Day 36: More Assessment

The skill assessments did not go as planned.

The Math 7 kids stumbled over questions that we have been covering for two weeks.  They didn't do as poorly as they could have, but it was very clear that they were not comfortable with the material.  When asked to write how we've been talking about multiplication, they wrote about division.

I had even left the wording on the board and kids who looked up still used the wording for division.

I'm not sure how to get them to examine their work and ask themselves "is this giving more or less than I started with?"

Over the last few days, I've been emphasizing the importance of using diagrams and our review yesterday was full of them.

The students who used diagrams on the quiz (including my English language learner) performed consistently better than those who didn't; somewhere in the range of 40% better.

There are issues with focus, attention, maturity and retention.  I've already had to move students in two separate classes because they can't seem to stop touching the people around them.  I point these out not as a way of excuse or blame-placing, but to identify the challenges that I need to overcome.

For the first time in a LONG time, I have faith in my lessons and methods.  It may be time to say that my seating arrangement (in groups of 4) isn't working for these classes and it's time to go back to rows for a while.

In Pre-Algebra, I can see a clear correlation between the attention that they pay to class and grades.  In addition, the kids who ask me questions on a regular basis are showing huge amounts of improvement.  This is no surprise.

There's also a MASSIVE difference in my classes.  Two classes have an average in the mid 80's while the third is hovering around 60.  Part of this is because of the time of day when the classes are held.  Another has to do with the make-up of the classes themselves.  The third class has a much higher percentage of students with special needs and IEPs.  That class is also bigger.

All of those are irrelevant since they are out of my hands, but it does show me that I need to attempt different interventions in that class.

The breakdown in Math 7 was similar, although not as extreme.

I'm incredibly fascinated by these charts.  They are sorted by overall score and not by name or other identifying marks.

What do you notice?

What do you wonder?


I wonder what I can be doing better for my students in the afternoon.

Day 35: Dot Placement

Tomorrow will be the next major skill assessment for Math 7 and Pre-Algebra.  We've spent a few weeks going over the material and refining our language and tomorrow will be their chance to demonstrate proficiency.

I am lazy.  I don't like making up my own assignments when someone else already has one I can use.  I don't like making up tests because that takes effort.

Since I've been using Standards-Based Grading, many things have become easier.  I don't grade homework and the classwork that we do isn't for points.  It's been two weeks since a student asked "is this being graded?" because they know that only the skill assessments are worth "points."

The trade off is that I have to spend a TON of more time and effort on my assessments.  I can no longer copy and paste questions from an online book because they don't line up with the skills in a cohesive way.

Rather than tailoring my lessons to the assessment, I need an assessment that is tailored to my lessons.  Since those don't exist, I need to create them.

There are some truly amazing resources online and in the math teacher community to which I belong.  I'm able to pull from those places, but nothing is exactly what I want.  So, grudgingly, I have to create my own assessments.

And I'm LOVING IT!

Not the actual "creation" because I'm still lazy but the level of control that I have is excellent. I'm phrasing things in very specific ways and recreating concepts in the specific fashions

At this point, all teachers reading this are wondering how I managed to go this long without regularly creating my own tests and are rolling their eyes at me.  I get it. I deserve that.

I was pretty pleased with the review on which we worked, since it looked very much like what will be on the test tomorrow.

Put the colored dots on the number line that match the corresponding number 

This was the work that one student did for her warm-up. It's awesome!

Near the end of the day, one of my students had a meltdown and stormed out.  I had a LOOOOONG talk with the rest of the class about their actions and behavior.  We talked about how behavior has consequences, whether or not we see them right away.  This student's meltdown wasn't their fault, but they didn't help.

Kids can be pretty cruel to each other, even when they don't realize it.

Day 34: Team Contract

After splitting my students into groups of 4 yesterday, we spoke about the long term plans for the Greenhouse Project.  They each received a Team Contract and Team Calendar and spent the class filling them out.

