This Year in Teaching

I can stand in front of a classroom all day long and teach. I’m actually pretty good at that. I explain well, I have a deep understanding of my subject so when half formed questions come up I can usually see where they are coming from, but this is not the way I teach. This method of teaching meets the needs of students like me, but I don’t teach students like me. Most people at the age of 13 don’t want to sit and take notes from a teacher. they want to talk, move, text, snap, whatever, anything except sit and take notes.

I won’t try to incorporate all that into my teaching. That would be forced. What I will do is to allow students to take more responsibility for learning. For me this means projects. I’m calling what I am doing this year project based learning, but it isn’t quite fully that. We have one project for each unit, but they are not always natural teachers of the content.

For example the first project will be rewriting a song so that the lyrics teach operations on rational numbers. The project, could be more natural if we asked the student to explore sound frequencies, but I am not going for pure project based learning, I’m going for standards based learning.

I know studying song lyrics won’t teach anything about operations on rational numbers, but writing the lyrics correctly will. Maybe it isn’t project based learning right away, maybe call it project based assessment except that the project will be given first and students can choose to learn from me or through other resources until they feel confident enough to finish the project (or test if they prefer that sort of assessment).

The organization of each unit is pretty simple. (and I use the word unit loosely as we mostly group units by strand of mathematics) Introduce the CCSS standards, walk students through how I make standards into objectives, have students break the objectives into learning targets through the questions they have. (a KWL chart) Next introduce the project and show how it meets the objectives. Show students resources we have that will allow them to learn the target skills  necessary to meet the objectives and allow them to choose how and when to learn those skills. (Still individualized learning and not personalized (or vice versa I always get those confused), but giving a lot of voice to the students).

The important thing is the student choice. They don’t actually have to do the project. They can learn all the skills from me and then take a test, they can learn all the skills, from another resource such as Khan Academy or CK12 and take a test. They can learn on their own and then do the project. They can learn on their own and then do a project of their own choosing. It doesn’t matter as long as they check in with me at least weekly and are working towards the goal as measured by mastering learning targets.

We will see how this shift in learning goes. Oh and did I mention we are also going 1 to 1 and shifting towards Standards Based Grading? I actually don’t think I could do this without those two elements, but first things first changing the culture of the classroom. No more work turned in for a grade, instead steady feedback on a long-term project.

Student Review

The school year is over time for me to give my first ever student survey of my teaching. I basically took my questions from

Questions Was I well organized? Did you understand what was going on? Did you learn how to learn independently? Do you think I improved since September? Did you feel safe? Were you, as a student, treated with respect?
Average 7 7 7 8 8 8
Overall 8

I think the students were much nicer to me than I would have been, or am I just too critical?

I’m not surprised the organization is low. I think I am pretty good at setting up a system, but not very good at sticking to it. That and 7th graders tend to pull me off task. It’s something I will always need to work on.

I’m also not surprised students were confused a lot. First that can be related to the organization, but I think more importantly it comes from the way I teach. We tried to do a lot of problem based learning and the students didn’t like that very much, especially at the end. Near the end of the year I had students beg me for worksheets and tests.

Even though the rubric we created was more like step by step guides many students still struggled with what and how to create a project. For example the second page of our last rubric had a list of components. Still students struggled with what to do. My mantra for the last week of the project was, “If you are not figuring out probability you are not doing your project right.” Still I had students spending hours on their game boards that didn’t include any form of probability at all. Sometimes teaching is like banging your head against the wall.

At least we learned something. Next year our projects will start with these very detailed rubrics, but I will actually shorten the work-time. What happens is students still work, work, work up until the final due date then turn in a project that doesn’t meet the criteria for success. No matter what feedback I give to them during the project, they only listen when I put a grade into the grade book.  (Not everyone, but quite a few anyway).

After the grade goes in and they see that low grade about half the students ask how they can make it up. So the plan is to allow everyone who wants to reopen their project and make improvements. It was my experience that after the grade is in and isn’t acceptable to the student that they begin to care.

It is still too focused on grades, but this is the first step. If I can teach students to see the relationship between the rubric and the grade maybe we can start getting students to pay attention to feedback before the grade goes in the book. It’s a thought anyway. My next post will have more detail on the changes we are going to make for next year.

This does lead me to the next rating, “did you learn how to learn”? I’m surprised that rating is so high, but maybe because most of my class time seems to be spent dealing with students who struggle with rubrics and only look at grades.

I’m glad I improved in the eyes of the students, they felt safe, and respected. This is the most important part of course. Students feel safe and respected, but perhaps not safe enough because many still don’t take risks in their work. I’ll try better next year.


I’m afraid I’m compromising mine. 

We started the year not knowing what we we’re doing. We kind of punted that first unit.

