Real Math

I saw this on twitter... quite funny.

Many Ways to Solve

While I don't technically teach math, it doesn't stop my love for it. Our rotations have broken up the division of labor so that my team essentially has specialists for math, reading/social studies, and science. I'll admit, my math usage in social studies has been minimal this year, but I hope to pick it up. Alas I digress.

In cleaning out my Google Reader, and the 200+ blog postings sitting awaiting my perusal, I stumbled upon a link from Dan Meyer. The general gist is that you have a pyramid of circles (many many circles) and you ask kids to "find the total number of circles." I imagine how my 5th graders would solve it. Counting them up for the less experience/savvy. Algebraically for the math savvy. Geometrically for the visual spatial. I looked at the table sitting next to it, which provided the row and number in each row, but quickly discarded it. I saw two triangles, and was going to find the total for each, at which point I stumbled upon the fact that they fit together to make what appears to be a square- LxW! Count up and down, multiply.

Our kids are doing double digit multiplication, which would mesh quite well. I'm considering taking it out on Wednesday prior to leaving for our midwinter break (probably not, but we'll see). To me there are two very clear illustrations: 1) there are a myriad of ways to solve math problems, you just need to find the one that works for you (no matter what problem), and 2) strong number sense and math fact knowledge will serve you well. Geometric sense/knowledge would be a bonus, but number sense for sure. If you are aware of patterns you will be in good shape- seeing each row increase by 2 (total and add). Or simply being able to break into parts and multiply.

Use Sparingly

I am 5 days from ending my student teaching. Most of the heavy lifting is over. Have I finished all my observations? Check. How about getting your final check-out meeting with your field instructor? Yep, check! You've been observed by your principal and master teacher? Most certainly. How about submitting your portfolio? Yes, although I will admit that I probably spent more time on the actual teaching than the portfolio itself, part of my field on what is the most important thing (teaching or photocopying and compiling?).

This past week also marked my 9th week of student teaching, and the beginning of my handover of responsibility. I've still taught math, writing, and science, which means I've been teaching quite a bit. But I am ok with that. The more experience the better. The only downside is having the kids seeing two very different styles/tolerances. Noise is one of those things where I am ok with a reasonably loud bubble, and my MT isn't quite as keen. You'll remember that I posted on this previously, and need to remind myself of that.

Now I have new found time! I can blog a bit more, which is great. The second thing is that I can go through my Google Reader, chalk full of 196 posts. Some of the best are...

• Brian at Learning is Messy was reflecting on his current (soon ending) 1:1 student/laptop ratio, and what that has meant for his kids and in his practice.
• The Reading Zone had a post about grading in the reading/writing workshop, as well as how to curriculum map. Both of those are things I am starting to think ahead to. Both posts have some books worth checking out (I can speak to the quality of the Strategies That Work book)
• I absolutely love seeing Dy/dan's posts come through my google reader. I think he inspires me to think about how we can use a variety of content to get kids thinking about math in real-world contexts. This looks at a music video where you can mute instruments, and what would that mean to the number of combinations that could be created. This one looked at a comparison between two very different math classes, and their interest level. I think one can read a ways into it, particularly from a class point of view and the notion of gatekeeping.
• The Doc is In had a pie graph that made me laugh, but not in the "ha ha ha ha ha!" sort of way, as I think it (sadly) ends up getting it right.
• I also read some running/sports blogs. The Science of Sport goes a little deeper into running, thinking a little (well, a lot) more critically about things. This looked at performance enhancing drugs in sport (sport being running, as they are non-US), and this looked a little deeper into pacing at the London Marathon vs the World Record. For me, it is like Dy/Dan's posts, but in a running context.

My last note comes in reflecting about an email I had with a principal friend. We were talking about the end of my student teaching, what was next, etc. Finding a job is paramount, but it will be a hurry up and wait type of situation as we had a RIF's all over the state. I mentioned how I was also running a marathon in Portland on the fourth of July. I told her I was hoping to be around 2:35, maybe a little more or less (certainly 2:30's). She was surprised I was able to manage both things- training (heavily at that) and student teaching. I hadn't thought about that. It is just what I do, and there wasn't much of a choice.