The contract is an outline that lays out the rights and responsibilities for each member of the group.  It needs to be filled out and signed with the consent of all group members.  This means that each group contract will look slightly different, but is a consensus of all parties.  I REALLY like this idea because it prevents certain discussions later.

If I assign the roles, there is benefit to having them work outside of their comfort zones, but (as anyone who has carried a group through a project in college) the job still needs to get done whether someone does it well or not.

The contract seems to bring a level of maturity to the process where each team member must actively determine for which role they would be best suited and can benefit the team.  The assessment at the end will be a group grade, but there will also be individual grades looking at whether or not the members completed the agreed-upon tasks.

They also, as a group, decide what happens with members who do not live up the bargain.  They are responsible to their peers, rather than to me.

The scope of this project is...enormous.  One teacher has me thinking about sunlight and pH of the soil.  Another teacher has me thinking about planning a field trip to a local gardening center for research.  I'm thinking about how to get stones engraved with local business names so we can honor sponsors.

In addition to all of this, I'm struggling with how much direction to give them and how much to let them run.  We will have multiple conversations over the next few weeks, but even as someone who likes to say "here's the idea, now run with it" I'm debating about the amount of structure.

With that said, the groups worked VERY well today.  All 3 were engaged in discussion over the contract, the roles they would take on and the timeline for the entire period.



I also had a conversation with the students from last week.  They asked for my help on a problem and then immediately jumped all over everything, derailing my explanation before I could even begin.

Me: "I know you're excited and curious and want to ask questions..."
Them: "If I have a question, I need to ask it!"
Me: "Yes.  And you should! Curiosity is how we learn.  But I also have a plan and a path. It's likely that I'm going to answer your question in the next breath, but I don't get a chance to get there.  On top of that, not everyone in the room thinks the way that you do and they need to be allowed to think and process.  So here's my suggestion for you.  When you have a question, ..."
Them: "Just shut up?"
Me:  **pausing to allow the irony sink in a bit** "No.  Don't shut up.  When you have a question, write it down. Let me finish my thought and I may be answering your question. OR, better yet, you may figure out the answer on your own."

This entire conversation was held in quiet voices while I was sitting at the desk with them.  I REALLY like these kids and I don't want to stifle their curiosity.  I NEVER want them to think that I don't want them to ask questions.  But I also want them to try to solve those problems themselves and to realize that they are part of a learning community.

Communities need to work together and respect the needs of all members.

Day 33: GeoGarden

I have spent considerable amount of time thinking about what I want to do in my Integrated Math class.  We spent a week or so working on coding and did a survey project before that.  Today, we started the project that will take about 4 weeks.

Congratulations! You are now all employed at Aion Engineering!  We have been contacted by GeoGreenhouses, a small startup focused on urban gardening.  They have asked us to help them to design a geodesic greenhouse that can be assembled in the yard to allow the growing of fruits, vegetables, herbs and flowers all year round.

As design teams, you are to create plans and blueprints for a greenhouse kit that can be purchased and assembled at home.  It must be as efficient as possible, using a minimal amount of heating/cooling elements.  It must be rigid and must maximize volume while minimizing surface area. 

Your team will then design a presentation, including a design for the interior layout of planting beds and a proposed itemized budget.

We talked a bit about the history of the geodesic design and Buckminster Fuller.  We talked about greenhouses and watched a brief video about a family in Colorado that built one in their backyard.

I assigned groups randomly and handed out the Team Contracts.  Tomorrow, we will be assigning roles and discussing how to keep the team together.


One of the first questions they asked was about whether we were actually going to build the designs.

I emailed the principal laying out my idea and talking about how it would benefit the school as a whole.  So far, my ideas have been well-received by my administration, but this one goes a bit further than previous proposals, so I sat with my fingers crossed for a while.

My principal was incredibly supportive!

He copied the shop teacher, the Earth science teacher and the cafeteria manager (who has been working on getting funding for such an endeavor) and suggested ways that we could integrate various other aspects of the school community.

