Traditionally, every level of math through eighth grade included a variety of strands: geometry, algebra, number sense, statistics. Did you know that when kindergartners organize buttons by color or shape they are already using algebraic reasoning? Obviously they don’t have an entire class called “Algebra for Kindergartners,” but sorting buttons is foundational to being able to sort variables and unlike terms in Algebra 1.

Additionally, math scores for elementary students are typically MUCH higher than the scores for junior high and high school students. And they usually aren’t even being taught by so-called math teachers. What is happening there that isn’t happening at higher levels?

Many high schools – including mine – are moving to what is called “Integrated Math,” which I see as emulating the long-proven success of K-8 math as well as simply applying decades of research as to how children best learn. It integrates geometry with algebra and statistics and forces kids to reason through difficult problems that might not have an obvious answer or one particular set of steps to get to the solution.

Please disregard the isolated examples of “common core math problems.” There is no such thing as a common core problem. It’s a set of standards, not a set of problems. How it gets taught is given just as much academic freedom as its predecessor. There are lousy problems that try to address Common Core standards and terrific problems that try to address Common Core standards.

Also, many publishers were quick to throw out a bunch of textbooks labeled Common Core. In more cases than not, it was just a new stamp or label on the previous edition, many times with the same publishing/printing mistakes that had already been discovered. Just because someone calls their material Common Core doesn’t mean they are representative of this shift.

I’m teaching 8th and 9th graders this year, and it’s fascinating to see the new integrated approach for 9th graders so closely emulate the 8th grade model. Traditionally 9th graders would take Algebra 1 or Geometry. And that’s it. There might be a few problems in the Algebra book here and there that are called “geometry connection” or something like that, but it’s not a concerted effort to truly mesh the disciplines on a constant basis. And it’s a focus on “enrichment instead of advancement.” In other words, being able to finish a textbook isn’t an automatic pass to the next one. They should learn the concepts more deeply before moving on. This is one of the biggest challenges as an educator: how to challenge those who “get it” quickly.

Think about it this way: if you were really proficient in your freshman English class, they wouldn’t throw you into English 10. Why do this in math, then? If math is seen as just a collection of facts and rigid steps, then you can “level up” quickly and just keep moving on. But if it’s seen as a rich, dynamic discipline that can be explored ever more deeply, then it’s pretty tough to completely master a topic. This is how it should be.

Don’t listen to Glenn Beck. This is not a federal movement. It was a grass-roots movement started by educators. Unfortunately this all happened contemporaneously to the ill-planned “Race to the Top” but Common Core was sponsored by the governors association and the top education officials in each state, not from the federal level.

At a STEM conference I attended last November, this startling statement was made: “This year’s kindergartners will retire in 2073. What are we doing in the classroom today that will truly make a difference in their lives and in their world?”

I dare say: not the same thing we have been doing.

]]>Exit slips are a great way to gauge immediate understanding of a concept. They don’t test long-term retention, and so it’s not a cure-all, but often at the end of class I give out slips of paper for students to complete a short exercise or critical thinking problem to test their understanding of the day’s concepts and objectives. (As an aside, I’ve also become a recent fan of “welcome slips” in addition to the warm-up — especially for a concept that might be a week or two old just to see if they truly “get it”).

So back to my exit slips: my main issue with these is always collection. I’m often squeezing these into the last 1-4 minutes of class, and so sometimes not everyone is finishing, leading to a general panic among the students about what to do with them or how to hand them in. I tried :

- having them leave them on their desks (only if there was a break or my prep right afterward)
- having one person in each 4-person group collect them, but this unfairly holds this person back from getting to their next destination. Even if it’s only a half-minute, this perceived difference can be frustrating to the student
- standing by the door and having them hand them to me on their way out. But it’s such a rush to get out the door that I’m having students give them to me upside down, backwards, etc., to where I find myself grabbing at quarter sheets of paper as if I’m juggling balls of jello.

I really want is to take 60-120 seconds, give a quick “+”, “1/2” or “0” to all the slips to see if they learned (and if I taught!). It helps me to know if where I hope to start the next day is appropriate or not. I am – admittedly – not very organized naturally, and so I have to work pretty hard to keep on top of paperwork. If I don’t do this right, it just becomes one more type of paper to accumulate in my classroom.

Enter “**the idea**.”

I took a small blue bin ($1 from the Dollar Tree), and right near the door I secured it to the wall with 3 screws.

Now they were set.

The next day I tried it out, and had all the classes just drop their slips into the bin on their way out.

Easy as pi(e).

A couple modifications I’ve made since then:

- I put a custom-fit portion of a manila folder inside the bin so that I don’t have to scrape the last few sheets off the bottom; I can just grab the folder out when I’m ready to take the slips.

- I put a small colored slip of paper on top of the stack after each class dismisses so I can easily segregate the slips by period at the end of the day – or any time sooner that I want to access them.

Now I can just grab the folder and go. By designing the right kind of problem, I can get through the whole stack (~120-140 sheets) in under 5 minutes. It provides excellent feedback as well as helpful direction for the next day’s lessons.

Many of my quizzes are on half-sheets of paper, so “the bin” also works well for this size of paper.

]]>Today’s lesson was finding the surface area of a cone. I had just gotten to this slide:

and was talking about the “wedge” that comprises the lateral surface area.

“It’s like … ” I said, and I got kind of excited. I walked quickly to the other side of the room. “It’s like when you stick a bunch of binders together with the spines all facing out. I frantically grabbed about 10-12 binders from my shelf and arranged them on a desk.”

That was the 2nd period oh-my-goodness-this-might-be-a-really-cool-visual-but-I-didn’t-prepare-for-it version. When my other geometry class came in, I was prepared. While they were doing their warm-up problem, I scooped up 8 binders and just plopped them onto an open desk. “That’s part of our lesson today, huh?” said one student sarcastically.

