I want to see the volcanoes

We live in Memphis, TN. The nearest volcano is…well, I have no idea. Volcanoes are just not a thing here or anywhere near us. So when my four year old said that he wanted to see “the volcanoes” while we were driving through a local park, I was a bit thrown off.

Me: What do the volcanoes look like?
Four year old: Um…they look like cows. and furry. four legs and horns. I want to see the volcanoes!

Think you know what he is talking about? In an article reflecting on mistakes in the math classroom, Dan Meyer encourages teachers to respond to incorrect answers with a simple question: what question did this student answer correctly? When I first read the article, I heard what Dan Meyer was saying about mistakes but let the idea faded away with all the other things that dont feel super important or relevant. But then came the volcanoes. My son knows what he wants to see and can describe a few characteristics about it, but he does not yet have the formal language to accurately name the thing. If I assume that my four year old is making sense and is actually describing something that both exists in Memphis and he has seen in the park, I can (probably) figure what he wants to see and can then help with the things he might not fully understand yet. If that idea makes sense in parenting, then maybe I need to take another look at it in mathematics.

 

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I just want to play…

On the way to soccer practice, I was talking to my son about his PE class.

Son: My teacher says that we are not good enough dribblers yet
Me: Do yall dribble in PE?
Son: No…and me and so and so ARE good dribblers…[he then he makes an “are you kidding me” face that I am 100% certain made when the teacher said …which is not endearing]
Me: What do you do in PE?
Son: We do figure 8 around the legs, the waist, stuff like that
Me: How do you like that?
Son: It is ok. But Dad…I just want to play.

I immediately thought of Lockhart’s Lament and how, inadvertently, the PE teacher had taken the dribbling and playing out of basketball in order to teach the players the fundamentals of the game. If this is your experience in basketball, you will probably end up looking for a different “game” to play. As a math teacher, the question I keep asking is how can I use the game to teach the game. I have not figured it out yet and am exploring this idea on a lesson by lesson basis, but I want to be about students playing and experiencing the game.

 

 

Is equal education big enough?

What does equal education mean and is it a big enough goal? Through various circumstances, I had the opportunity to compare two math lessons that were taught on the same topic. One school in our city is considered by most to be THE elite private Christian school. Based on what I have heard and seen, I think the opinions are well founded. Based on location, history and price, this school tends to serve the middle and upper class students in our city and does it very well. Another Christian school, located in a north Memphis, typically serves lower and middle income students and offsets tuition thanks to the generous support of nonprofit organizations in our city. Without this support, many students would probably not be able to afford a Christian education. This school also has a strong reputation, albeit a lesser one, and serves its students well.

This particular lesson was about subtracting two digit numbers. 52-19 and 75-42 would be two examples of problems that students would be expected to master at the end of instruction. What does equal education mean for these two schools with this very specific lesson? Well, I am happy to report that students at both schools had a very similar way of remembering how to subtract two digit numbers: “if there is more on the floor, go next door. If there is more on top, no need to stop.” Just to unpack the rhyme a little bit, in the 52-19 example, the “more on the floor” is the 9 being larger than the 2. We must “go next door” to the 5, “make it” a 4, and then make the 2 a 12. After all this, a student could subtract the 9 from the 12 and get a 3 and then take the newly made 4 and subtract the 1, getting a 3. The resulting answer is 33. In the 75-42 example, the “more on top” is the 5, so we dont “need to stop” by going next door and can just say 5 -2 = 3. From here, we take the 7 and subtract 4 from it, resulting in a 3.  Final answer: 33…still with me?

For this particular lesson, in these two very different schools, on this particular day, the education was equal…the only problem was that the education was equally lacking. While this lesson has numerous problems, the one that stands out to me is that the lesson does not make sense mathematically and therefore does not envision the students as sense makers. In order to learn this concept, students have to suspend thinking about how this concept connects to things they already know and why this particular concept makes sense mathematically. What is equal education? On the lesson level, the mathematical pursuit of equal education comes with built in assumptions that all students will be challenged to think mathematically and make sense of the mathematical and real-world around them. If we acknowledge these two assumptions, then the pursuit for equal education must go wherever mathematical thinking and sense making are absent, no matter where it leads. Every student, no matter their resources, even if they have an abundance of resources, deserves an equal math education, and I want to work to ensure that they ALL have it.

Two teachers…

They have the same curriculum. They co-plan and use the same materials that they adopted to meet the needs of their students. They are in the same PLC meetings. In terms of pedagogy, both teachers would probably have a similar direct instruction kind of style: they know math and can it explain it to their students. On paper, they have a very similar approaches to teaching math.

