Every time our math committee meets we are energized by the progress we’ve made but at the same time we feel deflated because there is so much more work ahead of us. Last week we were again reminded that our math units need bolstering.

On Wedesday we once again analyzed our progress using the Tri-state EQuIP Rubric designed by Achieve. For the 7th grade rational numbers unit there are four areas we need work on:

Linking Mathematical Practices to learning opportunities and assessment items.

We hadn’t formally identified the applicable MPs to each learning sheet and activity so we went back and did that. Examining our assessments was next. My colleague and I experienced a giant YIKES on the decimals assessment because hardly any items could be linked to a MP. Since we ran out of time we need to revise those items plus look at the other assessments in the unit.

Explicit writing, speaking, and listening opportunities

We made some progress here by modifying directions on some activities. For example our subtracting integers portfolio was modified to include two peer reviews. The next time I assign this task students will create a draft of their video using Explain Everything then two students will watch, listen, and provide written feedback before creating the final video.

Instructional supports

We have some intervention and enrichment resources but we need find more and better organize the ones we currently have. The rubric also identifies the need for a performance task for the unit. I think we inadvertently listed it in the instructional supports section.

Scoring rubrics and pre-assessment reflection plans

Formally identifying the characteristics of partial credit, high partial credit, and full credit are on the drawing board. We also need to create a pre-assessment reflection plan for students to identify their strengths and what they need to review. This also includes helping them design an action plan before they take the assessment.

I’ve been thinking a lot about effective effort. Should I expect students to give 100 percent effective effort if I don’t give 100 percent?  These thoughts are a work in progress. Right now I’m examining effort characterized through the lens of The Skillful Teacher and the 100% factor–a term to describe how both student and teacher should each give 100 percent to their respective responsibilities.

The Skillful Teacher identifies six attributes of effective effort: time, focus, resourcefulness, strategies, use of feedback, and commitment. It’s not realistic to expect students to give 100 percent, every class period, every single day. They’re kids; but I can give them abundant opportunities to experiment with these attributes–if I’m giving 100 percent.

### Time

Student: Do I budget my time, sometimes an extended amount of time, to meet high expectations? Do I not persist because the task is challenging and requires more time than I want to give?

Teacher: When assigning a project or when I expect “more time than usual” to be spent on an assignment,  do I estimate how much time will that be? Do I share that with the students? Do I negotiate time limits? Do I provide my students sufficient time in class to begin an assignment or project? Do I budget time in class to work on large projects?

Comment: I wish I had asked myself at least one of those questions when I assigned the subtracting integers student portfolio project.

### Focus

Student: Do I work with minimal distractions? Do I have a clear idea of the objective, the criteria for success, and exemplars so that I maintain focus on what the assignment is asking me to do?

Teacher: Is the objective clear; have I provided exemplars and explained the criteria for success? Do I monitor student work time by helping students prioritize and refocus their efforts on what is important? Is the work time environment conducive to learning?

Comment: I provide clear directions and criteria for success, but my 100% factor throttles down with helping students prioritize and refocus. When I had a homeroom, I created a solid work time environment, but I did not check in with each student and help prioritize their work. Some kids need that.

### Resourcefulness

Student: Do I attend math lab or seek the teacher for help? Do I have a study buddy, or study group? Do I use a list of online resources, textbooks, etc?

Teacher: Am I available to students? If students are not resourceful, do I insist they attend math lab? Do I model how to use various resources and where to find them? Have I provided a list of resources that are readily available?

Comment: I have mixed results in this area. In the first quarter I identified certain students and it was mandatory they attend math lab on a particular day of the week. As we made our way into the second quarter, I didn’t keep up with it. Now that we are at mid-term, I need to pull up the throttle. On a positive note I do have to say my students can easily access the online resources I’ve posted in Canvas.

### Strategies

Student: What reading, writing, thinking, and reasoning strategies do I use? What study tools do I create? What graphic organizers or summarization techniques do I use?  Do I know what to do when a strategy isn’t working?

Teacher: Do I teach strategies for transfer? Am I modeling relevant mathematical practice(s) and study strategies so my students can apply them? Do I model reading fix-up strategies and explicitly teach thinking and reasoning strategies?

Comment: I can write a thousand words on how I can improve on this topic. Our school improvement plan is in its second year of implementing thinking strategies in every subject. I’m still working on embedding them in my teaching. With respect to study tools, I sometimes fall off the wagon and forget to assign a study tool such as creating a practice test. Most of my students would not think to do it because it takes time.

### Use of feedback

Student: Do I apply or use feedback in order to improve my performance? How does that feedback inform me of my progress?