Board Games

Teaching in a split class is interesting. They are classes put together out of monetary convenience for the school district, not for the kids' learning! The funny thing is that I love multiage classrooms, and think that is how a split needs to be taught (not as a 1st grade, 2nd grade with divider down the middle!). I think the range can be wide, but it is going to be wide in any classroom. The benefits of having older students and younger students working together outweigh the range, at least to me.

As we use Everyday Math, and like many math curricular materials, teaching a multiage for math is very difficult. So we don't. That is right, we don't, or at least our class doesn't. My master teacher has the 2nd graders with the math specialist, and we take the 1st graders. Class size becomes ideal (10-13 each), and we can focus on what we need to focus on... except on Fridays! Fridays are when the math specialist isn't in, so we are all together.

I've tried to stay away from simply playing math games. While they are fun, and can reinforce concepts, I feel like they end up being 50 minutes of filler, the mathematical equivalent of empty calories. Today I've got a different plan, meshing the ideas. Both groups have worked on fractions, and both like playing games. How about using pattern blocks to make a board game? We are going to add in CHANCE spots where you can take a chance to move ahead a spot by answering a math fact question, and we are going to do some writing. The fractions come in as we identify the fraction of the total pieces (ie 5/12 pieces were blue pentagons). Identify shapes, identify fractions, creating math facts. We'll see how it goes.

I {heart} clipboards

Highlight of the day... all of the kids walking around the room with clipboards, asking each other what their favorite ______ was, and then compiling graphs. Well, not everyone was making a graph, but they were all engaged. It was a little loud, a little chaotic, but really awesome! Tomorrow I'm posting pictures of seeds in a bag... oh so cool!

Authentic Problems

As TeacherWife and I were talking to a Kindergarten teacher friend of our's, an aside comment came out:

...That is what I don't like very much about our math curriculum, it is difficult to integrate problem-based learning into it... and to connect the curriculum with authentic problems.

Ahhh, a problem I have been thinking about myself. The materials we use spiral quickly, which can be a good or bad thing (depends on your point of view). One view is that the quick spiral doesn't allow students to become proficient, let alone master, skills that they are faced with. Without proficiency, students will find trouble as they advance in their mathematical lives. But isn't the concept of mastery or proficiency a way of gatekeeping? The quick spiral gives students a chance to see that concept a myriad of times, and not simply in one concentrated effort.

The spiral was my issue, but I feel far better about it now. Where I struggle now is in connecting the materials (more specifically, the lessons as laid out) to an authentic problem. Part of the job, as a teacher, is to make kids care about what we are teaching. Why should I care about coins today, and polygons tomorrow?

All of this thinking comes as I am reading dy/dan's post about a ball hitting a can!

Reflections Eternal

The first full day is in the books. No one got hurt, no one got lost, kids were engaged, and kids were happy. Student teaching is an odd land where the classroom is in the control of someone new while still being the classroom of the master teacher. To help kids meet the learning objectives, you need to be sure you are clear about your expectations (or so I feel).

Crafting and demonstrating expectations in timely efficient way is an art. I bogged down while spending additional time in being clear with expectations. For the most part, it was effective as I'd say that 75% of the kiddos met those expectations and worked hard throughout the day. The other 25% weren't quite with it, and struggled to acclimate. I think some of that is pushing boundaries to see if I would push back or if I would relent. Another part of it is being clear, direct, and continuing to repeat those directions and expectations to them. They're kids, not robots, and they need many reminders.

Instructionally I felt ok. I was able to get through 4 reading conferences, and feel like I have a good idea where they are. Some other kiddos were tying up a literacy project, so the entire literacy block doesn't feel cohesive. Math was fantastic, and is probably where I feel the most comfortable currently. I was successful in integrating the virtual manipulative for money, which rolled straight into my own spin-off of the Everyday Math activity for the day. Writing is still a work in progress, which isn't surprising. Alas...