This second unit we took more time to plan exactly what we were going to teach. We lined up our standards, we organized our daily lessons around specific standards. Everything was nice and orderly.

So what happened, during the second unit each lesson is designed to teach a specific standard. That worked very well in the beginning, but now nearing the end of unit students can do math but they’re not really understanding math. They can all recite to me how to recognize a proportional relationship in a graph. They can all recognize a proportional relationship in a table. They all know the standard equation for a proportional relationship. The problem is they just don’t understand what any of that stuff to means.

When I start asking like students what does this letter mean in the equation or what does this number mean or what does this mean anytime they get angry at me ‘I don’t know what it means you just told me to put it there’. I’m falling into the trap of being a teacher I don’t like. Teaching to standards and modifying questions from the final. I’m saying this is how you solve these questions this is how you get to the answers but my students aren’t understanding math

Drowning in a Puddle

It has been seven or eight years since I have been in a classroom alone. The changes are drastic, but some things never change.


As a SIG school we are meeting and documenting everything. We are testing; Common Formative Assessment testing, Pre-testing, Post-testing., AIM testing, MAP testing, and PARCC testing. It’s a lot of tests. Sure I’m an anti-testing teacher, but I also see the value in knowing where your students stand in relation to what you are trying to teach. And while some of the tests I am required to give may not be worth the paper it is printed on (or the energy wasted in lighting up the pixels) I appreciate being forced to think so often about whether my kids are getting what I’m teaching. It can be easy to get caught up in how well you deliver the lessons and forget that the point is not the delivery but the reception.


I think back to the two weeks before school when I was doing my new teaching induction. I thought at the time what they were doing was great, and it was. It’s just that we spent a lot of time talking about adult things and not classroom things. We talked about the procedures for classroom management, district procedures, technology, copiers, etc… What we didn’t talk about was learning in our classrooms. We didn’t talk about curriculum, lesson planning, engaging students, formative assessments or any of that stuff.


Perhaps, after 15 years in education decorating classrooms, deciphering curriculum, and building engaging lessons shouldn’t be something that stumps me. But there I was less than  a week before school asking on twitter for advice on decorating my room. (And misspelling mathchat)


I do want my kids to do most of the decorating, I want them to show off the work they do as a group in the classroom, but I also can use the walls to create engaging learning spaces. I have the:


tape word wall,

and the:

tape box of addition, subtraction, multiplication, and division.

tape box of addition, subtraction, multiplication, and division.

I think I might do a quote wall as well. Most of it is empty at the moment, but slowly the kids are filling it up. I started with base vocabulary words from NWEA, but then asked the students to add their own. then I asked them to translate into Spanish. I just have to remember to build time for this into lessons. It can be one of the things you do when you finish your work early.


School has started and I don’t have time to craft decent lesson plans. I’m sure I’ll get used to all the work, but at the moment almost two weeks in the school year I’m still in survival mode.


It was nice having time to decorate my room, create a substitute folder, and learn some other things, but with the start of school what I’ve realized is I needed to take time to go over the curriculum more. Our first two weeks before school would have been more useful if we had sat down with our instructional coach and really hammered out a strong first two weeks or a month of teaching. An overview of the first unit. Not too detailed, just something like; here are the essential questions for unit 1, here are the standards that will be taught each week, here are a few ideas for lesson plans, etc…


Building procedures in the classroom are extremely important, however teaching procedures, like teaching anything else, has to be done within context. If my first couple of lessons of the school year are review lessons, I can spend more time in the lesson practicing things like, getting into and out of transitions, moving around the room, answering questions as a group, etc…  For me teaching is a procedure and I have a hard time visualizing exactly how I want my room to function until I’m actually designing the lessons and putting them into practice.

The First Day

It seemed like forever, but the day finally arrived. the first day of school. Traffic was crazy around the school as fresh-faced teenagers started showing up.


No uniforms this year, well the teachers all wore the same school t-shirt, but for tomorrow no uniforms for anyone, just a fairly loose dress code. (teachers are more restricted than students).


Not a lot of math on the first day either, mostly rules,, but I did manage to sneak a mention of Fibonacci. I think I’ll show this tree on Thursday.


On the first day Students learned to write on desks with dry erase markers. I promised to talk less. We took tours of the building.


Tomorrow we talk a bit about numbers. The task tomorrow will be to draw a Venn Diagram of all the groups of numbers then know. (Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers).


Feel free to add a snapshot of your diagram in the comments.



Weeks One and Two ‘No Math for You’

Week one and two at my new job, though technically I still don’t start until Monday.


The district I’m working for is one of the lowest performing districts in the state. It has been for quite some time. My first job as a teacher was at this district fifteen years ago and the reputation was bad then. Four or five years ago the state removed the elected school board and since then basically it has been run by a charter school company. Though it isn’t a charter district and the local union is still strong.


