# My students take their EOCT test tomorrow

I feel like a parent sending their child out into a storm. I’ve made sure their coat is buttoned, they have dry boots on their feet, and a good umbrella. They are prepared…. Or are they?

The state says this is an important assessment. I tell my students to answer the best they can, and leave no question unanswered. I think, I could have done more; why didn’t I go over this or that; we should have done more with probability; will they remember what capital B is in the area formula?! Oh well, it is their turn now. I want them to taste success, to let their grade reflect what they truly know, and, at the same time, afraid that their grade will reflect what they truly know!

EOCT : end of course test or end of career terrors…. Either way, we will know soon! No matter what, I’ve seen my kids grow. I am proud of what I’ve seen them learn. They will be okay, No Matter What! That test is just a snapshot of tomorrow, and after that it will be a blip in history. In the meantime, I hope they remember to use their umbrellas!!

#MTBoS30

# Who knew cooking was discrete math?

#MTBoS30 post two.

I was trying to help a student understand the reasoning required to find the shortest time possible to complete a project. His assignment had a chart and a map like grid of lines. The chart showed pre-requisites using letters, with the time to completion given. The student was struggling to understand what he was doing. I chose to assign context. Together we planned a thanksgiving dinner complete with time frames for everything from cranberry compote to pumpkin pie. The oven controlled the overall plan, as we determined the minimum time possible to complete the preparations! I think he got it, as he quickly completed three more paths. Interesting. Who knew all those Thanksgiving dinners were good for more than overdosing on Turkey and whipped cream covered slices of pie!

# Paper Cup Probabilities…

This is my first entry in #MTBoS30 Today I asked my 10th grade geometry class three questions (review time!)
1. What is the probability of rolling a one (using a regular six-sided cube)?
2. If you flipped a coin, would you expect it to come up heads?
3. What is the probability that a paper cup tossed in the air will land on its side?

The ensuing discussion involved certainty. First question:
1Ss: one out of six
Several other students chimed in in agreement.
Me: who can tell me how you can be so sure?
2 Ss: because the cube has six sides, and the sides are numbered one, two, three, four, (she is ticking off on her fingers; other students were nodding in agreement and telling her what to say) five, six, and there is only one side with one!
This class is usually not this involved. I think it had to do with the fact that they really KNEW this! (Confidence is a wonderful thing!)

Second question (key word here”” “expect”)
1 Ss: yes, well, no, (???) it could be heads or tails. I mean, you could expect a heads or a tails.
Me: why can’t you expect just heads?
1 Ss: because it’s 50%. (At this point, other students begin chiming in:
“Yeah, it’s 1/2!” “A coin has two sides” and similar statements.) The question wasn’t a straightforward question about a probability fraction, so I think that caused them to not feel as confident with the answer, until one student decoded it. Think: lemmings!

It was the third question that really threw them. I held up one of those small cups, like you find in a bathroom cup dispenser. I asked them to tell me what they thought the probability would be of the cup landing on its side when tossed. The guesses ranged from 1/2 to 340/500. As we looked at the cup, the guesses got more specific. Several students noticed that the cup had a top, a bottom, and a side. The reasoning followed that there should be a 1/3 chance of landing on its side. At this point there was quite a bit of agreement. This seemed very logical (and if the strongest kids in the class said so, it must be right! Lemmings, I’m telling ya!) Multiple students jumped on the bandwagon and agreed. (No one talked about surface ratios – I figured we could tackle that later!) Then I gave each student a paper cup and asked them to create 20 trials each. I deliberately refrained from telling them instructions for tossing the cup. I just walked around and watched. Some kids tossed (across the room!), some kids tossed on their desks. Some dropped the cups on the floor. I heard disappointment as Ss complained, “it’s landing on its side every time,” how do you make it land on its top?” “There is something wrong with this cup!”

The trials were listed on the board and tallied. The students really seemed puzzled as to why the results weren’t anywhere near what they expected. They were already arguing why this was so, so I put them in groups with the instruction to:
1. Compare the actual probability from the trials to the expected.
2. Come up with some reasons for the difference.
3. Pick a spokesperson to share their ideas with the class.

Then the bell rang! Okay. The debriefing happens Monday…

# Mathematical practices are more important than standards: Eating the Elephant

One really wonderful thing has come from the Common Core Standards: the 8 Mathematical Practices. Now, whether you love, hate or have no real opinion on the Common Core, please hear me out.

The 8 Mathematical Practices (MPs) are designed to produce good thinking, reasoning, defending and critiquing skills, as well as fostering perseverance (that GRIT
you may have been hearing about), and enforcing the idea of accuracy and attention to detail. These just happen to be the skill sets for success – in any field!

It is my observation that students who lack some or all (and many of the students I am teaching this year lack all) of these skills are struggling with learning.

We can say that this is a problem of laziness, we can blame it on years of spoonfed students, we can fuss about how it is next to impossible to change students’ learning (not completely impossible!), but in the end, we have to simply begin to eat this elephant. I believe that focusing on these 8 MPs will allow us and our students to taste success – of all kinds.

At my school, we are encouraged to be consistent: enforcing student dress codes, the tardy policy, class behavior, and other important policies that affect our students. We talk about success and poster-ize all sorts of great pithy sayings. Then we lament the way the students ignore all the great ideas and opportunities.

Why don’t we get consistent in a very specific way: the 8 MPs. Let’s apply them to every subject and evaluate students on how well they utilize these skills in every applicable assignment. Instead of warm and fuzzy quotes about success, make clear statements about the actual actions we require.

Rubrics are a good start – for you and me! What do these 8 MPs look like for your lesson? What will the student be doing? What will you do to facilitate these actions?