My plan is to have each group create a design and proposal on which (hopefully) the rest of the district will vote.  The winning design and budget will be the one that we build and utilize.  We can ask local business for sponsorship and donations.

I see incredible amounts of potential for this, now and in the future, including integrating the elementary in the growing and measurement of plant growth.

More important than any of this, the kids are enthusiastic about the idea.  I will need to work to keep that momentum going, but I hope I've hit one something that they will enjoy and work passionately for.

Day 32: Ruining The Story

My annoyance and frustration at having my students answer questions either before I ask them, or that I'm not asking at all sent me down an odd path today.

"For this next example, I don't want to hear any voices at all" I said, making direct and pointed eye contact with each student individually.

"I'm not asking you any questions or looking for any input.  I'm showing you my thought process.  If you have a question, you can ask that, but don't give me any answers, don't shout out numbers or steps or ideas.  Just be quiet and listen."

"For the next example, I'm being asked to give an estimate for the square root of 23.  I'm going to start by..."

Three hands immediately go up.  Two different students yell out "BETWEEN 4 AND 5!"

I'm having some deep internal struggles with this class.  I love the enthusiasm that some of the students are showing.  They love the problem solving aspects and are excited to move quickly through the material.  The issue, however, seems to be one of empathy and understanding of others in the room.

As with all classes, not everyone is at the same pace.  The students who are excited and ahead of the game are constantly running back and trying to drag the rest along.  It reminds me of children running through a museum or zoo, not allowing others to appreciate what they want.

The way that I design my lessons and my questions are in the form of a story.  I try to build scenery, characters, suspense and drama before coming to the conclusion.  When I teach a lesson, it's for a group and I attempt to bring them with me on a journey.  I have stops planned, sights to see and things to discover.


When The Sixth Sense was released, I went to see it with a group of friends.  In the first scene where Bruce Willis and Haley Joel Osment interact with each other, one of my friends looked down the line of us and said "something's weird with the mom. She's not talking to Bruce Willis.  I'll bet he's dead."

This was a pretty innocent statement and was just a theory.  However, since it turned out to be true, I watched the entire movie in a completely different light than I otherwise would have.


I don't want to crush the enthusiasm of my excited students.  I want them to be excited to come to class, excited to participate and excited when they discover things.  Added to this is the complication that they are middle school girls.

Middle school is typically the age where female students lose their excitement for math and science and I refuse to contribute to that.  These young ladies are talented and I want to push them forward.


I'm just not sure how to help them understand they can do those things without spoiling the surprises for anyone else.

Day 31: HexaSquares

With the success that we had in Math 7 yesterday with using the hexagons to talk about addition, subtraction and multiplication, I wanted to keep the process rolling.  Today, we added division.

As before, I started by having them talk about the operations in the language we've been using, talking about the concepts as physical quantities.  This is a much easier prospect when you have physical objects in front of you.

"15 divided by 3 is asking us how many groups of 3 can we find in 15."

Again, all of the students got their stacks of 48 hexagons.

"What is '48 divided by 8' asking of us?"
"How many groups of 8 are in 48?"
"Show me!"

And they did!

We did several different combinations, having them explain them each time.

I think I'm getting better at the kinds of questions that I'm asking and they are getting better at understanding what I'm asking.  Since we have stacking, interlocking blocks, tomorrow, I'm going to ask them what 4*6*2 would look like.

It also occurred to me that I could use the hexagons to talk about irrational numbers and square roots in my Pre-Algebra class.

So I did!

Each student got a set of 50 hexagons.  We discussed again what questions are being asked by squares and square roots.

"5 squared is asking us to find the area of the square that has side lengths of 5."
"The square root of 25 is asking us to find the side length of a square with an area of 25."


They played around with different combinations for a while, making squares from 16, 36 and 49 hexagons.

Near the end of the period, we began looking at how was could make a square from 17 blocks instead of 16.  Could we make a square from 24?