Teacher:  Do I give timely feedback and allow students to implement it? Do I provide student-friendly rubrics and criteria for success as a means of providing feedback? Does my feedback include other attributes of effective effort?

Comment: How do I readjust my lesson based on the feedback the students have given me? I devote a lot of time to providing feedback, both written and oral. Where I can improve is differentiating each lesson based on the feedback the students give me.

### Commitment

Student: Does my work ethic demonstrate a commitment to learning? Am I reflective and do I readjust my efforts to achieve my goals?

Teacher: Have I developed stamina in my students? Do I help students set goals that are specific, measurable, attainable, realistic, and timely?

Comment: My favorite question I ask myself is, “Are you interested, or are you committed?” Some days I have the stamina so I’m committed, other days I don’t have the energy, so I’m interested. I think that holds true for students as well.

My students are rising to the occasion. They never encountered the following type of problem before but by the second day they were becoming masters of the universe.

A little elephant has 12 peanuts. In the spirit of giving each day he gave away a fraction of his peanuts, kept the rest, and then ate one. These are the fractions he decided to give away:

$\large \frac{2}{3}, \frac{1}{4}, \frac{1}{8}$

In which order did he use the fractions so that he was left with just one peanut at the end?

This task is the second in a series of three. I wanted to give the students a challenge while practicing multiplying fractions, but I also wanted the problem to be approachable. Frankly I think it would have been a disaster had I not introduced the tree diagram the previous day. While in previous years students had used tree diagrams for an occasional probability problem that approach was the farthest thing from their minds. My goals for the lesson were to practice multiplication of fractions while using the diagram to organize their work.

As they became more comfortable with the tree diagram student work became more systematic. That freed up their brains to concentrate on what is happening with the fractional amount. Several groups needed to be reminded that the elephant gives away that amount, which means he keeps the rest, then eats one.

Here’s an example of how one group organized their work:

One student, Jeff, had missed the previous day’s lesson where I introduced the students to a simpler version of the problem involving only two fractions.

He admitted he was a bit confused, “There’s a lot to keep track of.”

At the start of day two’s lesson several students were able to determine which fractions to rule out as starting points. After I reviewed the first peanut task one student said, “We have to start with
$\large \frac{1}{2}$ because 3 doesn’t go into 14 evenly.”

On Monday, groups will tackle the third peanut task with minimal oversight. Those who finish early will work to create their own peanut task.

I want you to know that the inspiration for these problems was provided by the Peaches Today, Peaches Tomorrow task on the NRICH website. Part 2 of the series captivated me, yet I thought dealing with 6 fractions in a 41 minute period would be too much for my seventh graders. Designing these problems was a collaborative effort and I want to thank my colleagues for their help in creating a meaningful twist to the problem (give away instead of keep).

One of my colleagues created a student reflection sheet for students to complete at the end of each quarter. He then meets briefly with each one to discuss how they’re progressing on student skills. I’ve refined it just a bit, but I’m wondering what you would add or modify?

While I’ve met with only a few students this reflection has been incredibly valuable as talking points during last week’s parent-teacher conferences. I hate discussing grades. Our grade books are transparent so parents can see their student’s grade at any time. What I can give parents however is a sense of how their child sees himself as a learner.

This quarter the biggest talking point for several students was effective effort in terms of:

• 1) following the rubric or criteria of success, and
• 2) implementing feedback

for the integer portfolio project.

The portfolio was extremely time consuming to assess, but the project gave me incredible insight into a student’s understanding. The two biggest drawbacks to the project were some students didn’t submit all the artifacts and/or they’re implementation of the feedback I provided was done only after I got parents involved. These were the two elements I added to the reflection and they became the major talking point I had with parents. They will also become a major talking point when I meet with my students.

One talking point that we’re quite familiar with is class participation. Students know themselves pretty well and parents do too. But asking students to self assess on active class participation invites a conversation on why one would try not to participate or volunteer answers. Not meaning to dwell on the negative, I do want to say it also gives me the opportunity to provide positive attention and acknowledge those who do participate, collaborate, and actively listen.

Other areas on the reflection sheet include class time use, assignment completion, quality of work, and attitude. For next quarter I want to add something about assessment preparedness and retakes, but I haven’t found the words yet.

I’m interested in making this better so if you have something that works for you, please share.

Before we jump into adding and subtracting negative decimals I thought we should spend some time defining what estimation is and is not. That way students would be able to determine if their answer was reasonable. It took about a period and a half to clear up misconceptions but I think it was time well spent.

