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.

R's Reading Analysis and Lesson Plan

Analysis:

This analysis was based on a number of writing and spelling samples R shared with us. One of the writing pieces he shared was a final draft letter to his principal about change he would like to see at his school. The other piece of writing we looked at was a rough draft story about a mysterious bottle he found; this is going to be the piece of writing we focus on. The last thing we complete with him was a spelling inventory.

Meaning and Ownership of Writing Pieces:

The piece R shared with us was titled “The Bottle”. This was a fictional piece about a bottle that the main character found, which contained a note in it instruction him to go to the video store and purchase a new game that had just been released. The story was written in the first person context and was telling a fictitious story about R himself as the main character. Although my partner and I have not directly asked R about the meaning of this piece, it is obvious that he wrote about something of interest to him. Upon initially meeting R, we asked him what he likes to do for fun and how he spends his free time. He told us that he “really likes to play video games” and that he plays a lot on the weekends. This story seemed to be about a made up situation that contained elements that were in his everyday life. The other writing piece that R shared with us was a letter he had written to the principal of his school. This was a prompt from his teacher but one in which R seemed excited about. This was the first piece he shared with us and was eager to read us the story. The change that R was asking the principal for in this letter was the addition of two more tether ball courts. After R read us his piece we asked him why he chose to ask for tether ball courts and he replied, “I like to play on them and do not think there are enough for everyone at this school”. This was another example of R writing about things that are important in his life. Since I am curious about the types of writing R enjoys to do, in our next class with him I am going to ask him about the genera he enjoys writing about and I am also going to take a closer look at the topics he’s written about in his writing journal.

Six Traits Assessment System:

Ideas & Content

R’s rough draft piece was written with a narrow and manageable topic. This piece was relevant, telling, and had quality details, providing me with more information than what would have been obvious or predictable. Although this piece was clear and detailed, at times the ideas were not expanded enough to show a strong sense of purpose. It was very obvious that R was writing from knowledge and experience. During one of our conversations with him he told us that he enjoyed video games, which is what this piece of writing is about. At the end of the piece, I was left with questions that could have been answered with more information.

Organization

Through this piece, it was obvious that R has a strong sense of his organizational abilities. He could have added a more inviting introduction, but wrapped his story up with a very satisfying conclusion. R uses great transitions such as “seconds later” and “thirty long minutes later” which show that his ideas are clearly connected. This piece was written in a story form and has logical and effective sequencing. There were a few times in this piece where R could have added more time on details that were important. The title of this piece is “The Bottle”, which is very fitting for the story, however, could have been changed to something less obvious and more interesting.

Voice

R makes an attempt to connect with the audience in this piece, but does so in a bit of an impersonal manner. He also reveals a bit of personal details, but had he added more it would have improved his voice in this piece. Through R’s use of relevant details and expository style it is obvious that he has commitment to the topic. R ends this piece with “I’ll never forget the mysterious bottle.”

Word Choice

R uses very specific and accurate words throughout this piece, making it very easy to understand what the writer means. Striking phrases were also used to catch the reader’s attention, such as “… and hurry before their all sold out.” The piece reads very easy and naturally. A number of changes were made during the revision process which showed R’s recognition of using the right words to make his intended statement.

Sentence Fluency

This piece’s sentences are constructed in a simple manner and lack an opportunity for expressive oral reading. The sentences vary in length and structure and sometimes contain creative and appropriate connectives. While some sentences are original in their connectives, many begin the same way and follow the same pattern. At times, R followed the same pattern of subject-verb-object and made his sentences lack individuality.

Conventions

Conventions were one of R’s main strengths. Other than a few spelling errors, the piece had correct punctuation, capitalization, and grammar usage. One area where R could grow is with his paragraphing. While I can see what the main point of each paragraph is supposed to be, I originally had a hard time figuring out the topic of each paragraph and how they all connect to the introduction and conclusion. Since this is a rough draft, it is unclear if R made all of the necessary editing for the final paper.

Spelling:

R’s writing sample contained a few errors, but were all corrected except for two during revision. Words that were originally spelled incorrectly, and then revised, were “examene” changed to “examine”, “heared” changed to “heard”, “thirdy” changed to “thirty”, and “bootle” changed to “bottle”. “Trafic” for “traffic” and “finially” for “finally” were the two words that were misspelled and not corrected on our copy of the revised piece. Through this piece it was obvious that R was having trouble with double consonants. The spelling inventory was also proof that R was at this stage in his spelling. While he only missed two, one was “oposition” instead of “opposition” with the double “p” consonant. The other word that was missed on the spelling inventory was “pleasher” for “pleasure”. This shows that R is also still working on diagraphs and blends.

Lesson Plan:

*Same as Katie’s

Objectives:

The student will understand the way a double consonant affects the vowel sound in a word.

Standards:

3.3.1    Spells words appropriate for the grade level accurately.

Materials:

List of words with single consonants that cause a long vowel sound

List of words with double consonants that cause a short vowel sound

White board

Dry erase marker

Eraser

Instructional Strategies:

• The teacher will begin the lesson by giving the student a list of 15-20 words, of varied lengths, that either follow the rule of double consonants creating a short vowel sound or words that have a single consonant and a long vowel sound.  Some of these words will be ones misspelled in the students writing.  Using words from the student's own writing and incorporating this into the patterns in other words will make the spelling more relevant to the student (Templeton and Morris, 1999). 

