A word about teaching to the test…

It’s testing season here in Michigan, the dawn of a new age! Last fall’s paper and pencil MEAP is replaced with the this spring’s computer-driven M-Step.

And the M-Step is putting a lot of pressure on districts to reconsider what “test readiness” even means. What skills are required of a student who is having to transition from a question like this:

MEAP Grade 8 Practice

to something like this?

MStep Practice Grade 8

The “Performance Task” is another new type of test item. Teachers lead a scripted discussion through a content exploration. Students get time to discuss, explore, ask questions. Then they go off to answer a question based on the experience they just had. This all combines to create a startling amount of new experiences all in the same year.

Preparing educators for this newness was a large chunk of my work as my colleagues and I provided workshops to help explore this testing experience that is new for all of our students. As I had discussions with genuinely and appropriately concerned teachers and administrators, there were a few recurring concerns that bubbled to the surface.

1. What if a student knows the right answer, but has computer/technical skills that prohibit him/her from answering that question correctly (or in a reasonable amount of time)?

2. How are the non-traditional items going to be graded? (Non-traditional… rubric scored items, items with more than one correct answer, the drag-n-drop question like the number line one above, etc.)

Certainly there were lots of other concerns, but these two kept coming back again and again with good reason. We want to make sure that our students are getting recognized for the knowledge and skill they possess. This new test presents a new set of potential barriers.

So, how do you get around those barriers? Well, one way is to teach to the test.

“Teaching to the test” as a phrase is usually not seen as a good thing. Although, I can remember a conversation with a district leader a while back who was quite proud of the fact that curriculum decisions for their math department were based almost solely on what was on the ACT… he refrained from using the term “teaching-to-the-test”.

This pride fits in with recent statement from a colleague. “Teaching to the test is only a bad thing if the test is no good.”

Now, that having been said, there are a lot of people right now in Michigan who are feeling like the M-Step is no good and they might be right. As I write this, we’ve just completed our second day of testing, so I’m going to reserve judgement until we’re more than 48 hours into this new experience.

But regardless, that sample question from above…

MStep Practice Grade 8

… isn’t a ridiculous question. It lends itself to considering if teaching strategically in such a way that students could do that (which is motivated primarily by the fact that a high-stakes, state-level standardized summative assessment is going to ask them to do it) is a bad thing? I would suggest that this is a task that most 8th grade math teachers would want their students to be able to do. Where the conflict arises is when teachers or districts aren’t inclined (or able) to provide exploration or assessment of this skill in a computerized way. The test becomes a motivation to have to change course. So we find ourselves faced with “teaching to the test.”

So, if we’re going to be “teaching to the test” anyway, what situations can we design for our students that while we are probably only doing ten because they will be on the test, are still, in the end, high-quality experiences for the students to have?

One suggestion comes out of this blog post from Fawn Nguyen who is trying to help the students interpret a scoring rubric. That was one of her goals, because her second goal was to help the students focus on a set of skills they will need to be successful on the test they are going to take in May.

The skills she’s referring to: “For them to attend to the same thoroughness and precision in their own solution writing when it’s their turn…”

While Ms. Nguyen is openly “teaching to the test”, that skill she’s highlighting is a valuable one. I encourage you to read the post. The tone of it doesn’t sound like someone who begrudgingly throws test prep items at her students, but rather a teacher who saw an opportunity to weave test prep into an experience that ultimately led to student feedback like this:

I believe this was helpful because when I take the test, I will be more aware of the questions and what is expected of me. I will make sure to always back up my answers with evidence.

I’ve talked to a lot of teachers (math, ELA, social studies) who’ve expressed frustration that their students won’t “always back up their answers with evidence”. Ms. Nguyen provides us an example of how a test prep experience can be used to further broader goals.

And I think, in the end, given the stress and strain that these testing situations put on all of us, it’s nice to see an example that reminds us that teachers still have ability to make decisions that end up as net positives for our students.

Why do we collect student work?

 

 

 

For a couple reasons, I’m sure. Here’s one of mine: to turn it around and let them see it.

Best Proof Snip

 

“Here are four proofs written by your classmates. Which of them is the best? Why? Which of them comes in second place? What would the second place proof need to change in order to tie for first?”

 

Such good conversations arise when students explore decent examples of their own work compared to their classmates. And they don’t have to be time-consuming. If the work suits it, you could create a 5-minute opener comparing just two pieces of work. It can be a wonderful way for a student to recognize his/her own mistakes without me, as teacher, having to reveal them. Such recognition is a wonderful evidence of internalization of the content… real learning that can be used to solve problems.

