gave me hope that math can be taught in an exciting way and the students can come out with not only confidence in the ability to get the right answer (like me) but also have a complete sense of what numbers are and how they relate to everything else.

Teaching Versus Exploring

This week in math class we discussed a number of things. One of which was about identifying a shape based on given information. As a group, we completed a worksheet that gave the following clues:

• It is a closed figure with four straight sides.

• One of its angles measures 45degrees.

• One of its angles measures 135degrees.

• Another angle measures 45degrees.

• Another angel measures 135degrees.

• Two of its sides are parallel.

• Its other two sides are parallel.

• All of its sides have the same length.

• Its diagonals bisect each other.

• Its diagonals are perpendicular.

And then we were asked: What is the shape?

This was a great activity in that it forced students to think about the elements of shapes and how they affect the way the shape looks. While I was completing this activity, I found myself guessing a number of different shapes and then seeing if they fit the criteria. I see this activity as a great way to get the students to look at, not only the shape that is represented, but other shapes and their elements as well. Another thing that we briefly discussed in class was the website wolframalpha.com. This is a website where the user inputs an equation or question and is given the answer. Along with the solution, work is shown and terms are defined. I found this to be a great tool and can see it being a great way to provide parents a resource that can be helpful in working with their students. While some teachers would argue that you want to make students get the answers, the reality is that this is not always possible after leaving the classroom, even after a well taught lesson. For whatever reason, students go home and forget how to properly complete math, another reality is that many students are either above their parent’s ability in math or being taught in a different way than their parents were taught. This website allows students to go online and get help with their math homework. If a student is able to clarify simple questions, they will be better prepared for completing their whole assignment.

One conversation that was brought up in class, that left me thinking, was about teaching students versus allowing students to explore. There were a number of people from class who felt like they would have been more successful with the worksheet had they been taught more background knowledge. However, I feel strongly about allowing students an opportunity to discover their own knowledge. I have found that when students can take ownership of new knowledge they become more likely to apply it to other areas of learning and exploring. After thinking about this more I have decided that it seems most logical to teach both ways. There seems to be some lessons where exploration could be really powerful and other lessons where it seems crucial to provide background information and key terms/ideas. My question then becomes: is one way of teaching more valuable, or is my assumption, that it depends, correct?

Geometry Sketch Pad & Fathom

In math this week we spent a little bit of time in the computer lab as well as in the classroom. In the computer lab, we worked on two different programs. The first program was called geometry sketch pad and dealt with geometric shapes. This was a great tool in terms of looking at the properties of different shapes and recognizing how these shapes can be moved in different directions and still hold true to their properties. The task we were given was to copy a picture by adjusting a number of different shapes. Although I am usually fairly comfortable with math, this activity made me a bit uncomfortable. I was having trouble seeing each shape as its individual properties rather than all of them together as a whole picture. Another program that we explored was fathom. This program dealt with creating graphs and charts of information. One really fascinating thing this program did was collected data from a website and put it into an easy to read chart.

In a future classroom, I could see myself using both of these programs. I would use the sketch pad if I was teaching higher level math. The way we used this program was very effective in allowing me to see how shapes can remain the same shape but appear very different than how they may normally be shown. This program also has many chances for differentiated instruction. I am looking forward to exploring it more and finding more useful ways to incorporate it into my future classes. As far as the fathom program, I could see this being a huge resource in teaching tables, graphs, charts, and almost anything else that has to do with data. I could also see myself using this program in the lower level classes to make charts and graphs that I can provide to the students.

Overall, this week in math provided me with a glimpse into the computer world of math. My only question is, now what? Where are we going to go in the computer/math world from here. It seems like just when you think they have thought of everything, something else cooler and more helpful is developed. I cannot image what will be next!

Healthy Competition as a Motivator

As the quarter is moving forward, I am finding myself becoming more comfortable and excited about teaching upper level math. After class, I found myself thinking a lot about making math fun for upper level math students. Although I have a lot of passion for teaching and learning math, I am also aware that many students do not share my enthusiasm. Finding ways to get students excited about math is essential to their appreciation and overall success. Something that we did this week, that proved to be a good motivator for me this week was adding a little competition aspect. When we were asked to make the giraffe out of the tiles. When our teacher made the comment "lets see who can figure it out first" I became completely engaged in the activity and was excited and eager to complete the task.