I live to give it another go tomorrow with the wealth of today's new found knowledge.

Integrating Technology

I hope to integrate some technology into my teaching this Spring. We only have one student usable computer, but that isn't a big deal to me. I am excited about the kids creating, or at least creating the audio for, a podcast. I'd like to make a series of them that could go on the school website. This will likely be related to an All-About unit that I want kids to write. The other option is during a poetry unit. I'm also considering using tech in a PhotoStory way, which would be to have student artwork on screen with voice (re: student) narration to the artwork.

I want to use the National Library of Virtual Manipulatives during math in our math opening too! I have a wiki that I've "started" but I don't have any content yet. The model I'm using is here. It is a project to be worked on over the next few weeks.

As TeacherWife told me yesterday, you will have a ton of ideas but you'll likely only get a chance to implement some of them in this short period. Those are the words that I need to keep in mind when I worry that I'm not meeting my own expectations.

Content Knowledge Flowing Like a Wide River

I am wrestling with the notion of depth vs breadth. I worry about having strong pedagogy, and having strong practice, but lacking strong pedagogical content knowledge. More specifically, I worry that I won't really know enough within given content areas to help my kiddos along. I know that you continue to learn, but that doesn't give me much consolation at the onset.

This all comes from a conversation about math curriculum, and knowing what to skip. A colleague was saying that she was unsure as to why the master teacher skipped a section of a lesson that my colleague thought was important for the content knowledge for students. How do you know when it is appropriate? How do you know that your kids won't be lost by skipping that section?

Moments in Time

There were two moments that stuck out today. The first came in math where we were working on "Attribute Rules." Each student had either a circle, rectangle, square, triangle or hexagon. The shapes were different colors, thickness, and proportion. We were going through what a hexagon was... a shape with 6 sides and 6 corners. I proceeded to draw a hexagon, but inverted from the one the student was holding.... the chaos that ensued! "No that isn't a hexagon" "It can't be." I asked each for a thumbs up or down about whether they thought it WAS or WASN'T, and had them give reasons why... "It isn't because it doesn't have 6 sides." Count them, "One, two, hey wait a minute, it has 6 sides... and there are 6 corners." The aha moment was priceless!

The next moment was when we finally booted up the teacher workstation (cpu) that sits next to the document camera. I feel like a threshold was crossed by simply pushing the ON button. We've now got one functional, Internet ready computer in the classroom. I've also got my Stereo cable so that we can plug the computer into the speaker system (not to mention an Ipod, etc). Oh the places we'll go! (Sorry, no links today, just text!).

Math and Democracy

In our Math Methods course on Wednesday I was struck by a statement from our professor. To paraphrase: the curricular materials are a guide for the material that needs to be covered, but it isn't the bible; you can supplement and teach in many ways to meet the needs of your kids assuming you cover the same content. I'm sorry if that doesn't do the actual wording due diligence, but that is how I internalized it.

That led me to a Saturday morning conversation with my wife, a 2nd/3rd grade teacher. I told her what I learned, as state above, to which she said that it depends on where you are (good point). If you are in some districts, say Bellevue, you are expected to stay close to the script. Teachers essentially become actors in a play of content dispersal, and the art of teaching is reduced to the act of reading a set of cue cards.

What does that have to do with me? Well I am reading through the lesson for tomorrow, Attribute Rules in Everyday Math's 1st Grade Lesson Guide. Much of the lesson has the teacher directing students, instead of having the teacher set up an environment where they can explore and classify shapes. Why have the teacher tell the students with red shapes go to a place in the room? Why not instead have the students try to work out what is in common, and classify? Why not seek more student input, and get them engaged in the process? There are certainly some great parts of the lesson guide, but I wish there was a more concerted effort to have students share their ideas with their peers in small/whole group settings.

Everyday Math

I've really tried to diversify the blogs I am reading. Most of the posts hitting my Google Reader are literacy or policy focused. I find that to be a little funny, as I have always been stronger mathematically than verbally (as much as I am strong verbal/linguistic person- I don't shut up!). Over the past two weeks I have been looking for good math blogs.