 

Why do you collect student work?

 

Student Blogging: Off and Running

After the encouragement of a few folks (among them, Hedge (@approx_normal), Zach (@z_cress), and Jennifer (@RealJMcCreight)), I decided to move forward with my admittedly medium-rare idea to have a class start a blogging community. I needed their encouragement because I hadn’t ever SEEN anything like this done before in math class. I’ve seen examples at the elementary level. I’ve heard about English teachers doing this, but the benefits of active engagement in a blogging community to a class of math students was purely hypothetical.

So, with that in mind, I decided to leap (and then look at where I was once I landed.)

curious? alg2point0atphs.wordpress.com/

I decided to leap…

I sold it to them in this spirit: Algebra II is the last math class that Michigan specifically requires high school students to successfully complete in order to graduate. That makes Algebra II the series finale. This is the last season. A sitcom that they have been watching daily since 2004 begins it’s final season this fall. They have spent more than a decade learning different kinds of mathematics and Algebra II is where we show off how it all fits together. We are able to reveal where it was all leading.

The blog acts as an extension of that. If they are going to take anything of value from the dozen years of math we lead them through, they are going to have to internalize their experiences. The blog is going to give them an opportunity to make visible a portion of that internalization.

Here are the structures I am using:

I am requiring a single post per week, along with a single meaningful comment on another person’s blog per week. A post should be between 150-500 words (because they asked). This is designed to enter them into the world that I know exists for more bloggers than just me. That is, becoming observant of the world around you thinking what you might write about. (The first topic I asked them to write about was the most enjoyable math-related experience they can recall in math class.)

They are required to follow all of their classmates’ blogs. This ensures that their WordPress homepage readers are displaying recent posts.

I have a rubric that I will be following to hold student’s accountable for actively participating in the blogging community.

 

Already, this has allowed us to consider a variety of different relevant topics that are not normally relevant to a math classroom, but are darned interesting to talk about. The value of pictures and story-telling in conveying meaning, the consideration of audience, the use of images and movie clips, digital citizenship, etc.

It has worked to make the class more holistic, which needed to happen if we are really going to take the series finale approach to this course. There’s value in that because the last 10 years of math class haven’t just been about math content. They’ve been about math habits, problem-solving techniques, specific tools, vocabulary, and a variety of technology. To focus purely on content would be to miss an opportunity to help them make sense of all of those experiences.

And to solidify those things is to provide a springboard to launch the students into an opportunity for spin-offs once this required Michigan math series has reached its conclusion.

Here are the handouts I used to introduce the blogging community to the students. None of these handouts stood alone. All of them were given as part of a large-group question-and-answer session, so keep that in mind as you read them and notice details left somewhat vague.

Handout 1

Handout 2

Handout 3

My Most Recent Thoughts About Student Blogging

I have spent the last few months processing this temptation to integrate student blogging into my instructional practice. I have some medium-rare ideas. And some Iron Chef colleagues who do a nice job of focusing my thoughts and cooking medium-rare ideas. Like this very evening in a conversation with two such colleagues:

 

 

Like… bingo. That’s it.

 

So, here’s are my goals. Here’s what I’d like to accomplish:

A. I want to give the students a meaningful way to explore math topics, or think mathematically when they aren’t in my classroom. I don’t trust traditional homework problems to achieve this goal. I think there is value in understanding that in class we spend an hour exploring thoughts and ideas that have real value during that hour and the other 23 hours of the day. I’d like to create SOME mechanism that enforces that.

B. I want to give the students a chance to develop their own voice when talking, writing, and reasoning mathematically. Too often, I use gimmicky phrases, memorized lingo, and rigid vocabulary to guide student language. There are wonderful reasons for this. But, I want them to develop their own voice, too. I’d like to see them develop their own ability to verbalize a mathematical idea and…

C. I want to open the students’ ideas up to each other and to the greater math and educational community. I feel like this will offer a level of authenticity that simply having the students submit their work to me wouldn’t. Also, I want them to be able to think about the mathematical statements of another student and respond. I want to break away from this idea that the students produce work simply for my review. A mathematical statement isn’t good and valuable simply because I say so.

I think blogging can do that. I am sure other things can do that. Perhaps other things that are easier. Or less risky. Or have undergone better battle-testing. Or…

 

And as for the second question. The evidence would be a gradual improvement in the math discourse in class. More people talking, and talking better. Explorations becoming richer. Questions becoming an increasingly regular occurrence. Students trusting each other, and themselves, and not looking at me as the lone mathematical authority in the room. We would begin to talk and explore together, and sense-making would become a bigger and bigger part of what we do.

