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.

Continuing to use iPod Touches

As this quarter has begun picking up pace, I must admit that I am not finding the time to effectively use the iPod touch in the classroom. I struggle with this because while I feel like it is such a great opportunity, I also feel like when I do bring it out it becomes a bit of a distraction and takes up more time than I meant for it to. I have also felt like it would be inappropriate to bring it out during a lesson my main teacher is teaching (which has been most lessons). Time management as well as deciding who deserves to use the tool have both been factors in my lack of inclusion of the iPod in my instruction. 

My opinion about the iPod touch may have been completely different had our class had the opportunity to use 26 of them. I was conflicted when it came to deciding who was going to get to use the iPod and who was not going to get to use it. There were a number of students who benefited from having it available to use during math for support, while there were two students who I thought made more progress with it. I had a hard time being the one to make that judgment call... I guess its called being a teacher! 

One thing I did find really useful, however, was being able to use the iPod touch for whole class discussions. There were a few times where my students were discussing Lewis and Clark and Sacajawea and they asked me historical questions I did not know the answers to. The next week, during social studies, I had the iPod touch out and ready to use as a reference guide. I allowed the students 10 minutes to ask any reasonable question they could while I looked up the answers. This proved to be a great ways to get them interested in the content and also quench their curiosity about particular issues/events/people. 

To be honest, I think I would have found my time with the iPod touch to be more fulfilling had it not come during the busiest quarter yet. I hope that I will have another opportunity to work with new technology and find more time to incorporate it into my teaching. 

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!

Continuing to Use the iPod Touch in the Classroom

As I am becoming more comfortable with my technology skills, I am becoming braver about introducing it to my students. This has really begun to pay off. I have been using the iPod touch in a number of different ways, both in the class and also in my schooling. One very useful thing I have recently begun playing around with is the voice recorded and text transcriber. While I live in Seattle and am teaching in Everett, I am finding myself in the car a lot. Being able to record my immediate thoughts after class has really helped in assessing the students and planning appropriately. Being able to transcribe my recording to text makes it really easy to go back to and reread; to check for particular patterns or to remind myself what worked well and what didn't in my lessons and interaction with my students.

As far as having the iPod touch available to students, I have realized this can be a bit problematic at times. While it is obvious that it is a great resource for the students, I am conflicted by the fact that I only have one to share, leaving very little time per student and/or an unequal opportunity for my students. One situation that I found particularly difficult was during a math lesson. I was teaching about long division and realized quickly that a few of my students were not understanding my lesson at all due to their unfamiliarity with their multiplication facts. I decided that I was going to allow one of my students to work on his multiplication facts on the iPod, on an app called ArithmeTick. This was great for this one student, however there we a few other students who were equally low in their math development. To make this fair I decided to have each of the students use the iPod touch for 10 minutes and then allow someone else to use it. The logistics of this worked out okay but I am not confident that all three of these students were successful in effectively using the app. It seemed like right when the students got comfortable with how the app worked they had to give it up.

This leads me to my question for the week. How does a teacher go about acquiring technology tools when the school does not have the resources to fund them? I know there are grants available, but are there other ways in which a teacher can propose to get tools like iPod touches? It is such a shame that there are so many great gadgets out there that can help with teacher instruction and student understanding and many schools/teachers do not have access to them.

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.

Moving From Assessment to Instruction

Unfortunately, I was unable to meet with R this week, but luckily my partner did and I was able to catch up on how their time was spent. I was informed that R read fluently and comprehended both the Amelia Earhart piece as well as the piece on steam engines. This came as no surprise to me. In all of our conferences with R, he has demonstrated strong fluency in his reading and has been very precise in his comprehension and retelling.

One interesting thing that my partner told me was that, while she expected that he would respond stronger to the piece of his initial choice (the steam engine piece), this was not the case. While he was proficient in both readings, she felt like he was strongest with the Amelia Earhart piece. She suggested that this had to do with the fact that R had more background knowledge on this topic. I completely agree with my partners thinking. In our past meetings with R, he has shown special interest in topics that are relevant to his prior knowledge and areas of interest. During our first informal reading conference with him, R chose to read Holes rather than another book we suggested to him because the cover showed a boy his age. Being able to read about a character his age made the reading more appealing to him.

From these observations, as well as other things we have learned about R, it is obvious that grade level text is easy for him to read, comprehend, and make inferences about. One idea I had about pushing R's reading and comprehending skills would be to provide him the opportunity to explore other types of writing. A lesson on poetry would be valuable for R, considering it pushes for deeper thinking and compression, while also being engaging and relevant. R could also greatly benefit exposure to higher grade level readings.