 With the inclusion of competition, my question becomes how does a teacher include competition into the class but does not do so at the cost of any lower level students. For me, the competition aspect helped me become more engaged, but was this only because I knew I was capable of “winning”? I would hate to include an element into my teaching of math that could cause some students to retract more than they may already.

Including competition into my teaching will be something I am going to think about and explore more. While I can see so many benefits, I am also aware of the costs. One other thing that I took away from this weeks math lesson was the idea of uniting reading, writing, and math into one interdisciplinary lesson. This is another sticky situation where students can get a boost in their confidence in math from their strengths in reading and writing, or their math can be negatively affected due to difficulties in reading and writing. It is obvious that there are way to many things for one new teacher to know, I am going to have to rely on my peers for ideas about both including competition and teaching math in conjunction with reading and writing.

Physically Teaching Math

This week in math, we did a number of things including a paper folding activity that had us looking at and talking about shapes and we also began developing our group, interdisciplinary lesson plan. Our instructor had us draw a line segment on a piece of paper and then asked us to make geometrical comparisons and shapes using the segment we drew. First we had to fold a line perpendicular to our segment and then one parallel. Then we had to make a square where our line segment was one of its sides. The second activity we did, involved simply folding and discussing the shapes we were making. The end product of the folding activity was a box. This week made me think about how important it is to physically display geometry. This is a subject that seems to be a challenge to most students. The activities we did this week proved that geometry can be easily simplified by having the students make physical displays of the information.

One question that came to mind this week was about interdisciplinary lessons and how math plays a role in this. My question is how much math needs to be present in a lesson for it to be considered a math lesson? While looking online for a lesson plan to use for our group interdisciplinary lesson, I found that many lessons that claim to have a math element simply have a number element. Some of the lessons I found look at numbers but do not actually have the students do any sort of mathematical computing with the numbers. Is this really considered an integrated math lesson? It seems to me that a lesson should have some sort of computing or analyzing element to be considered a math lesson.

Overall, this week taught me about the importance of physically teaching math (especially geometry) and made me think about how to incorporate math into other subjects and areas of interest to my students. The box activity was a great way to teach us about shapes while also getting us excited about creating an actual project. I could see this being a great activity in the classroom. Getting students excited about learning is an easy way to get them to buy into the task at hand and the learning that goes along with that.

Virtually Manipulating

It is amazing how many wonderful tools there are for teaching math, and a bit pathetic how much teachers dismiss them from their instruction. I have not only complete my own schooling in math, but I have also helped out with and observed many other math classes and tutoring sessions. It continues to baffle me, all of the great tools and manipulative that would make learning math so much more accessible for students. This week, in class, we worked with a mira. This is a plastic square that is used to reflect lines of symmetry. I have witnessed many students, and also myself, struggle through geometry, reflections, and lines of symmetry. This tool could have come in handy in these situations. The mira makes it easy to see what is actually happening, versus simply learning the line of symmetry rule. This week we also looked at gapminder.com. This is an amazing website that allows students to look at math through an interdisciplinary lens. Getting students to look at math with a different mindset allows the students to experience real life application.

One question that arose for me this week was in regards to equally sharing virtual manipulatives, when they are not accessible to every student at the same time. In my main placement, there are only 5 student computers with limited space around each one. I have talked with the teacher about how she evenly splits up computer usage between all students in a fair way. After having played around with the manipulatives, I realize that each student can gain something important from this tool. However, it is obvious that some students require more differentiated instruction and benefit more from virtual manipulatives. My question becomes, how does a teacher prioritize who gets to use virtual math manipulatives (i.e. the iPod touch and computer) when supply is limited? Is it more important that all students get an even turn using the virtual tools or that certain students, who would benefit more from them, get more opportunities to use them?

There were two great tools that we looked at this week that are going into my box of teaching tools. The mira is a great tool for helping students with reflections and lines of symmetry. Should I get a job in a middle school, this will be one tool I would invest in. The gapminder.com website is another great resource. This is not the first week we have used this website and each time we looked at, we did so with different objectives. I can foresee using this tool in a number of different tools. I am also confident that my students will find this website as fascinating as I did when I first played with it. Overall, another great week and an ever expanding teaching tool box.