I can’t really comment on the changes that have been made because I don’t really know, but I can tell most of the administrators at the schools and the district office have changed. Whether they were fired or left on their own I have no idea.


It has been very nice starting two weeks before the students at my new school. We are in the second year of a School Improvement Grant (SIG). This means our school will be leading a lot of programs, but we will also be expected to collect a lot of data.


The first week was just for teachers new to the district. Three half days helping us get comfortable with the district and some of the procedures. Of course it still wasn’t enough and there were a boatload of suggestion at the end of the third day, but the concept is great and the practice was useful, even for an old goal like myself.


Over the weekend the principal invited all staff, old and new to her house for an informal get together. I really enjoyed the opportunity to meet everyone in such a relaxed atmosphere.


This second week was 2 1/2 days of work in our schools. A full day on NWEA reports. Half day of getting to know each other, co-teaching and PLC planning, building substitute folders, and a few other things including an excellent ELL role play. A teacher taught a lesson in German to blank stares and then taught it again with some ELL support. It was probably the biggest eye opener of the week for most of us.


So far, two weeks in, I still haven’t seen the math curriculum or taught a lesson,  but I’m feeling fairly comfortable with my co-workers. I’ve also been trying to decorate my room, but I’m not very good at that. My walls are still mostly blank.


I want to put some inspirational quotes on the walls, but just a few. I would rather the students choose some of those and put them on the walls. I also don’t want to put math posters on the wall, because I would rather my students made those posters and hung them. So for now My walls are blank. It kind of felt wrong at first so I asked on twitter. the response was basically the same.


What I wouldn’t do for some whiteboard paint everywhere in the room.

Better Homework

In yesterday’s problem we took apart a poorly designed math homework. Essentially the math textbook asked the students to practice a highly sophisticated method of addition.


The strategy for breaking one number and adding it to the first to make a 10 then mentally adding the rest is great, but probably should come naturally as it occurs to students as opposed to being forced on them. The real problem is the students who need it the most probably wouldn’t come upon this strategy naturally. So what we have to do is teach this strategy to our students so they can add it to their arsenal of weapons to use when solving math problems. We want to do all of this without actually walking them through a step by step process.

Why not just teach a strategy straight out? Two reasons: First teaching a procedure doesn’t always lead to “ownership” of the procedure. Second, because that isn’t the hard part of math. The hard part is recognizing when it might be the best strategy to use. (Which I suppose is kind of the definition of ownership.)

So for homework (and I am really against homework, but if you insist on giving it at least make it painless and force the parents to be involved as more than a checker of correctness) I might take these same problems and then ask them to choose one and talk out a strategy. They could use a phone or iPad to record the strategy, or call my google voice number and leave a message, They could tell it to their parents, or in any number or methods. The one caveat might be, if they are leaving me a recording it has to be less than 15 second long. (Do you ever notice how much you ramble when you are unsure of yourself?),  The next day I might ask two or three or even four students if I could play their recording or if they would like to explain their method. Then I could ask the rest of the class if they tried a similar or different method.

Another alternative, I could ask them to ask their parents to solve one of the problems in their head and teach them the steps they took. Then the student would have to do a different problem and explain the steps back to their parents.

A third alternative, I might ask the students to choose one problem and ask the them to solve it in 3 different ways. Explaining their work each time. I like to encourage a voice recording the when a procedure is new, because it is easier for the kids, I just want them to keep redoing it until it is short enough so that I can listen to 30 in less than a week.

Yes the textbook and I would like to teach the students all of the great strategies for addition, but I think they are going about it the wrong way. They are pulling each strategy out and teaching it explicitly, so instead of learning one way of “doing” addition students are forced to learn a plethora of ways to “do” addition. Completely missing the point of understanding the concept of addition and choosing the best strategy based on the situation.

By asking students to talk about how they solve a problem in their head, especially with others like parents, students are exposed to a variety of strategies for “doing” math.  By choosing to have students explain a few different methods the teacher can then make sure each child is exposed to all the strategies she feels the students should know. Now instead of asking students to solve a problem by the “making tens” method we can ask students which method did they choose. Did you choose Bobby’s method, Sarah’s mom’s method, etc… and why did you choose that method?

The point is not to make students practice problems, but to give them an arsenal to choose from and the knowledge of which weapon works in which situation.

Math Homework

What is wrong with this homework?

Nothing really. Actually, it showcases an excellent strategy for addition.

What you are supposed to do is make a ten, which makes it easier to add the rest.

Take the example 29 + 52. Look at the first number 9 + 1 = 10, take a 1 away from 52 and add it to the 29 to get 30. Then add the remaining 51 to 30, which can be done in your head.