We talked about how we couldn't do it with whole hexagons, but instead would need pieces of hexagons.

Them: "For a square with an area of 17, side lengths of 4 are too small, but side lengths of 5 are too big. It has to be somewhere in between."
Me: "So let's estimate. Do you think it's closer to 4 or closer to 5? Give me as an estimate."
Them: "4.1 or 4.2."

I built a GeoGebra applet that showed us exactly what it would be and, since we've been working with estimates for 30 days now, it was a pretty easy sell.

We also began looking at where to plot those square roots on a number line.  That will continue tomorrow.


After class, a student who has been particularly distracted and distracting for the past month came up and told me how much he liked using the blocks.  He was on point today and I made sure to tell him so.  He said the blocks help him to understand what's going on, especially with the multiplication and division.

Nothing works for everyone, but everyone has something that works for them.

Day 30: Assistance

After posting about my frustration yesterday, I had some excellent conversations on Twitter.  There were many suggestions made about how I could improve the lesson to hit my desired point a bit harder and create a solid impression on the students.

Traditional mathematical education starts with the abstract and moves towards the concrete.

"Here's the formula. Now let's use it."

More progressive education moves in the opposite direction.

"Here's a pattern or characteristic of physical objects.  Let's figure out what's going on here."

The former of these approaches is often much easier on the teacher, but rarely is helpful for the student.


During one of the conversations last night, I realized that I needed to do more with the physical aspects of multiplication and division and less with the abstract (for now).  This is doubly true if I want my students talking about these operations using a specific language of those physical objects.

@getting_sharper they didn't. Any suggestions on how I could frame those questions?

— Justin (@JustinAion) October 5, 2016

@JustinAion in other words keep the whole the same so less attention is on finding "the answer" and more about communicating actions

— Charlotte D Sharpe (@getting_sharper) October 5, 2016

@JustinAion like, "if we have 48 apples, how could they be arranged on 2 tables?"

— Charlotte D Sharpe (@getting_sharper) October 5, 2016

@JustinAion revoicing student responses as addition (40 and 8 more) and multiplication (2 groups of 24) and division

— Charlotte D Sharpe (@getting_sharper) October 5, 2016

 It is by will alone I set my mind in motion...

Or, more accurately, it is by incredibly helpful suggestions from brilliant educators alone that I set my mind in motion.

Since I wanted them to work on these either individually or in pairs, I had a logistics problem.  I don't have 48 apples for each of my students.  I also decided against stopping to buy a giant bag of M&Ms on my way to work for obvious reasons.

Thankfully, I happen to have a giant tub of interlocking hexagonal building blocks and my OCD has been nudging at me to sort them anyway!

I spent the morning putting them into stacks of 10 and then groups of 50.

Each student got 50 hexagons and was told to put 2 aside so they had 48 (because there are tons of great factors for 48!) I emphasized that since we all had the same number of blocks, the answer was always going to be 48, but what I wanted to see was the representation.


"Show me 40 + 8."
"48!!"
"...Yes. I know. Nicely done. Now show me how you know that."
Second Student: "48!"
**slow blink** "Good. Show me."

Then we got the hang of it and they were really into it!

We moved from addition to subtraction to multiplication.  Each time, I reminded them to talk about it in the language of groups.

"Show me 6*8."
**they do**
"Tell us what you have there."
"We needed to make 6 groups of 8, so I made 6 stacks of 8 blocks."
"Nice. What about you?"
"I made 6 rows with 8 blocks in each row."

We got a slower start than I would have liked, so we didn't get to division today, but that will be tomorrow.

When my 5-minutes-left alarm went off, and they were cleaning up, I asked them what they thought of the activity.  The majority expressed that they thought it really helped them to understand what was going on and, particularly, the language that we're using.

I have a student who is an English Language Learner and I watched her thrive more today than in any other activity we've done so far.

I am indebted to Charlotte for pushing my thinking in this direction!