Math and Technology

Well, I have made it through my second week this quarter and am finding myself already completely overloaded. I am not simply overwhelmed with the amount of work I am having to do for class, but also with the huge amount of critical information I am being taught and having to put into practice in my main placement classroom. This week in math we talked about technologies role in the math world and we also practiced using manipulatives. A short conversation about technology in the classroom made me realize how much math and technology coexist. Technology has changed not only how people are learning math, but also what math people need to know. Technology has taken over our lives and with this it has impacted every aspect of teaching. There are many positive things that are now possible because of technology but there are also many new lessons that come with the inclusion of technology. This is one area where it is obvious that teachers must stay current and continue their education. Working with the manipulatives was also very educational. Although I have worked with the algebra tiles and beans before, I found new uses for both. Just within our class, using both of these manipulatives proved to be very helpful tools. All of us were able to see the math being done versus just using the rules.

One question that I thought about during math class this week was about being creative in math. I began thinking about how I can put a twist on math at my main placement, to make it more interesting and engaging. This got me thinking about if it is possible to be too creative while designing a lesson plan. I feel like the obvious answer is no, the more creativity the better. However, I would assume that for some students this could get in the way of the math at hand. One example I am thinking about is a project my class did. The students were learning about multiplication towers and rather than making a simple multiplication roll on one long strip of paper, the students were asked to cut out a piece of paper for each multiplication problem and tape them together to make one strip. Although this activity was a success, I was thinking about how for some students, the simple task of cutting out pieces could have overwhelmed the activity. My question can be asked across all subjects as well. Is there ever a point when being creative in a lesson plan can take away from the actual learning that is intended to take place?

When I get a classroom of my own, and even when I began teaching more in my main placement, I hope to bring in a number of elements that I am being taught in this quarters math class. It seems like technology can be a very powerful tool. I am eager to get students excited about math and hopefully but getting to their level (the technology level) they will realize that the language of math is not different but a part of their language of technology. Manipulatives are an obvious tool to use while teaching math and I am hoping I will get a chance to show the students the new, helpful ways to use them.

Teaching What's in your Head

Well, another quarter has begun and with that comes more BLOGGING!!! This quarter, however, I am presented with the challenge of blogging about math. It was only a few months ago that I thought math, being my favorite subject, would be easy to learn, teach, and talk about. The last quarter has shown me otherwise. I spent two days a week for the last three months in a seventh grade math class at Eckstein Middle School. This experience, although very exciting and extremely educational for me, has shown me that being able to do math and having the ability to effectively teach math are extremely different! Talking about something that happens so obliviously in my head has shown to be a very taughnting task.

This first weeks class has helped me think about ways to make teaching math more engaging and meaningful for the students. One specific thing that our class discussed was the actual amount of math students should be responsible for. We discussed how much more effective one good question is versus repetitive practice on problems that pushes for no deeper thinking. In class, we spent a lot of time looking closely at only a couple of problems. These problems force us to think about not only the simple math within the problems, but also different strategies for solving and real life application. I found it very interesting how everyone looks at things in a unique way and sees such differences. In class we also looked at patterns. This made it very obvious that all of us notice different things within the same information. One question that came up for me throughout todays class was in regards to all students being listened to in small groups. How does a teacher be sure that all students are heard in a group, especially when a student has an incorrect answer? We have been talking a lot the past two quarters about the process versus the correct answer. I think it is important that students with the wrong answer are not over shadowed by the majority (which are usually the group of students who had reached the correct answer) because seeing all students thinking can teach everyone something, even the students who got the answer right.

When I get a classroom of mine, I will be sure to think critically about the quality of questions I ask versus the quantity. My main focus will be on getting the students to think more in depth about one question instead of drilling simple math thinking applications into them. I will also be paying close attention to groups, in math and in all subjects, and try to create a community where all students have a voice and can bring great material to a conversation even if they do not always get the right answer. I am eager to get in the classroom and try out these strategies, but am also looking forward to my next couple of weeks in my math class to gain a better appreciation for teaching math.