We’re not just teaching math…

The old adage goes “I don’t teach math. I teach children.” That line typically gets used when an educator’s focus is a bit out of balance with respect to empathetic student-centered attitudes and content-driven, fidelity-to-curriculum attitudes. There needs to be a balance and it can be tricky to find sometimes.

In addition to that, there is another balance that needs to be struck. The balance between the math content in a curriculum and the other skills the students are going to need to learn the math content. Some of these skills are considered “soft skills” by some. These are things like communication skills, presentations, research, teamwork. I’ve always been a bit uncomfortable with the term “soft skills”. (We can talk more about that another time if you want).

Beyond those, there are some “hard” skills that some math teachers just feel isn’t their job to teach. These are things like technology skills, reading, writing, and supplementary (often much lower-level) math skills. I’ve been in a variety of math classrooms talking to teachers of high school math who feel like they just shouldn’t have to teach fractions, long division, and reading.

Yet, increasingly math classes are starting to look like this.

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We’re not just teaching math…

And those skills, be them “soft” or “hard” will directly impact our students’ ability to learn the math content that we are hoping they’ll learn. I think it is important that we math teachers simply expect to have to teach our students to do everything we need them to do to be successful in our math classes.

And this includes remembering that teaching and learning have some recurring patterns when done successfully: teacher modeling, student exploration, student individual practice, formative assessment, feedback. These are things that exist in every successful math class I’ve seen. (Depending on teacher philosophy, the order of the steps might not be the same in every classroom, but the steps are all still there.)

Very few teachers will tell you that you can skip that teaching-and-learning process for the math content.

Many more will skip that teaching-and-learning process with the “softer” parts of their curriculum.

Perhaps, I should back up and discuss how I see “curriculum”. From the teacher perspective, curriculum includes both the “what” of the learning, but also the “how”. And if a math teacher has students whose math experience looks like this…

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… as is increasingly becoming the case, then the curriculum probably includes three fairly broad categories.

Math Content: This would include the primary learning targets for the course, but also the prerequisite math knowledge that the students need to advance successfully to the new content.

Learning Tools: Depending on the class this might include a couple of devices (calculators, iOS devices, laptops, Chromebooks) and any other manipulatives (Alge-blocks, patty paper, compasses, protractors, etc.). If the learning will require the use of these tools, then the learning of these tools is every bit as much a learning objective as the math content.

Classroom Procedures: Where will the schedule be posted? Where will handouts be made available? How does a student turn in assignments? Where should a student look when he/she has been absent? What does a student do when they are trying to work at home and find themselves paralyzed by confusion?

If a student struggles to learn well the content in any of those three areas, that student will start riding the struggle bus pretty quickly. The first step to avoid this is to recognize that we are going to have to actively teach all of the things students need to know to be successful in our class. How many of us run a formative assessment where the learning target of the assessment is “Students will be able to use a compass”? How many of us give feedback on the learning target “students will know how to create table with ordered pairs on Desmos”?

Remember, we don’t teach math. We teach children to learn math. And that requires us math teachers to remember that there’s actually a lot more than math knowledge that students will need to be successful in our classes.

How the other half works

I was a classroom teacher until this past November. The last 6+ years were spent in the high school math classroom. I got pretty comfortable in the high school classroom. In my new role, I’m collaborating with teachers at all levels.

In fact, I was fortunate enough to explore the extremes of that spectrum in the last week. A few days ago, I spent about a half-hour brainstorming with a teacher regarding his calculus class. He had some outstanding (and quite lofty) goals about integrating STEM ideas of authentic problem-solving and authentic assessment, experimentation, design and engineering into his calculus class. I didn’t have much to offer him, I’m sorry to say. I’ve never seen a class operate in the way that he was hoping.

Two days later, I was observing a math instructional strategy for about a half-hour in a kindergarten classroom. The teacher was fantastic: talented, warm with her students, and quite skilled in the areas of classroom management and math instruction. I was observing her class as they explored some quantity discrimination with manipulatives. Beans for counters and a spinner to determine whether that pair of students would express a “greater than” or “less than” sentence. I really enjoyed this teacher’s style. She chuckled as she said, “whoever decided that beans and spinners should be used together with kindergartners really should have rethought that.”

It got me thinking about my own background. Teaching is immersive. It isn’t something you do, it’s something you are. Even aside from all of the time a teacher spends in his/her classroom (or working outside of their classroom), the work is very stressful and requires a lot of mental energy. Teachers seek other teachers’ counsel, other teachers’ advice.

In the end, no one can help a frustrated teacher quite like another teacher who has walked a mile (or seven) in the same frustrated shoes.

This reality leads to two very understandable outcomes. First, many teachers I’ve talked to have expressed that advice is only helpful when targeted directly to their specific situation. (“Well, that fella had some good things to say, but has he ever tried to teach Algebra I? No…” I’ve heard different variations on this many times.)

Second, there is often a huge, HUGE disconnect between secondary teachers and elementary teachers. Since 2005, I have been a team member in three different districts as a secondary teacher (one very big, one very small, and one medium) and I can think of exactly two times… TWO… that I was in a instructional math meeting that involved bringing any elementary teachers in.

