Checking for Understanding

I need to come up with a much more structured way of teaching new concepts and checking for understanding before assessing. As I’m sitting grading the latest grade 8 quizzes on solving equations, it’s becoming clearer and clearer to me that I didn’t do a very good job of it this round. 

Idea #1: direct instruct in small chunks, then do lots  and lots of checking for understanding whole class using whiteboards (or the students’ favorite: writing with whiteboard markers on their desks) and other formative assessment tools. This could take DAYS given the complexity and rigor of some concepts. And obviously some concepts don’t lend themselves well to this format. This could get boring though…

Idea #2: use a Daily 5-ish workshop format with small bursts of instruction, followed by Cafe menu choices and small group work with the teacher. This would take some massaging, but I’ve tried it already and I think it could work with some tweaking. This allows for more creativity, and one of the menu choices could be working with whiteboards (because they love whiteboards as long as that isn’t the only formative assessment tool we use). 

Idea #3: maybe it’s an engagement issue? In that case, a PBL structure with small bursts of mini-lesson instruction as needed is the answer. Again, this allows for much more creativity, and then the instruction is really guided by student interest. 

Idea #4: I got nothin’. Ideas, anyone?

Oy vey…I need a drink. 


Reading Apprenticeship and Math Part 2: Talking to the Text

As mentioned here, I’m participating in a fantastic professional development series on Reading Apprenticeship in my school district.  As a math teacher, I was driven to explore ways to pull in reading strategies to my classroom since the curriculum we use is heavy on reading.  

Many of our students are 1-2 grade levels below where they should be in reading.  What I’ve learned through this training is that so many of our intensive reading programs designed to help students become “better” readers focus more on fluency and decoding and less on comprehension.  This leads students to believe that to be a “great reader” they need to read quickly and fluidly.  Comprehension takes a back seat.  


Example of a word problem in the Grade 7 workbook. Oy vey!


Example of a crazy-difficult problem that my Math 8 students historically have trouble understanding.

Just LOOK at those problems!  I’m here to tell you that even I had to re-read these several times to understand what the heck was being asked…and I’m *ahem* several years older than my students.  

Hence, the need for some good strategies.  

Enter, Reading Apprenticeship.

And here’s where we went with it:

I took a typical problem and did a think-aloud.  I spoke what my brain was thinking as I worked through reading a problem. I didn’t even attempt to solve or build an equation or anything mathematical.  I.  Just.  Read.  And talked.  And re-read.  And talked some more.  And talked to the text (took notes…CRAZY notes) all over the problem.  Then I stopped.  

I asked students to discuss in their small groups what they heard me say and saw me do.  

And we made lists.  


Strategies lists from 4 of 5 of my classes. You see some talking to the text above the lists.

I took the lists and combined them:

And we have a living list!  We will continue to add as we go, but what a great start!  

And here is what my 8th grade students were able to do with it (the first three problems were teacher models, the last two were done in groups):


My favorite because of the question he asks to the left of #4–how cool is that?


I love the modifications this student made, and the fact they added “conjunction” to their notes on #4.


We didn’t focus on correct equations, but rather on the talking-to-the-text process.

In all fairness, I can’t take total credit for their amazing-ness with this strategy.  They have been immersed in Reading Apprenticeship with two spectacular language arts teachers in our wing (7th and 8th grade) over the past two years.  I’m merely expanding the students’ Reading Apprenticeship universe.  

I’ll keep on with this, slowly and steadily getting the students to do it more independently.  My next wish is to develop their metacognition so they can think about their processes and understand when  and where they make mathematical mistakes.  For now, I’m very happy with where we’ve come.  

Rubric Grading

I’ve decided I REALLY like my grading system. I think parents and students like it also. It takes some getting used to because it’s different than what they’re used to, but I believe it gives the best picture of WHAT a student KNOWS. And the students and their parents like that it gives students room to continue learning and growing with specific learning targets. As such, retakes are an essential part of this process.

I use a slight variation of Sarah Hagan’s “A, B, Not Yet” rubric scoring system (read about it here and here).  I started out using B also, but changed it to C mid year, because C to me means “average”. I like color-coding, so students’ folders have a list of learning targets pasted to the front. That’s where I mark their scores.  

Student folder after the first quiz of the unit.

Same student’s folder after the second quiz of the unit.

These learning targets are the assignment names I enter into our online grading program. “NY” translates to 55%, “C” translates to 75%, and “A” translates to 100%. I also record homework, but as credit/no credit so that the real weight of a student’s grades lies on the learning targets. These learning targets are flexible and can improve all the way up until the end of the quarter, provided the student practices the concepts and either requests a retake, or (if I include those concepts) shows improvement on the next quiz. 

I prefer this grading system to what I’ve done in the past (recording assignments and tests as points correct out of a total) because I can look at their grades and get an accurate  picture of how a student is learning in my class without necessarily keeping a portfolio. I’ve also come to believe that points correct out of a total and recording homework grades with more weight is more a measure of a student’s work ethic, organizational skills, and behavior than of their actual learning.  (I can thank  Rick Wormeli and his book “Fair Isn’t Always Equal” for that–and the many discussions I’ve participated in on Twitter). 

I’ll probably continue tweaking this process, but for now I’m fairly pleased with the results. 