However, in the actual classroom, the implementation is very very different. In one teacher’s class, students are always doing the thing. I say “doing the thing” because, most times, what the teacher asks is not anything groundbreaking, it is not something someone would tweet about or get high praise from an admin, just basic old school teaching. And, just about every day, all students do it. And they learn. Based on the metric used by our state, they learn a lot.

In the other class, time seems to slow to a crawl. While this class is not the polar opposite of the other one, it does seem less urgent and more distracted, as if a different half of the class is always thinking about something else at any one time. And they dont learn as much…not even close.

My response to this situation has been some version of “engage students through the content” or “make the math accessible”…but, as I am looking at the data from both classes, I am wondering if perhaps the easier, more permanent solution to the second classroom comes from the domains of classroom leadership and student relationships. Instead of letting some students call out the answers, a teacher can ask a question, give long amounts of wait time, and then let all students discuss it….all year long. With student relationships, a teacher can notice specific relationships are struggling and then ask the students to have lunch, come after school to play board games, or just ask about their weekend during bellwork. Over and over again a teacher can do any of these moves and it will help a student feel known and safe and will increase the likelihood that the students will learn that day. While I realize that math content taught in a student centered and humanizing way can lead to improvement in classroom leadership and student relationships, I feel that those adjustments happen as individual lessons improve and are very hard to transfer consistently from day to day. So what am I really saying? I think I am moving towards the middle of an unknown spectrum that is not math specific…and I am trying to be ok with that.

 

Conflicting Messages

I believe that the opening sequence of a lesson should be assessable to all students, activate prior knowledge, and lead to accomplishing a grade level objective. I believe this, have taught this, and have seen it be pretty effective.

I met with a graduate the other day and she told me about her meeting with another math coach from an organization I respect. This coach taught her class and it was, in her words, “AMAZING.” He did “spend time telling my students that I was doing everything wrong.” According to the coach, the opening sequence of a lesson should be in context, challenging to all students, and be a situation that involves multiple representations. students be encouraged to draw a picture, make a table, and graph it. Students should write a gist statement, read the situation with a partner, and then draw a picture of it. When finished drawing, students should make a table and graph it. All this should be done every day. According to the “other coach,” the teacher should also pick one behavior every day, tell students what it is, and then give them points for meeting expectation for the behavior.

Obviously, this conversation rubbed me the wrong way and lead me to do some self-analysis. What was it about this conversation bothered me?

1. Not a fan about the coach building rapport with students by showing up a new teacher. Maybe not his intent but not cool either.

2. Not a fan of a coach hitting a fastball out of the park and then leaving the teacher to handle curve balls and sliders. I believe in context, discourse, challenging all students, and multiple representations. But once you leave behind the comforts of the quadratic formula and all the wonderful context that quadratic functions offer, you are facing with standards that involved addition, subtraction, and multiplication of complex numbers. What context do we do use with this? What do we do with the remainder theorem or countless other standards that are procedural and not application based? I need to learn more math, particularly above Algebra 1, but I tend to lean on the curriculum experts and they (Eureka and Illustrative mainly) dont offer much in term of context.

3. I do not believe that behavior should be graded. I hardly believe in grades at all but I certainly don’t think a students grade should be directly related to whether the student met the behavior expectations or not. If we have to use grades, I believe the grade should reflect the level of understanding of a particular concept.

What do I take away from this conversation?
1. Look for ways to open with context and have a routine for what students can do in groups with the routine. I like that ALOT!

2. Be explicit for the one behavior that you are looking for that day, what it looks like, what it doesnt look like, and then positive narrate like crazy when you see it.

3. Dump the ego. When I am co-planning or co-teaching with teachers, be sure to put myself out there and take the tough lessons in the tough classes.

4. Dump the ego part two. Teachers hear conflicting messages ALL THE TIME. I need to be in these spots more often and, when I hear what another math coach says, reflect on my beliefs about math, accept the good, and calmly let the rest go.

 

 

 

 

How old was Jesus in…?

According to historians, the best guess for Jesus birth was 4BC. What year would Jesus have turned 2000 years old? Hint #1: the answer is not 1996.

According to a book I am reading, when the calendar was established , the number zero did not exist in Western Europe. Therefore, in calendar math, the year before 1AD is 1BC, not year 0. Armed with that knowledge, what year would Jesus turn 2000 years old? Hint #2: make it an easier problem.

How old would Jesus be in 3BC?

How old would Jesus be in 1BC?

How old would Jesus be in 1AD?

How old would Jesus be in 4AD?