Both times, the vibe was very much, “Hey listen, you elementary school teachers are making our jobs harder, so I tell ya what: why don’t you let us tell you how this should be done and then we’ll all get back to work.” I’m sorry to say that I’m not blaming others. I know this is how I was in those meetings.

As a secondary teacher, I never had a classroom full of students who were struggling to understand that 5 x 2 = 10. Sure, I had students who certainly didn’t know their multiplication facts, but I never had to build 5 x 2 = 10 as new knowledge. What’s that like?

As a secondary teacher, I never had a classroom full of students who needed time to develop the understanding of the statement: “If you are counting objects, the last number you say is the number of objects there are.” What’s that like? How do you structure that lesson? How do you differentiate that?

I’ve never watched a student struggle to learn a new topic only to realize that the reason they are struggling is that they don’t know how to read or conceptualize that the two digit number they are seeing on the page in front of them. I had some students who didn’t read well, but I don’t recall having a student in class who didn’t know what 12 meant.

But there are places where this is commonplace. And I’ve learned so much by having to consider what math education looks like at this level. And it makes me wish that I had been forced to walk a mile or two in their footsteps while I was struggling to understand why my students couldn’t understand fractions.

In the modern times, it seems there is a resurgent appreciation for collaboration, classroom observations, and teachers learning from each other. I wonder what value it might add to a teaching staff to have the teachers from the high school take a day to watch expert practitioners at the elementary level? And what value might it add to have the kindergarten teacher sit-in on an Algebra I lesson?

Flipped Learning and a bit on Zaption

You know, flipped learning is a precarious structure. In some sense, it seems quite progressive, empowering to the student, allowing the student to take ownership of his/her own learning. In another sense, though, it replaces live teacher lectures with video-recorded teacher lectures, which actually seems like a backwards step. Clearly not all instructional models that include videos are created equal.

Now, I have been an advocate of a while of using video to enhance instruction, if for no other reason than that a properly-chosen, properly-timed video can grab students attention really well when they are tired of interacting with me and with each other. However, videos largely have the problem of being passive activities for the students.

I’ve tried a variety of different things to attempt to add some interactivity to videos. There’s the ol’ pausing-the-clip-every-90-seconds-to-engage-the-students-yourself technique. I used this move when I taught physics. “Hollywood Physics” was where we’d watch a clips filled with delicious energy transformations or breakdowns in Newton’s laws. Lots of pausing and discussing.

I’ve also used tools to try to embed questions that break the video up and make the students reflect or predict. This little ditty from 2011, The Bowl Problem, although not my best work, reflects a desire to try to create a video that has some interactive elements to it. That was created with a digital camera and PowerPoint. It was prohibitively time-consuming. There has to be a better way.

And Zaption might be it. I’m not a spokesperson for these folks. In fact, they are not the only service out there that embeds interactivity into videos (Educanon and Bubblr are two others). I just found Zaption to be the easiest to use and the most useful as a formative assessment tool.

In trying to learn how to use Zaption, I made this quiz video. Go ahead and give it a try. (I’ll be able to tell you more about the built-in, free analytic tools if I can get lots of people to take the quiz. So please, give it a try.)

You don’t get to see your results, which will bother some, but the results are tallied and shown in a series of well-made reports that has the potential to inform a teacher about how students engaged the video (it shows how long the video was watched, how many times each questions got skipped, etc.), and give you some insight as to their understanding of the content.

It’s not a perfect tool. If you wanted to use it in an actual quizzing/grading type set-up, the grading of the results might be a little tricky. Additionally, this, like every bit of instructional tech, has a learning curve. Having said that, though, I found that choosing the right video to practice on was the slowest part and that the process of creating the questions to be pretty easy to pick up.

Flipped learning has its critics (I have been among them at times), because there is a demand for instructional technology to get implemented meaningfully. Instructional technology isn’t a savior. However, the effective use of instructional technology does have the potential to make a huge dent in some of the improvements we need to make. We want it to give us a chance to do things that we previously had to work too hard to do. Tools like Zaption help make a previously passive activity, like watching a video, potentially more active for the students and informative for the instructor.


Update on 2 Jan:

Since posting this, I’ve received a tweet about an additional software to embed instructional items into videos. And since I’m mentioning Zaption, Educanon, and Blubbr, I figured it was only fair to add this one. I’ll just show you the tweet.


More thoughts on Education’s “Game-Changer”

Photo credit: Maria Ly - used under Creative Commons

Photo credit: Maria Ly – used under Creative Commons

I’m intrigued by the idea of finding/developing the next “game-changer” in education. My last post tossed out one suggestion. After a conversation with a colleague today, I have another idea.

First some background: I want to relate this idea to the medical world and professional (or large college) sports. So, in those areas there are successful teams and less successful teams. Those teams are built of individual members strategically collected because of their individual skill strengths.