Reading Apprenticeship and Math

I’m attending a Reading Apprenticeship training in our district that is just fantastic. I can’t say enough about it: the trainer is fabulous, the content is fabulous, the strategies are fabulous…nuff said. 

So, I’m attempting to bring some of the strategies I’ve learned into my math classroom. 

The last few days my 7th graders have been making posters of word problems and creating tape diagram and algebraic solutions. Instead of each group presenting their posters one at a time, I had them do a gallery walk instead.  They had post-its–enough for one per poster, and prompts for comments to make. I gave them 10 minutes to travel with their groups and discuss the prompts, writing responses on their post-its to place on the posters. 


A lot of students made this same comment, so this gave me an opportunity to address misconceptions with a mini lesson after the gallery walk.


One prompt was to notice what was going on mathematically with the poster.


Another prompt was to state anything that confused them when viewing the poster.


This gallery walk really got them talking. Students were much more engaged in this activity than they would have been sitting and listening to 6 different presentations. 


Students were completely engaged for the duration of the activity.


Students looked to each other for clarification and discussion rather than to me. It was great!


They seemed to truly analyze the work so that they could provide authentic feedback to their peers.



1) My first group of 7th graders was better at this than my second group–and they are typically lower achieving. 

2) Although I gave focus prompts for accountability, some students tended to focus on the aesthetics rather than the math. 

3) It was obvious they had done this activity before because they got right to it and understood the routine without much in-depth explanation. 

4) This was a great opportunity for formative assessment. 

My next goal is to bring in think aloud  and talk-to-the-text activities. I’ve started some talking to the text with my 8th graders, but not enough to reflect upon yet. That’s for the next blog post!

If Math Was…

A food, what would it be?

“If math was a food, it would be beef jerky because it’s hard to chew and math is hard to do.”

“If math was a food, it would be an apple because it can sometimes be hard to do and not fun, but during other times it can be a little bit easier and more pleasurable.”

“If math was a food it would be a good thing because you can keep multiplying it until you’re full.”

“If math was a food it would probably be noodles.  You first start off with hard noodles, then as you learn (a.k.a. boil the noodles) it gets soft (a.k.a. easier).”

“Pie. Since a lot of math problems involve pi.”

“If math was a fruit, it would be grapes.  Math would be grapes because grapes don’t come in one.  They come in multiples, just how math has multiple numbers or equations.  The vines on grapes can represent that they all connect to each other or that there’s different ways like how you can find different ways (to do things) in math.”

“Kale.  I would say math is kale because I don’t like doing math but I know that if I do it it will only help me in life.  Same with kale.  I don’t like eating it but if I do then it helps me in life by staying healthy.”

“If math was a food it would be a potato. Hard before you cook it but gets soft after boiling it for awhile.”

“If math were a food it would be chicken because everything tastes like chicken and everything uses math!”

“Grapes, because you can add and subtract them.  Sometimes it is hard (raisins).”

Weather, what would it be?

“If math was a weather I think I would describe it as a rainy day because when it rains most people want to get out of the rain and not deal with it. As for math most people want to run away from it, but at the end of the day math is important because you use numbers everyday.”

“If math was a weather, it would be sunny and cloudy because I like math but I don’t like homework.”

“Sunny because math is fun and keeps me excited with energy.”

“I think it would be rain, but it would suddenly turn into a natural disaster when a test comes.”

“If math was a weather, math would be cloudy weather.  It would be a cloudy weather because in math it can sometimes be confusing and dark clouds blur your thoughts.  But behind the clouds, the sun is always shining so when the clouds go away you get the idea.”

“If math was weather, it would be rain because sometimes you like it, or sometimes it can ruin your day.”

“Math would be lightning because lightning is fast and most times I can answer questions fast.”


Thoughts on Homework Differentiation

I am trying to be more intentional with the homework I assign this year.  The number one concern I hear from parents every year is that the math their children are learning has become too difficult for them to help with.  And I’m fairly certain that the number one reason students don’t do their homework is because they think it’s too hard.  So, what I’ve started doing is choosing homework assignments that I feel students can do independently and that include skills that supplement what we are doing in the classroom.  In the 8 days that I’ve been doing this, I’ve seen a much higher percentage of homework return from students.  It has also given me a lot of good information about their math confidence and what skills they need further work in.

In the first 8 days I had to rely on previous grade level standards to design homework simply because we hadn’t done enough work on the standards we are learning currently.  Now that we are getting deeper into the curriculum, it’s time for students to practice what we’ve been learning in class.  We use Engage New York for our math curriculum, and I find that it is very “word-heavy” and often too rigorous for struggling students to do independently. Because I spent some time this summer breaking apart the standards into smaller, kid-friendly chunks, I’ve been able to use that information to create homework that my struggling learners can do but that still covers the grade level standards.

What I struggle with now is how to assign them this differentiated homework without singling them out.  Maybe I could put students into colored groups (like the leveled reading groups of old) and students get certain assignments based on their group? I’m not sure, but what I don’t want is a system that will be too hard to manage.

Class Website

I started a class website today.  I tried to make it simple without too many pages that I have to keep updated.  My main purpose is to have a calendar for parents and students to access for homework due dates and important school events.  I added a class newsletter page–I hope I’m not being too ambitious and biting off more than I can chew! However, I always try to think from a parent standpoint, and this is something I would appreciate from my child’s teacher.  Any ideas what to include in the first newsletter of the year?  Leave a comment below or tweet me @nmcaligrl.