The basic structure of the lesson was 15 minutes of group work using giant whiteboards, followed by a 10 minute a gallery walk for feedback, then the remainder of the period to refine their definitions and examples.

I posted the following directions: Create your “bestest” definition of estimation and provide one example and non-example.

Here are the first drafts of student work from one of my classes:

Some groups were on the right track, but their definitions and examples could be more explicit. When it came time for the gallery walk the groups examined each others’ work, commenting on two things: one thing they like about the work and one thing that needs clarification. Groups struggling with the definition or example/non-example really benefited from seeing others’ work. The post it feedback also helped them to refine thinking.

At the end of the period I asked students to use their iPads to take a photo of their work and the next day we debriefed. The definition of estimation being an educated guess was lacking for me, so I added the phrase, “by using a strategy.” I think  that condition to the definition will allow us to continue our estimation conversation when we talk about scaling up or down with proportional reasoning.

Having students create their own version helped them participate in the final draft. We talked about where rounding occurs in estimation so we could identify the characteristics. One student thought it helpful to include arrows to clarify what is being rounded, and I threw in my caveat about using a strategy as part of the definition.

While it took a lot of time the students ended up owning the definition more than if I had told them what to write in their notes. The collaboration and post it feedback also helped those students who may have had some trouble getting started on their own.

Somehow there’s a disconnect between my writing expectations in math and what’s being turned in. For the subtracting integers portfolio which I’ve written about here and here I provided ample time, included both the criteria for success and rubric, plus discussed the reflection in class on multiple occasions. Either I’m not making my expectations clear or my students are not used to doing reflective writing that includes an analysis. I’m guessing it’s both so I created a graphic organizer to help them be more reflective and analytical.

First of all here’s the rubric the students are using:

And here’s an example that would benefit from a graphic organizer:

“In my portfolio I use multiple strategies. For the first thing we had to We had to use visual models you things certain ways to solve it. Such as -x -y or x-(-y). Then we had to use five positive numbers and negative to do this I first made a bunch of positive and negitive fives and just put it together and solve it and then I just made of a problem of -20+ positive 25 equals five.”

The student below is beginning to meet my expectations, though a revision using a graphic organizer will help provide specific evidence that’s currently missing.

“I can solve problems without giving up. What I used to help me was examples from the past worksheets that we did a while ago. … I can use math tools and explain what I use them. I used a number line as a math tool and I use this to show in understand my work. Kind of like a visual for me. I can work carefully and check my work.  I work carefully keeping my work organize and neat. I also check my work by doing the opposite of the problem and see if it kind of matches. It’s hard to explain…”

This Written reflection subtracting integers graphic organizer isn’t perfect, but I think it will help.  I’ve clarified and provided some examples of insightful analysis:

Using the graphic organizer, students now have a work space to brainstorm which of the eight math practices were utilized and how.

Image edited for space. Practices 5-8 are also listed on the graphic organizer, just not shown.

On Monday, I’ll share student work samples and ask the students to both critique and evaluate the reflections based on the rubric and graphic organizer.

I’ll update and report progress in my next post.

A couple of weeks ago I wrote a piece about student portfolios, specifically a subtracting integers portfolio my students were about to create. Their media of choice is Explain Everything. Now that the projects are trickling in I’m discovering conceptual errors which I might have overlooked on a traditional paper-pencil assessment. Here’s an example:

While the screenshot does capture the number line error when subtracting a positive number, I’m drawn to the student’s voice and explanation, “Since 2 is negative I move to the right.” The portfolio is no longer a thing to grade, there’s a human being behind that work and I can see and hear her. Her portfolio submission has instead become a formative assessment.

This next problem demonstrates further confusion. Here 2 is negative, but she moves to the left.

The student below, on the other hand, has mastered subtracting integers. She begins by demonstrating the number line movements, explains why she moved to the right, then proceeds to show its equivalence by adding the opposite.

When solving this equation the student admitted to a lot of guess and check, however I’m not bothered by the extra practice she got from doing the problem.

After introducing this slide she explained how she turned it into an addition problem by adding the opposite.

Then she solved.

So far my favorite student created real world problem is:

Only three projects have been submitted thus far, but I’m anticipating most of my time will be spent giving feedback rather than issuing grades. I don’t feel comfortable grading something that’s a work in progress. In terms of time, the portfolios run between 6 and 7 minutes each. I really need to front load the time now so it will be easier later when the students apply the integer rules to negative fractions and decimals.

Update:

Here’s another project I looked at this morning. How much conceptual understanding does this student have? He provides no explanation and relies on adding the opposite to demonstrate the number line. Also, he only provided a screenshot of the equivalence problem with no explanation of how it was solved.