In medicine, general practitioners handle small ailments. Larger ailments get referred to specialist. Each specialist focuses on a much more focused area of health: Back, allergies, ear-nose-throat, kidneys, endocrine system. If the person needs surgery, then send them to a person who is skilled in that. That person has their own team with someone who is skilled in anesthesia. And none of these people deal with patients paying their bills. There are receptionists and accountants for that.

In sports, same idea. There are lineman, backs, receivers, ends… and that’s just on offense. There are a separate set of defenders.

So, what does this have to do education?

Teaching well requires a crazy amount of skills. Just think of the things that teachers need to do: They need to design and deliver lessons to engage all learners, modify for those reluctant, adapt for those with special needs. They need to assess the learning of each one of the diverse learners, interpret the deficiencies and provide meaningful feedback, often redesigning learning opportunities targeting the weak areas. The process of classroom management often requires afterhours follow-through like parent calls, detentions, sit-downs with counselors or principals. They need to take, record, report out, and interpret a variety of student data points. Believe it or not, that’s the bare minimum.

What if they want to sit on committees? Coach? Get involved in the union? Community? After school clubs?

Why did anyone ever think this was a job for one person?

So, it got a what-if.

What if we broke that job into two parts. And by that, I mean we asked our professional educators to do half of those tasks. We’ll have two separate roles. I’ll call them the “instructor” and the “evaluator”.

The instructor would handle the parts of the job that dealt with instructing the students. Designing/delivering lessons and course materials, managing the classroom, disciplining students, accommodating, grouping, etc.

The evaluator would handle the formative and summative assessments, data analysis, feedback, parent contacts based on learner struggles, etc.

Then, we team up. Each core team would consist of four highly-effective instructors in each core area and maybe two or three evaluators. All of these people are certified teachers in the areas that they are working. Included in the team would be a number of support folks that could provide consulting for accommodating struggling learners and/or modifying to support students with disabilities. There would be a designated meeting time at least three times a week for the teams to discuss what the assessment data is showing and to inform decision-making.

Yeah, it sounds a little strange, but it changes the game. And it does so in some pretty important areas.

This allows teachers to focus on one of the two gigantic, essential, “can’t-get-rid-of-it” areas of teaching that are becoming so intense and so technical that it is becoming increasingly difficult to do them both. Who has time to design/develop/deliver powerful, scaffolded, differentiated lessons AND design/deliver/record/analyze meaningful, informative assessments and provide meaningful feedback in a timely manner. Especially considering the community relations work increasingly required in both areas?

But what if each teacher was only responsible for one or the other of those? Instead of two teachers taxed, stressed and burned out trying to climb the whole mountain, what if one of them spent all his/her time on instruction and the other spent all his/her time on assessment.

If the two were consistently and effectively collaborating, then the flow of information would supply both of them.

Then the instructor could be present while the students were learning and not leaving them alone to grade papers.

Then the evaluator could effectively tend to the students in the assessment experience and not ignore them to get a jump start entering the data.

Then the instructor could update groups and seating arrangements several times a week instead of surrendering all his/her creative time to printing reports and stuffing them in binders.

Then the data wouldn’t become a paper to be printed, filed, and ignored, but instead would be examined and used to inform future assessments and instruction.

Marzano, Hattie, Boaler (most reformers in fact) talk about the power and overwhelming positive impact of layered, intentionally-designed learning activities. (What does Boaler call them? Low floor, high ceiling? I might be wrong about that, but the spirit is correct…). They also talk about the power of meaningful, well-planned assessments with thoughtful, timely feedback.

So, here’s my second game-changing idea: What if, in order for both of those things to have the impact on students that we all know they can have, we need to accept that it is too tall an order for one person to do alone?

A few words about failure…

I just finished up a day on campus at Michigan State University attending the Michigan Virtual University Symposium. It was a daylong set of discussions and panels dedicated to blended and online learning.

There were a lot of interesting discussion points to be sure, but the one that is going to stick with me the longest is, perhaps, the one that we try the hardest to forget:


Toward the end of the day, in the final panel discussion, the value of failure came out multiple times. The process of learning REQUIRES a certain amount of failure. Failure lets us know that we are pushing ourselves to grow. Failure is a sign that we are trying to put new understanding into practice. Failure gives use opportunities to check our progress toward a goal that sits out in front of us… a goal we haven’t reached yet, but continue to reach for.

We should fail sometimes and our students should see us do it. If we are really trying to show our students that we are lifelong learners, then we need to show our students what learning really looks like.

Many, many students are under the unfortunate impression that failing is something that weak students do and succeeding something that strong students do. While, the latter is certainly true, the former is certainly not.

Failing is something that happens with practically each first try at a new skill. Failing is something that is a natural part of the learning process. It is natural and it is helpful.

I am not sure this education system of ours is encouraging that fact – not of its administrators, teachers, or students. We expect progress now. We expect implementation to demonstrate immediate results. We want our teachers to teach in such a way that our students don’t get wrong answers.

Perhaps what we need to do is get back to the basics of learning. If at first you don’t succeed, try, try again.