Saturday, November 17, 2012

Desks versus Tables

When I first came into my class room it was full of desks. Desks for my students. This seemed reasonable to me. One of my supervisors suggested that I try tables. Truth be told, I was kind of excited by the idea. It seemed it would be nice to have all my lovely students sitting around tables, collaboratively working diligently on whatever tasks were necessary in order to engage their education. 

It's been about 10 weeks now that I've been with the tables. Make no mistake, I have not been the best at managing the misbehavior of my students (the topic of a different post, yet written). That said, it occurs to me that having my students sit at tables makes it very easy for my students to be social when they ought to be listening. If I was better at keeping their attention, the tables would be great. As is, the tables make my classroom environment rather not conducive to ordered, focused learning. 

And that's what I have to say about that, at least for the time being. 

Sunday, September 9, 2012

I teach math; that's my job; I have no other responsibilities.... (New Blogger Initiation Post 4)

So this week, for the new blogger initiative, I'm just going to post whatever I want! Boosh. 

I'm a math teacher, this is true. I'm also a new math teacher. I'm finding that my job is about 80% teaching math and 20% things that I have no real business doing. 

Like announcing the freshmen and JV football games. Don't get me wrong. I volunteered for that opportunity. I think it'll be a great way to become part of the community at my school. I've done two games thus far and I'm pretty much loving it. Yes, it requires one of my nights every week. And I need those nights these first few weeks to get my feet under me. But it's fun to get up in that booth and watch my students pushing hard to get some work done. It's even exciting every once in a while. 

All that said, I've never announced any sporting event. I'm not very good at it. I'm slowly learning how to keep track of all the players on the field, forcing myself to associate names with numbers. I make jokes with the other faculty in the booth. We shoot each other puzzled looks when the officials huddle after every play. It's a good time. 

In short, it is turning out to be exactly what I was hoping for: a good way to inch my way into my school's community. 

Tuesday, September 4, 2012

Favorite Math Quote (New Blogger Initiation Post 3)

Today on New Blogger Initiation:

Is there a quotation about mathematics that you like? If so, what it is and why do you like it?

My favorite math quote comes from Galileo, 

"Mathematics is the language with which God has written the universe" 

I love this quote because it totally fits the way I think. Everything I see/hear/experience, I do so in the language of mathematics. The fact that math is a language (i.e. a way to communicate any idea) is something that I try to emphasize to my students. It's important that they come to understand math as a way of talking about things that would otherwise be very cumbersome and/or imprecise to talk about. 

That's all for today! 

Monday, August 27, 2012

Generalizing (New Blogger Initiation Post 2)

As part of the New Blogger Initiation, here's my second post. This time the prompt I got was to respond to an xkcd comic. If you aren't familiar with xkcd, check it out: it's one of my favorites. The particular comic I was prompted to respond to was this one (titled, "How it Works"):

I like this comic because I see it happen a lot. I think it's pretty obvious these days when this sort of thing leads to sex stereotyping (as in the comic). As a teacher, particularly of math (the language of precision), I think it is very important for me to make sure this sort of thing doesn't happen in my classroom. Or in any other classroom for that matter. One person having or not having a particular ability has very little to do with anyone else's ability, even if the two share a commonality (e.g. sex, age, gender, hair color). It's important that I impress upon my students a way of thinking that encourages them to see where connections exist between two things and where they don't exist. 

Friday, August 24, 2012

Organizing the Physical Classroom (Student Teaching Summary Post 6)

Oh finally the student teaching posts are over! Here's what I think is important where the physical classroom is concerned:

- Energy source Something for students to munch on if they're really needing it. 

- Water

- Writing surfaces Students need some hard surface to write on. 

- Community display This might be a wall or a smart/white/chalk board. It's a place where all kinds of information can be easily displayed for all to see. 

- Teacher office space

- Movement space I think it's important to make sure there's plenty of room for people to move around the room. 

- Coat rack You know, in case there're rainy coats to be hung. 

- Absorbant rugs at entrances Again, rain kind of happens every once in a while here in Oregon. If there are no rugs at the entrances and exits, the floors will be very hazardous. 

- Anonymous feedback system I want my students to have a way to let me know what's working for them and what's not working for them. I'd prefer it to be anonymous (not publicly displayed) so that I'm the only one who sees the comments. This is the kind of thing that I'll introduce on day 1 and then only every refer to again to let students know that I'm getting their feedback and making adjustments as necessary. 

- Organizational system Things need a place to go. And they ought to be made to exist there. In my life, there is no room for exception to this. And I intend to ensure my classroom is a clean organized space at all times. 