The one that got me thinking today was Exploring Mathematics Around, which reminded me a little bit of using Voicethreads in the way that it inspires conversation around images. At any rate, that got me thinking about math in my own life... (dy/dan is also really good!)

• You're at Costco and you want cereal. You'll eat either the Cheerios or the Honey Bunches of Oats. Both are tasty, but which is cheaper? Well Cheerios is $6.99 for 49 ounces, while H.B.O. is $6.95 for 48 ounces. Where do you get more bang for your buck?... How about comparing whether to get sugar at Costco versus at Fred Meyer (i.e. bulk vs non)? It can seem like splitting hairs, but we're in a recession!
• You've just run 15 miles in 1:28:30, and you are planning to run a 15K and a marathon (26.2 miles/42.2K) in the next 3 months. Assuming your fitness stays the same, and you ran the same pace for both of those runs, how would you finish? Would a 10 mile run in 54:00 yield the same results or different?

I use math everyday, and I am not sure I ever really considered that I would. It isn't just shapes but mental math and calculations we do on a daily basis.

What I Learned Through Google Reader Pt2

I have been inspired by This Week In Education's blog posts of the day/week, and have wanted to share some great things coming into my Google Reader...

• I found this over at Kitchen Table Math, and found it to be highly amusing. Is it educational? Yes, for the simple fact that you should be careful dancing/walking on treadmills. Additionally I would posit that there is quite a bit of visual/spatial intelligence being utilized.
• If you are going to say you did something, you best have been sure to have done it. Something smells fishy, and dy/dan has a lesson that might weed out any lying. In addition I like the real-world applications and critical thinking skills embedded into this lesson.
• Curriculum Matters cited a study stating what we knew all along (didn't we?)... kids need unstructured play time in the early years, not the instruction that has started to creep into Pre-K and K.

What I Learned!?

I learned that I really like science and math. I find them to be easier to wrap my brain around, maybe because they are concrete. These content areas also happen to have guides that give me concrete examples of what can be done. What gets me is following along without making the necessary adjustments to get the lesson to work in your classroom.

I learned that I want my kids to read for pleasure. I need variety in my reading block of time, and I want kids to be practicing reading books that they want to read. Reading can go in many different directions, and can also be structured in a myriad of ways. I have some ideas for how I want to structure my literacy block.

I've learned that you need to be ready for anything, including teaching the next lesson in the series. I made the mistake of getting a project started in writing, but not thinking of step numero dos. What is the next step in the how to writing? I got them started, I got them engaged... Now what?!

Piggybacking... I've learned that the teacher's job is never done. I've photocopied the writing from our writer's workshop, and am going to make a determination of where the students need to go to have a how-to book that works.

Monday marks the first day that I will submit my Memoir Monday to Two Writing Teachers. You don't get better at teaching writing unless you practice it yourself. I can't wait!

Engaging Lessons

I am only teaching sporadic lessons during this quarter, and tomorrow I get a chance to tackle science and math. In truth, I tackle science every Tuesday with our kiddos, but this is my first foray into math. The lessons couldn't be more different.

The Seattle School District uses the Everyday Math curriculum set. It is a highly recursive curriculum, and tomorrow I am introducing Turn-Around Facts for the first time (5.10 of the 1st Grade guide). I looks like the lesson is 3/4 whole group, which will have it's plusses as far as bringing forth discoveries about patterns in the facts, etc. To some degree there is a level of comfort in the sheet with the facts that the student needs to fill in. But is that really engaging? Isn't there a better way?

Fast forward about 2 hours and I'll be in science. We are working with the concept of balance, and more specifically how weight and position affect balance, not to mention the position of the fulcrum. It is a 45 minute block (too short, I know!) that seems to run out too quick. The kids are engaged, and the only real struggle comes in teaching kids how to be partners with others (particularly those not their best friends). There I struggle more with having effective whole class discussion in a limited time than having an effective lesson. If only I could intermingle the best parts of each of the lessons.... there is still time!

(note: credit to penywise at morguefile for the above photo)