The publisher even made it simple for you by putting a nice helpful line underneath the number they want you to break apart.

helpful hint

Lets try the first problem. Now go back the the first number and ask yourself 5 plus what equals 10? Yes, 5 + 5 = 10, so I need to take a 5 from the second number (27) and add it to 35 to make a nice round 40.


Then we finish the problem with the left overs from the original addend. I hope you didn’t add 27, because we took the 5 from the 27 leaving ourselves with just 22.


40 + 22 = 62.


Do you understand how to do the math now?


Good, because this is an excellent strategy for addition. To use this strategy requires you to be fluent in your addition facts up to 10, which also happens to be one of the common core standards for 1st grade math.

Then you should be able to add by tens (also a common core standard). It wasn’t explicitly asked for on this sheet, but my son’s teacher was nice enough to give out number lines on which they had practiced adding two digit numbers starting from a ten.

Again, I say this is an excellent strategy for addition, especially addition of two digit numbers. When I shared the picture I asked “What is wrong with this homework?” There is nothing wrong with the math, but everything is wrong with the homework.

What is happening is they are taking an advanced addition strategy and teaching it explicitly, then going back and asking students to practice it over and over again. This is no different than going back to the old days and requiring students to line up the number one above the other and adding down the lines. It is actually worse because that strategy is often the most effective way to add any two random numbers on paper. The strategy above is probably one of the easiest if you were asked to add two numbers in your head. (The second easiest for me at any rate.)

Instead of teaching students how to do this strategy it would be better to contrive a method for discovering this method in the classroom and hope that someone brought it up during a number talk. Even if they didn’t come up with this specific strategy I wouldn’t force it on students, rather the goal is to get them comfortable in discovering and using new strategies and as they progressed through the years they will discover it. You will see in the series of videos some ways to use number discussions in a classroom. Even those non-teachers should watch the first video at least.


Practicing someone else’s strategy for solving math doesn’t teach us how to do math, it teaches us how to follow directions.
Now my question is, “How would you make this problem better?” My suggestions tomorrow.

(edited for typos and readability)

Writing Math

What is the cost of, the simplicity of writing with a pencil, vs learning to write math for a computer – with the more powerful responses that come with it?

The conversation started with feedback. Research has shown that feedback is important. -> Many math software provide simple right or wrong feedback quickly. -> Too often this feedback is more the fault of syntax errors than actual math errors -> programmers add hints, or expand the possibilities of correct answers -> kids still hate it.

Teachers follow-up saying, basically feedback has to start with what the student is doing and thinking and start customizing from there.

The holy grail is for a computer to recognize the typical mistakes, often mistakes can be put into general categories, and send a standard, but custom, message to each students as they need it, preferably in the form of a question so that students actually solve the problem instead of waiting for the computer to do it for them.

I saw a company trying to do something like this through hints, but I think they needed to get more data on which mistakes meant what hint to actually give.

While the cost of learning to write for a computer program is high and the feedback so far doesn’t seem that great, I start to think of programs such as Geogebra and Desmos and the feedback they give, even though they don’t advertise their feedback.

When I was learning Calculus, before the widespread use of Maple (I remember struggling to input equations correctly then waiting minutes for the graph to load), I never made the connection between functions, tables, and graphs. I got lost in the calculations, which took too long (and I was faster than most at the calculations).

Fast forward fifteen years and I’m teaching middle school Algebra and we are given a class set of graphing calculators, suddenly relationships between numbers and graphs are evident. Which, brings us to the age-old question, “How much of teaching math is teaching understanding and how much is teaching the mechanics?” or “How com we never really understand something until we try to teach it.”

The question for teachers I suppose it:

“How long do I let my students practice on the computer with the limited feedback, and how much time do I have to work with individual students?”

Multiplication table

An exercise or extended unit in learning the multiplication table for 3rd grade.

 Previous knowledge – how to figure out answers to one digit by one digit multiplication, but not fluent or fast. Depending on the option students will probably have to know how to upload pictures, paste them into a document, and resize them.


Cameras for each student

computers or printers and papers etc….


Start with a simple multiplication table


Or even simpler


Have student complete the multiplication table by adding pictures to represent the answers.


With students I might ask them to find a different representation for each number. Or I would ask them always use the the same picture for the commutative expression (ie 4X2 is the same as 2X4) I also might allow them to use the same picture to represent different numbers. For example the dartboard might also represent 24 because there are 8 pieces of pie and three colors each.


Options and extensions

Have students find several representations of each number and choose their favorite.

Have the entire class work on the project at one time. Split class into groups each are responsible for their own section of the times tables.

Create a class poster to hang on the wall.

Have students work on a section at a time.

Have students take pictures at home and put them into the times table at school.

Print out the pictures and have students cut and paste onto a larger board.

Have students draw pictures instead of take pictures