- Implication that the classroom extends beyond its physical bounds/connection between the classroom & the not classroom Something like a plant would be nice. Just something to remind students what they're fighting for. 

I'm most excited about this list. I've never had my own classroom before and I'm pretty sure about 50% of this list is probably a really bad idea. I just don't know what 50% yet. Only time will tell.... 

Building Community in the Classroom (Student Teaching Summary Post 5)

Post 5 of 6 for my student teaching thoughts. These are my thoughts on building community in the classroom. 

- Empathy Care about the students and their lives. They will reciprocate. After all,  community is just a bunch of people all caring about the same things. 

- Have students help build at least some of the classroom rules/regulations Giving students some control over the environment ought to give them ownership of the class. Feeling responsible for something helps build a sense of commitment and caring for that thing, which is the class in this case. 

- Employ activity (e.g. physical movement, intellectual stimulation) that encourages students to get to know, care about, and trust one another   If you have tips or hints on how to do this well, I welcome them in the comments.

- Be myself everyday I know full well that if I try to fake it, my students will know and resent me for it. Resentful students do not care about anything. 

That's all I've got there. It's not very specific. I'm going to be working on coming up with some more concrete ideas as I go along: not ideal, I know but as good as it gets for now. Please let me know if you have any input on building community in a classroom. 

Getting (& Keeping) Students on Task (Student Teaching Summary Post 4)

Here's a post detailing the thoughts I had as a student teacher concerning getting and keeping students on task. 

- Do it again If students don't get a classroom behavior or expectation right the first time, show them what they did wrong, model how to do it write and have them do it again, until they get it right. This is a technique from Teach Like a Champion. I don't love everything in that book but this one I can get behind. 

- Everyday: Remind students of upcoming homework and assessments, state the day's date, provide students with a daily agenda I think this is pretty important for keeping students focused on the task at hand. 

- Employing group work: 

The idea behind this graphic is that each student's desk (represented by rectangles) is positioned so that the student can have an easy to get to partner (blue elipse). Students can work mostly in partners. When needed, they can work in groups of four (red boxes). The pairs in each group may rely on each other for help during pair work, if they need to. During group work, neighboring groups can offer help to one another. The teacher is then only a support when several neighboring groups are stumped (or moving at very different speeds). 

- Establish the purpose for the course early on (why should students care about what's happening in this course?) This is another important point for helping students find and keep their focus in class. 

- Find out, at the beginning of the year/semester, what working algorithms (e.g. individual work time, group work, guided practice) work best for each class Some classes may work better with an emphasis on different types of work. It's good to have a little bit of all of these elements but maybe you have a little more of one then another if you know your class will work better that way. 

- Provide specific, daily learning targets as well as unit-long learning targets Another focusing point. 

There you have it. Some thoughts I had about time on task while student teaching. 

Getting (& Keeping) Students' Attention (Student Teaching Summary Post 3)

Here's another short post. This one concerns things I want to implement in order to get and keep my students' attention. 

- Routine (I find the routines are ways to get people to do things without them even having to think about it. Making routines routine in my classroom should help get my students' attention because they'll be expecting me to be getting their attention)

- Wait/Have patience (Waiting silently was probably the most effective way I found last year for getting my students' attention. They knew when they needed to quiet themselves down when I was just standing there waiting for them.)

These short posts are nice to write. Quick thoughts but well worth sharing, I think. 

Wednesday, August 22, 2012

Grading (Student Teaching Summary Post 2)

This is going to be a pretty short post. Here's the very short list of things I want to make sure I'm doing concerning grading this coming year.

- Have an answer key or a very well written rubric to help make grading a mindless task

- When employing standards-based grading, make sure that essential skills (those that aren't covered by your standards) are still part of the curriculum

- Provide a rubric for feedback that is given to students (i.e. a rubric with which I can rate the quality of feedback that I'm giving students)  side note: This may or may not be something that I tell my students about. Mostly I just want to make sure that I'm giving my students quality feedback. 

That's it for grading. Told you it'd be short. As always, comments and feedback are super welcome. 

Tuesday, August 21, 2012

Assignments, Assessments, & Evaluations (Student Teaching Summary Post 1)

Through the course of my student teaching experience, I had several ideas & epiphanies. Here are those that apply to assignments, assessments, & evaluations. 