I told you. Medium-rare ideas.

I’m hoping that some more of my Iron Chef colleagues will take my ideas, season them, finish cooking them, and help me turn them into an action plan.

claimtoken-53f7440dd13f5

My advice to the newly “en-Twitter-Blogged” (reflection on #edcampmm )

Today I got to meet a lot of folks at EdCamp Mid-Michigan in Charlotte, MI. Some of them are seasoned tweeters and bloggers (Elizabeth Wellfare – @ealfoster or Tara Becker-Utess @t_becker10, for example) and some are just starting out. A couple of people got set up with their very first Twitter handles today. Welcome. I talked to a couple folks who are interested in starting their own blogs (or rethinking the way they use the blog they already have).

Now, that EdCamp is over, we start the “now what?” stage of all the new stuff we learned.

What are we going to do with it?

How intensely do we want to attack it?

How is it going to be useful to us in the practice of constantly improving as educators?

All of these are fantastic questions. We discussed some of these issues already, but I want to offer a bit of encouragement and advice.

First, don’t be afraid to be selfish. (I believe Dan Meyer – @ddmeyer gave this same advice a few weeks back). By that, I mean that you are likely going to take a WHOLE LOT more than you give for a while as you start out in the world of twitter and blogging. That’s okay.

The first major idea is trying to decide what you want the Twitter feed or the blog to do for you and your professional practice. Sometimes the first step in that is seeing what other people are doing. How do they tweet? What do they tweet about? How do they use #hashtags? What do they blog about? What types of blogs/tweets are interesting for you to read?

Tweet and blog about the stuff you find interesting. Your blog and your tweets should AT LEAST be interesting to you.

Second, keep at it. When you first start tweeting/blogging, chances are that you (and a very few other people) are going to be the only ones reading. That’s okay. That changes over time. The more you write/tweet/interact/question/comment/favorite the more you will find people who are trying to do the same things you are doing. And THAT is what you want. You want to begin to form a network of people who are all trying to support each other in common goals.

Now, if you are brand new to this, follow me at @hs_math_phys. When you start your blog, tweet me the link to your blog. I look forward to reading your ideas and thoughts.

Finally, if you want a nice network of people who want to read your thoughts, check out The MathTwitterBlogoSphere homepage for a ton of GREAT bloggers and tweeters. Don’t let the name fool you, it’s not just for math teachers. There are takeaways for educators of all makes and models. They are good people.

Welcome to our world. Please don’t be a stranger. And Please, let me know what I can do to be helpful.

Student blogging has me thinking… (reaching out for help once again.)

I think I want to try student blogging next year in my Algebra II classes. I’ve only ever taught Algebra II once and I didn’t do a particularly wonderful job.

It was the sense-making that really got to me. My students were pretty good at learn procedures and algorithms, but the long-term retention was remarkably low. I have seen several examples of student blogging and feel like if I framed the discussion questions properly and encouraged the students to read each other’s posts, and comment. That could… COULD… open up a different mathematical thinking experience for the students.

If that were used to supplement the number-crunching practice, and the group problem-solving and exploration, that could potentially act as a way to deepen (or at least broaden) the thinking that the students were being asked to do. In addition, the opportunity for the entire internet to read and respond can add an extra-level of interaction. The students wouldn’t have to apply their real name if they didn’t want to. There is a chance for creative anonymity.

All of that being said, if you have your students blog, will you please comment on this so that I can pick your brain on what’s worked, what hasn’t, what to watch out for and what to definitely do! Links to other blog post would be much appreciated. E-mail this post to people you know who do this. I would love a rich, challenging comment section on this one. And trust me, if you don’t help me, I will make my own idea and learn this the hard way!

 

 

NPR wants to advise your pizza order…

Quoctrung Bui from NPR says that there are at least 74476 reasons that you should always get the bigger pizza. (The article has an awesome interactive graph, too!)

If we could mix the article with a math exploration, we could provide an awesome opportunity for a math-literacy activity that can combine reasoning, reading, writing, and some number-crunching all in the same experience. That’s a nice combination. Also I suspect the content hits close to home for most students. (The leadership in our district is often looking for opportunities to increase authentic reading and writing in math classes. This seems to fit the bill quite well.)

Here’s an activity:

Although without fail, the menus from a variety of local pizza joints will probably be a bit more engaging. (Look for an update coming soon…)

Shauverino Pizziano

But the big question is why?

According to Bui: “The math of why bigger pizzas are such a good deal is simple: A pizza is a circle, and the area of a circle increases with the square of the radius.” 

Yup… that’s pretty much it.