I used to like Robert Marzano's ideas. Now, I couldn't possibly disagree with him more.

His obsession with data is appealing to administrators and central district staff who use his name (along with Mike Schmoker, Charlotte Danielson and the whole list of educational pedagogy specialists) as justification for every plan they have. But Marzano's way of enumerating things often makes us data rich and information poor. Much of his data relies heavily upon putting a number to something that's often arbitrary to the casual observer. For instance, no matter how often someone tries to put a number 1 through 4 on something within a rubric and give it dimensions, teachers might still want to rely on a 3.5 or a 1.5 to describe what's happening in that dimension. Nor does putting a number to something let us see things more holistically.

So let's grow beyond that.

We ought to rethink professional learning communities with our "subject" teams. Meeting with colleagues around our topics of study is critical to our never-ending professional development. Most of my colleagues agree that having these conversations about math matters more than input from outside consultants, book studies, or any other set of meetings we attend on a yearly basis.

When having conversations about math, here are some things I've seen that work, as both a math teacher and a math coach.

## Create the Curriculum with Your Team; If Not, Learn!

Working with different educators, I've found one of the common threads with new teachers is that they never learn how to create a curriculum map, pacing calendar or unit map. Part of that stems from states creating the material themselves and dumping it into their schools so that every teacher in every classroom in every school in every district is in the same exact place no matter where their representatives go.

The problem with this is that not every child is the same, much less every classroom. Once teachers get handed the curriculum, some of them assume the thinking behind it is complete, and they just have to follow what they see. That never works.

Instead, teachers should develop curricula in teams. If they can come together, line up topics that they decide to cover, and gather appropriate materials, the conversations will run more smoothly throughout the year. Not only does this lead to less confusion, but any common struggles come to the fore pretty early on, and sharing assessments becomes a breeze.

## Keep This Rule of Thumb: Complete, Consistent, Correct

By "complete, consistent, correct," I mean we should allow multiple pathways to a correct answer that a) allow for full understanding of a given procedure, b) can be used time and again without fail, and c) actually have a sound basis in math. While it sounds constricting, it removes some of the limitations we've set for ourselves when looking at student work.

For instance, when finding 25% of 80, the most basic thing we can do is turn the percent into a decimal (0.25) and multiply that decimal by 80. The result is 20. Yet when I presented this problem to a seventh grade class just learning this, one of the students astutely observed that 10% of 80 is 8, and 25% is just 10% + 10% + 5%. They doubled 8 (16), then took half of 8 (4), and added the results (16 + 4 = 20).

Some teachers might mark that incorrect because it doesn't follow the exact procedure they asked for, but we really should accept such a response fully, not just because of the answer, but because the procedure the student used works time and again.

## Focus on the Evidence of Student Learning, Please

Having conversations around students always leads down a slippery slope about their competence for math. In other words, some colleagues find a name on their roster and say, "They can't even do *this* much! How can you expect them to do *that*?!" If someone in the meeting is unwilling to address this statement productively, it often leads to eye rolls and headaches.

Instead, let's redirect our professional conversations to just the evidence of student learning. For instance, we can establish a set of things that a team can do during the time given, such as creating tasks or having discussions around curriculum revision. Once we focus ourselves on instruction during those times, the conversations become more fluid. Because of math's technical aspects, fluid conversation means so much more because we can't afford to lose time on items that don't flow with students' actual learning.

Overall, we need our professional learning communities to work for us. We need to foster a collaborative spirit, and it makes no sense to constantly complain about children's deficiencies or make changes based on educational fads and not on viable best practices. Simply casting doubt on everything that crosses our desks doesn't help us grow, either.

The key is to keep it simple. No amount of jargon or professional books can usurp a team of teachers that come together on a consistent basis and focus on getting the math right. Robert Marzano would agree.

## Comments (4)

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## Your thoughts are echoed in

Your thoughts are echoed in my building when it comes to math instruction. My building is in year two of a complete overall of how we view and teach math. Up until last year many of my colleagues and I taught math for procedural understanding and instrumental learning because this was how we were taught and really didn’t know another way. With the mentoring of our math coach we have (and continue to have) a paradigm shift in the area of math instructional. Now our focus is on conceptual and relational understanding in which all approaches to problem-solving are considered.

Most of our math instruction now focuses on real life problem-solving that places a demand on students demonstrating “their” understanding and not on the way the teacher says to do it. The children’s thinking is validated when given opportunities to share their strategies with their peers, and this strategy may be the one that works for the “struggling” math student. Sometimes students’ thinking and approaches to solving problems is so “creative” that teachers also learn and adopt new processes.

One of the most challenging aspects of teaching for conceptual understanding is getting parents to sign on. Some parents do want to help, but they only know how to use the procedures, rules, and tricks they were taught. This comes up quite a bit when parents help with homework and during parent/teacher conferences. Some of our sister schools and districts are still committed to their procedure- based teaching, and we find these students don’t understand why they carry out certain procedures, it’s just how their teacher showed them how to arrive at the correct answer.

The only drawback, if there is one, is students identifying and developing a strategy that will work for “them” consistently. Sometimes when students are exposed to so many routes of problem-solving they are not mature or savvy enough to identify what will in fact work for them.

## Thanks for the thought

Thanks for the thought provoking post. Love reading with the morning coffee!

I really agree with the complete, consistent, correct. Our board has really taken hold of collaborative, problem based math learning as of late, so this is good for me to pass on to my staff.

It made me think of the importance of examining what we value as educators - is curriculum ( or math procedure) the end, or is the end the development of the higher order thinking skills, the learning process, the student discourse? I'm for the latter.

Relates to a post on testing, what are we measuring knowing? Or learning?

## Thanks for the though

Thanks for the though provoking post. Love reading with the morning coffee!

I really agree with the complete, consistent, correct. Our board has really taken hold of collaborative, problem based math learning as of late, so this is good for me to pass on to my staff.

It made me think of the importance of examining what we value as educators - is curriculum ( or math procedure) the end, or is the end the development of the higher order thinking skills, the learning process, the student discourse? I'm for the latter.

Relates to a post on testing, what are we measuring knowing? Or learning?

## "For instance, when finding

"For instance, when finding 25% of 80, the most basic thing we can do is turn the percent into a decimal (0.25) and multiply that decimal by 80. The result is 20. Yet when I presented this problem to a seventh grade class just learning this, one of the students astutely observed that 10% of 80 is 8, and 25% is just 10% + 10% + 5%. They doubled 8 (16), then took half of 8 (4), and added the results (16 + 4 = 20).

SOME TEACHERS MIGHT MARK THAT INCORRECT BECAUSE IT DOESN'T FOLLOW THE EXACT PROCEDURE THEY ASKED FOR..." [emphasis mine].

That makes me want to scream and is the reason I got certified to teach math. When the teacher insists, "Just do it my way..." children frequently stop trusting their own math intuition, stop trying to understand, and that's when the downhill slide in math starts. Even though the teacher should make some attempt to help students see why other procedures ALSO yield the right answer, if a solution is mathematically correct, IT'S MATHEMATICALLY CORRECT.

Ironically, when you say the most basic solution is to convert 25% to a decimal and multiply by 80; for me the "most basic" solution is the one I can do in my head which in this case has to do with the fact that 25% is 1/4; so I would multiply 80 by 1/4 (i.e., divide 80 by 4) and get 20. (This is exactly how my math-hating teenage daughter said she would do it, too...)

Good post; important thoughts. Thanks for posting!