- Provide homework/practice before and after giving an assessment/evaluation for any given unit/standard

- Use the following table to put variety in student practice and assessment:

(only one correct response)
something easily memorized
recognition (t/f)
medium to memorize 
recognition (matching), recall (fill in the blank)
difficult to memorize
cold recall
apply out of context
(likely one correct response)
simple practice problems
mid-level practice problems
high-level practice problem
apply in context
(potentially multiple correct responses)
simple scenario/ story problem

(ala 2A)
mid-level scenario/story problem

(ala 2B)
high-level scenario/story problem

(ala 2C)
(infinite possibilities for correct response)
making something simple

(ala 2A-2B)
making something with moderate complexity

(ala 2C-3A)
making something with high complexity

(ala 3B-3C)

This table probably doesn't make a lot of sense if you're not me. So below I've put in a table that has some examples of what I'm thinking about. Let me know, in the comments,  how it doesn't make sense, if it doesn't make sense, and I can further clarify. Also let me know if you want examples that are more specific to your needs.

(only one correct response)
true/false, or multiple choice questions
Provide the definition for _________
apply out of context
(likely one correct response)
solve for x:
apply in context
(potentially multiple correct responses)
Johnny has five apples before giving some to Tammy. Afterwards, Johnny has two apples. How many apples were given to Tammy
My backyard has a fence. The fence is 30 feet long and encompasses the whole yard. If my yard is a regular geometrical shape, what shape might it be if each side is > 2 feet? 
Our school website says the school grounds covers 3,000 sq. ft. Prove that this is either correct or incorrect. 
(infinite possibilities for correct response)
create and solve an algebra problem 
create a problem that requires the distributive property to solve
write a story problem to go with the equation y=3x-2
find an example of the concepts we've been covering in class from your life; write a story problem describing what you come up with

- Hold office hours everyday to help with assignments:
  + Monday    = for A-level students
  + Tuesday   = for B-level students
  + Wednesday = for C-level students
  + Thursday  = for D/F-level students
  + Friday    = Peer tutoring sessions
  + Alternatively, provide some other meaningful structure for who should come and/or what is going to happen during the office hours. 

- I really like an article by Margaret Schwan Smith and Mary Kay Stein called "Selecting and Creating Mathematical Tasks: from Research to Practice." It breaks all work that's done in a math class into four levels of demand: memorization, procedures without connections, procedures with connections, and doing mathematics. Their thoughts & ideas in this paper really guide my thinking about assignments, assessments, & evaluations. I find myself asking, 'What is the level of demand for this task? What ought to be the level of demand for this task? What level of demand are my students ready for at this point in the unit/semester/year?' 

That pretty much sums up my thoughts about assignments, assessments, & evaluations. This was a long post. If you made it all the way through, FIVE STARS for you! Yea, STARS! 

Wednesday, August 15, 2012

Summary Thoughts From A Year of Student Teaching

So, though the summer has already come and gone, I think it's important for me to reflect on my student teaching experience in the 2011-2012 school year. 

I spent the whole year student teaching in a Geometry class. Actually, I'm not going to talk much about that at all. Instead I'm going to take the next few blog posts to put down the things that I came up with as a student teacher, which I want to implement going forward. I've broken these things down into several categories. Maybe you find them useful. Maybe you find them interesting. At the very least I hope that they'll serve as some reference point for what I find important and what my priorities are as a math educator. 

I'll put up one new post per category, as follows:

1) Assignments, Assessments, & Evaluation
2) Grading
3) Getting (& Keeping) Students' Attention
4) Getting (& Keeping) Students On Task
5) Building Community in the Classroom
6) Organizing the Physical Classroom

Some of these posts will probably be pretty long and some of them will probably be very short. I'm going to try to roll them all out by next Friday (8/24/2012). 

What is this blog about anyway? (New Blogger Initiation Post 1)

For those of you unaware, I am new to the blogging world. I am new to the teaching world (at least new to being a teacher). I found, in my random bumblings, this great blog post encouraging folks who are new to the 'mathtwitterblogosphere' to join together and write four blog posts to start off the new year. 'This is exactly what I need!' I thought to myself. So here I am writing my first New Blog Initiation post of 2012. I was given the following prompt to write about: 

Where does the name of your blog originate? Why did you choose that? (Bonus follow up: Why did you decide to blog?)

I thought this was a great way to start my blogging (yes, I know I've already posted a few things but we're starting fresh here). I wanted to title my blog something that would make it really easy to tell what my blog was all about. I wanted it to be short enough that it wouldn't look daunting to read but I wanted it meaningful enough that you could read it and go, 'oh. I know what this is about.' Since I intend this blog to cover all things math education from my own personal perspective, I thought the title A Beginner's View of Math Education was an apt title. 