Right now, my class is working with Quadratics. For geometry students, this involves vocabulary (standard form, vertex form, parabola, factoring… All the way to identifying the vertex points x and y, and the roots, zeros, and x- and y-intercepts, depending on the application). There are word problems. There is graphing and interpretations of graphs. All of this comes with multiple steps, plugging answers back in to get the next answer, using a different process to get vertex information, identifying that nasty domain, range, max, min, up, down…. Some of the equations can take a full page, or more. And then we ask them to check their answer (and watch their heads explode as they cry, “this is too much work!” Or the class dissolves into disruption!) Did I mention that they must also decide which answer is reasonable? (Distance and time can’t be negative, right?!?)

All I am saying is that if we review the skills needed to navigate that last paragraph, it is pretty clear that without the MPs, our students will struggle. Yet many teachers remain perplexed as to why the students don’t “get it”, even after repeated, differentiated, broken apart, 1-2-3 lessons. I think by focusing on teaching standards we are missing the more important focus on the learning postures of our students. Don’t get me wrong, we do need to identify the focus of the lesson because the students need to know what success looks like. They also need to know what success feels like, and sometimes that feels like impatience, frustration, and trying again and again, but then again, it will also begin to feel like SUCCESS. (Which can be pretty heady stuff!)

My recommendation for “Eating the Elephant” is the very basic answer of “one bite at a time”:

First bite: post the practices on your wall. (Talk with your students- let them tell you what they think the practices mean, and what this will look and feel like during a lesson.)

Second Bite: before and during a lesson, in addition to talking about the focus of the learning, also identify and recognize the practices that you see your students engaging in. A smile, a thumbs up, an encouraging comment; all go a long way towards motivating and keeping students trying.

Third bite: grade for these practices. Let parents know what we need from Johnny and Suzy. That it’s about more than homework and cramming for a test. It is about more than just being able to work 20 identical algorithms without understanding. It is about giving their kids confidence, mining for that long-buried curiosity that will take them farther than anything else we can do as teachers.

Fourth bite: tell your administrators. Ask them to speak directly to these expectations across all disciplines. Let every student “poster-ize” the practice they think will be the hardest one. Put them across the school instead of the slick marketing slogans that students don’t bother reading. Watch as they say to their friends, “that one is mine. I am working on it. My next poster is gonna be the (insert MP# here)!”

My posters go up Monday. I’ll keep you posted on the results. Oh, and could you please pass the salt?!

picture credit:Sarah at Everybody is a Genius blog

# Common Core Aligned Lessons: Rich Tasks, or Same Stuff, just re-aligned?

I got an email from Achieve just this week inviting teachers to start testing the lessons on the Achieve the Core website.

I was so excited! All of this with one search tool! I clicked through: There were lessons for every standard! I clicked again: For every grade! I quickly clicked on the lesson promising to teach students to find the zeroes of quadratic equations (that’s such an important concept and I was looking to expand on the rich task we used in the workshop). And then… Well, does anybody remember the sound the record player made when the needle would slip and slide across the vinyl??

Since attending Common Core Standards training this summer, where we learned how to implement rich tasks for conceptual learning, and learning about Dan Meyer’s work, I have been interested in sources of these strong lessons and in modifying many of my existing lessons. The Stanford class ‘How To Learn Maths’ cemented my desire to get even better at teaching math through numeracy, rich visualizing, and good questions to get students thinking about what the numbers they are using really represent.

Here is what I found:
My click on the quadratic lesson connected me to the website Share My Lesson. The lesson plan was beautifully written: standards, number of days, list of materials (hmmm, a graphing calculator, but not graph paper?), the detailed notes handout- one for each day of the two day lesson (fill in the blank), and even a group ‘discovery activity’. Further down, there is a chart with a column of expected student answers/misconceptions, etc. that looked interesting, (in fact, that was the best part) and another section with a three column ‘prior knowledge, current knowledge, future knowledge’ chart (although prior and current knowledge would seem to be the same thing, but current knowledge is apparently what they are supposed to learn in the lesson; which makes that future knowledge in my book!)

There isn’t any instruction on the formative assessment, although perhaps the teacher will make sure the blanks on the notes are correctly filled in…

I fast-forwarded to the instructions for the lesson: graph (using the calculator) four given quadratic equations and identify the zeros. Hmmm. How are they supposed to know this? I checked the prior knowledge column on the lesson plan. Nope. Nothing about zeros. The current knowledge column (remember: the goal of the lesson) was that the student ‘would be able to’ find the zeros of the factors of the quadratic. Factors? But we didn’t factor anything. Oh, wait, it says here that factoring is the next lesson! STOP!!!

Where is the rich task? Where is the productive struggle? Where are the mathematical practices?

This great lesson, common core aligned and all, appears to be more of the ‘feed kids details and have them take notes’. Even the group activity, having them find the differences in the graphs isn’t creating the conceptual understanding of what they are doing, what the graph represents…. Can you feel my frustration here?!

We (teachers) are going to have to undergo a shift in thinking about what good lessons look like. It is going to require kicking out textbooks and no longer training students how to get good at multiple choice tests. This is a paradigm shift. Yet, here is the Achieve the Core website leading teachers to more of the same dry, lecture heavy, notes and memorization-filled stuff!

In the interest of good reporting, I went to two other lessons, one for sixth grade on fractions, and one for eighth grade algebra. They were similarly structured.

If you are interested in what this national resource of lessons is offering – and interested in helping improve the lessons – then here is your chance (you might even win stuff!):

Participate in the Common Core Challenge:
1. Watch short videos of master teachers while using the CCSS Instructional Practice Guides
2. Apply what you saw to a lesson of your own