• The student(s) will use a white board to put the words into categories however (s)he chooses.  (Words are written out to reinforce correct spelling as well as to make the student aware of the patterns as he is writing them).  As this is happening, the teacher will be doing a formative assessment to see how the student choses to sort the words.

•  After the words are sorted, the teacher will discuss with the student(s) how the sorting decisions were made.  Based on this, the teacher may ask to see if there is a different way to sort the words, or, if more support is needed, may sort them and ask the student what (s)he notices about the patterns (both in spelling and sound).

• The teacher will then explain how words with a double consonant before the vowel sound different than some words with a single consonant before the vowel.  She will then model (using words from the sort as well as new words) how she thinks aloud when spelling about the way the word sounds and how that relates to how they are spelled.

• The teacher will repeat the process, asking the student to spell the words aloud with her.

• After guided practice, the student will independently practice correctly using these types of words in his writing over the course of the week.

Assessment:

Teacher will assess student ability to spell words correctly by assessing their knowledge while the student sorts the words and through a spelling test using some of the words from the word sort as well as new words that follow the same spelling patterns.  The teacher will look for correct spelling of the words both on the spelling tests and in the student's writing.  

Differentiated Instruction Using the iPod

This quarter is off to a great start. I have begun working with my 4th grade main placement class again and am finding that the material I have been learning about in my classes can finally be put to the test. However, I am finding that there are many more elements to running a successful class than I initially recognized. I am discovering that one of the most challenging things to do effectively in the classroom is to teach in a way that ensures all students success. When it comes to the needs of my students I am finding that differentiated instruction is the most crucial aspect of a number of student’s success. This quarter, we have been given an iPod touch in which we are learning and exploring different was of incorporating technology into our classrooms. I have just begun working with this as a tool for differentiating instruction but am already finding many helpful uses for the iPod touch.

One of the students that I have been working with a lot is an ELL student and therefore requires differentiated instruction. On one occasion I allowed this student to use my iPod touch, the iTranslate app, during silent reading time to look up words that he was not familiar with. Both he and I found this to be a very helpful app on the iPod touch. He was able to read with more understanding and when I asked him if he liked using the iPod for this reason he told me it was fun. The only problem that arose from this situation was that this student asks every day during silent reading to use the iPod touch and is a bit against using the translating book that the teacher got as a resource for him.

One other situation in which the iPod touch came into use was for my student who is a bit behind in her multiplication facts. She has flash cards to study with but rarely stays on task while studying them. There was an app I found on the iPod that helped students work on their math facts. This app was great for this student as well as other students who have trouble focusing on studying their math facts. By having students study their math facts through technology it makes their learning more relatable to their everyday lives.

Another tool on the iPod touch that I have not had any of my students use, but am eager to try out is the recording element. There are a few students in my class that are exceptionally good at writing. I thought one helpful use of the recorder would be to have the students read their story and record the reading. They could then play the recording back and listen to their story. In our class, when the students finish their stories they have the option to read their story to a partner and receive feedback. I think using the recorder would be another good way to allow the students to hear their story and make changes.


Overall, I have found that through the iPod touch I have been able to add differentiate instruction to my lessons in a fun, practical way. I am excited to see what else I can do with my iPod touch to help differentiate instruction. I strongly believe that by creating a fun learning environment that reaches students at their level of familiarity entices students to become actively engaged. So far, the iPod touch is proving to the link between students and learning.

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.                                                              

Building Relationships

Is it enough to just be smart, or know a lot of information, to be a good teacher? I think that the obvious answer to this question is no but how often is this type of question really dealt with? Of all of my schooling and learning about how to teach, I do not ever recall being given a lesson on how to talk to students. We read one great book about how to talk to children in a way that they will understand, but I am thinking about this in more of a relationship building manner. This quarter I have been teaching in a middle school and I am realizing more than ever that it is so crucial to build a relationship with students and gain their trust before they will be able to learn you. I can remember back to my own schooling, and it was about middle school where my relationship with my teachers went way far south. I would argue that this was partly because my social life with my friends was beginning to interrupt my relationship with my teachers, but also because my teachers had too many students to be vested in me. This cannot be the reason middle school and high school students and their teachers have such disconnects.


My dyad instructor has dedicated much of her time to working with each student individually. Luckily their class schedule has a homeroom period where they can come see her and during class she also allows quite a bit of time to be spent working on an assignment, leaving her a chance to speak with students who otherwise fly under the radar. A teacher told me a really powerful piece of advice a few weeks ago. She told me in all of her years of working in the high school she has noticed that when students are aware that she cares about their learning, they care more about their own learning. I realize that teaching is not a chance for me to become best friends with all of my students, but if finding out their favorite sport or listening to a problem or two of theirs helps them to be a better learner, I am game! And I can always use more friends, even if their 10 ;)