I initially wanted to start blogging because I sometimes feel like I have good ideas (like my idea for transitioning to common core state standards). And I wanted an outlet for sharing those ideas. Now that I'm getting into it, I hope that this blog turns into a place that I can post questions that I have as well. Especially if I can make some math teacher blogger friends through this new blogger initiative! 

So there you have it. Hopefully more great ideas, questions, thoughts, and experiences will follow! 

Thursday, March 1, 2012

Math Gloooooooory!

Try this math review game and let me know how it works. 

Here are the rules:

  • The game will proceed one round at a time
  • Each round will last 8–n minutes where n is the number of the round of the game (e.g. the first round will be 7 minutes, the second 6 minutes)
  • Each round will consist of one problem to solve
  • The game officials walk around the room only to check answers (no help will be given, only confirmation or denial of solutions)
  • Students are grouped into teams
  • As soon as everyone in a team has the solution written down in completion, all members of that group raise their hands
  • The solution will be checked by the official(s)
  • Every group who gets the correct solution will be rewarded with 1 point
  • The group who finishes first will be rewarded 2 points
  • The team who has the most points at the end of 7 rounds wins the prize!


  • Let students pick team names
  • Offer one get out of homework free token as the prize
  • Try different timing schemes for different complexity of units to review

Adapting to Common Core State Standards

The other day, my mother and I were discussing how to get ready for the coming Common Core State Standards (CCSS). She's a middle school math teacher in Oregon and part of her district's committee for transitioning from the Oregon State Standards (OSS) to the CCSS. 

Getting ready for the CCSS is a daunting task. As compared to the OSS, the Common Core standards are written using different language, contain different amounts of detail and instruction, are organized differently, and necessitate a different approach to assessment. It's no wonder educators all over the state are feeling overwhelmed. We've gotten used to the OSS and now we have to start again, from the ground up, with these new standards. 

Like it or not, the CCSS are coming and we need to be ready. That's where the committee that my mom is on comes in. She and her comrades are responsible for reconstructing their curriculum as necessary to accomodate these new standards. Which brings us back to the point of this post, which is to write about what my mom and I discussed. 

As an engineer, my first inclination is to identify the goal, identify the context, plan a solution, execute that solution, and then check to make sure the solution actually accomplishes the goal (in that order). So that's what I did with my mom. The goal of our conversation was to figure out how her district could make sure their students were meeting proficiency for the new standards. Here's the plan we came up with:

1) Divide the standards up among the grade level teachers (e.g., there are 29 CCSS 6th grade standards for math and 5 6th grade math teachers at my mom's school, so each teacher gets 6 standards)

2) Each teacher fills out the table below for their standard (seen below with examples and italicized explanations)

Standard Text Knowledge Reasoning Demonstration Product
6.NS.2: Fluently divide multi-digit numbers using the standard algorithm (This is verbatim the text of the standard) the algorithm for division (this is all the rote knowledge that students need to be proficient at the standard) methodical step-by-step reasoning skills (these are all the reasoning skills that students need to be successful at this standard)
perform the standard algorithm for division (this is a list of everything the students need to demonstrate in order to be successful at this standard)
N/A (This is a list of all the things that students need to produce or create in order to be successful at this standard)
6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plate. Use tables to compare ratios

b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowe in 35 hours? At what rate were lawns being mowed?

c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Vocabulary: rate, ratio

1) Compare rates and ratios 
2) Reason connections between rates/ratios and real-world situations
1) Plot values on coordinate plane
2) Solve unit rate problems
3) Convert percentages to fractions & decimals
Table of equivalent ratios

3) Each teacher devises several example assessments appropriate for the type of task (i.e., knowledge, reasoning, demonstration, product) required for each standard (devised via Marzano's thing) 

4) All the teachers for the grade level get together and develop a full set of assessments for all the standards for that grade (e.g., the 6th grade teachers get together and develop a full list of assessments for the 6th grade standards)

5) Create a timeline dictated by the assessments (e.g., determine when each assessment needs to be given to the students so that every assessment created in step 3 is given within the full school year)

6) Teachers develop lesson plans as part of a professional learning community that will provide each student the opportunity to pass each assessment

When we were coming up with this plan we were thinking that each teacher could be responsible for creating a set of example assessments for each standard. Filling in the table should help guide exactly what kind of assessments would really show that students are proficient at each standard. Then, when all the teachers get together, they can share out what they have and work together to make a rigorous battery of assessments for each standard. 

Yes, this would take a lot of work. But what's worse, spending the time now to set things up right in the first place or slapping something together now and spending the next ten years picking up the pieces? 

Just a thought.