“Actually, yes.”

When I got to the slide above, I had them write down the images, then put their pencils down and gather around me. I arranged the binders like so:

I had all 27 students within about 4 feet of me. They were all starting to get the connection.

“Ah, so the edges of the binders are the blue lines (the slant height),” one said. The image was being projected right next to me.

As if on queue, another said “and the spines are the green arc.”

“How many of you have tried to do this on a shelf?” There was a collective appreciation for this dilemma.

“And how do you resolve it?”

A bunch of them said “turn every other one around.”

:”Like this?”

“Yeah,” they all said. While they made the initial connection, I think many probably thought they were just helping me with an unrelated problem (too many binders on the shelf).

“So what shape is this top surface now?”

Then they saw it. “A rectangle.”

From this point, connecting the fact that we’d split up the wedge into pieces that we reassembled into a rectangle was obvious. And this normally pretty complicated conclusion

]]>“I get to turn the lights on and off all week,” our son (our oldest of 3) boasted last week. “And I even get a piece of candy at the end of the week.”

Cheap help, but even candies would get a little tough to keep on hand. Especially with 5 groups of students coming through my doors each day, and especially with my mid-late afternoon appetite. But there is one currency that all high schoolers appreciate.

Extra credit.

I had a whiteboard in my room that I had never found a good use for. It’s too small to use for lecture/discussion, but too big for a student to have at their desk. So I fashioned this:

Now all I have to do is draw three names each week. My lights are taken care of. My projectors are both on (yes there are two in my room). Homework is collected and the previous day’s (or days’) worth of paperwork is handed back. Another person is my go-to for handing out worksheets and is also the back-up for the other two duties for when someone is absent.

At the end of the week, they get a voucher. The voucher gives them one of the following:

– an excused tardy up to 3 minutes

– a restroom break during class (HALL PASS is boldly printed on the reverse in case they use it for this)

– a free homework assignment

– if none of the above, extra credit at the end of the semester

My only concern was buy-in. But I was honest with them. I told them where I got the idea. I reminded them how fun it can be to help with some simple tasks in class, and that they essentially get extra credit for helping out. The amount of extra credit they get is very inconsequential; 1 free homework last semester would have been worth about 1/3 of 1% of their semester grade. But already classes are helping remind their peers about their duties if they forget. “Mr. Ratliff, aren’t you taking Stephen’s job?” a few asked when I was handing back quizzes today. “Indeed I am,” I said. “And Stephen still gets the extra credit!”

I’ve created short 1/3-page job descriptions to give at the beginning of the week to the 3 lucky ones in each period. I probably save 2-4 minutes each period. But I also get old papers passed out much more quickly now, which honestly was just not happening very frequently before. If at all.

Even for just the time savings, though: 2 minutes • 5 instructional periods • 5 days per week = 50 minutes

Add to this I already have significantly less paperwork to look at in my outboxes.

Maybe I won’t make every single student love my class. But I sure am loving my class a little more.

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I’m writing with inspiration from an 8-week project being steered by MTBoS. I’ve had a couple personal blogs over time, but this one will have a decidedly different focus. I first discovered this project through Dan Meyer’s twitter feed.

Following with the prompt for this week, My first entry is going to discuss **a favorite rich question from my class**.

It’s my 6th year teaching. It’s my 2nd year at my current school. I feel more organized, more focused on my content, more in control of my classes, and like my kids are learning multitudes more than in any other year. Part of it is the experience behind me. Part of it is reaching a 2nd year at a school (only happened one other time so far) with prospects as certain as could be expected that this is the beginning of a beautiful relationship.

But quality learning requires more out of everyone.

It requires more effort out of the students.

It requires discipline on my part to know what questions I will and which questions I will NOT answer.

It requires quick thinking on my feet to help address and triage questions around the room when 6 to 9 groups are working on a problem.

This week all of my classes had an introduction to a process called *reciprocal teaching*. In RT, groups of 3-4 students complete a small number of problems (so far no more than 4) in a period. They are required to follow a procedure where they:

– CLARIFY what they do and do not understand

– PREDICT what they think the answer will be or what it will look like

– SOLVE using math operations and procedures *(NB: this is usually the only process required by a math problem*)

– SUMMARIZE their thinking and their math

– CONTEXTUALIZE the final answer

All of the writing requires complete sentences. And it is D-I-double F-icult to extract the thinking at first. During the first couple problems, I end up having a lot of conversations like this:

** “Mr. Ratliff, can you tell me if this looks right?”**“Oh, Josh, I’d love to help you, but you haven’t written anything about what you do or don’t understand or made a prediction about the problem.”

By this time I either get an explanation, which I ask them to put into writing, or I get something like** “I can’t explain it, I just know it,”** to which I reply “I’m not convinced. Why don’t you visit with your group and I’ll come back by in a few minutes to see how you are all doing. If you’re still stuck at that point, I’ll be glad to give you a couple pointers.”

A colleague at another high school with similar groupwork mentioned that he requires all group members to raise their hands before he will stop by.

Right before setting my Algebra 1 students loose on Day 2 with problems 3-6, I handed them back their problems from the previous day and then showed them these 6 examples from the previous day (students saw work from a different period). The performance on Day 2 showed vast improvement even with more difficult problems. FWIW, the respective scores of these 6 pages (out of 10) were 1, 1, 9, 9, 10, and 2. Note that the math only constitutes 20% of the possible points.

I’m excited to hear about what you have to think about this, if you’ve used something similar, if you’re inspired to do so, or any constructive feedback you have about this sort of activity.

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