Goal: student portfolios

I haven’t seen much talk lately on twitter or in the blogosphere about portfolios. I want to deepen students’ understanding of concepts so I thought I’d steal/modify a portfolio idea that was shared at last week’s math curriculum meeting. If you can help me figure out a way to add more choice while still addressing the concepts, I’d love your input. As it stands right now choice is limited to product, and in a small way–process.

The original idea shared was too open ended for me, “Prove you have mastered the learning objective.” While I’m a free spirit in many ways I think the students need some focus so I came up with specific criteria for both the artifacts and written reflections, along with a rubric for each.

Subtracting Integers Criteria for Success


Submit three artifacts demonstrating conceptual understanding of subtracting integers. Record your thinking using Explain Everything, iMovie, or other format.

  • create visual models. Include the following scenarios:
    • x– y
    • x– y
    • x– (– y)
    • x– (– y)
  • create and solve an equation using a series of five different positive and negative integers on BOTH sides of the equation to make the statement true.
    • Example: –a – (– b) + c – d – (–e) = f + (– g) – (– h)  –  i + (– j)
  • create and solve an original, real-world integer problem where absolute value is applied.

Here’s the artifact rubric. It’s generic so it can be applied to any collection of artifacts. I didn’t include point equivalents or percentages because I want the students to focus on the “feedback”. They’ll be able to resubmit.



Submit a written reflection of your artifacts. Include:

  • an analysis of the artifacts
  • the math practices applied and how you have applied them
  • the modes of representation used
  • proper grammar, spelling, conventions

Here’s the reflection rubric. It’s also generic.


When I’m ready to grade I’ll translate the levels into percent equivalents. For example:

  • Level 4 = 100%
  • Level 3 = 90%
  • Level 2 = 70%
  • Level 1 = 60%
  • Level 0 = 50%

As the portfolios are turned in I’ll share student work and let you know how it goes.

Other bloggers sharing their goals can be found by clicking the link below.


Good, bad, ineffective feedback using Canvas

Last week I introduced integers using a James Tanton Math Without Words visual puzzle.  Below are examples of the student feedback I gave. I used our new Canvas LMS system as the work flow, but what’s important is the varying degrees of feedback I found myself giving students.

Since some students don’t bother to read feedback–especially when everyone, including me, is getting used to Canvas, I started class by asking the students to pull up the assignment and read the comments.

The student below read my feedback and asked very politely, “What am I supposed to do?” This is yet another reason why I will never earn National Board Certification.

Had I thought about it ahead of time, my feedback should have read, “If every bump is a hill and every dip is a valley, what remains?” That’s something I did for another student. See last image.

I gave this kid nothing. At best I offer hope and a growth mindset but in terms of informative and constructive feedback, it’s terrible–absolutely terrible.

Here’s another student. I acknowledge he’s made the connection to integers, but…

canvas feedback3

…I should have added this:

For students who clearly made the connection to integers, I should have been prepared to offer feedback that extended their thinking, but I wasn’t.


Here’s another example of awful feedback. I acknowledge the problems are correct, but I offer nothing.

canvas feedback2
I should have extended this student’s thinking. I could have added, “If these were numbers what would they be?”

Finally, here’s some feedback that is potentially helpful.


When I gave the feedback I didn’t have a plan. I just viewed the student work one at a time and made comments. That made my feedback inconsistent and not effective. What I should have done was examine the student work collectively, and prepare feedback based on common misunderstandings and extending student thinking.


Boring bit: vocab makeover

This 3-2-1 summary is a bit different. I’ve been focused on one thing, that was talked about by two people, more than 3 days ago.

What I’m talking about is Justin Aion’s recent post and twitter chat with Tracy Zager on vocab. The major takeaway is that a need must be created for a vocab lesson to stick.


Next week I’m starting number properties and I’d be a fool to not apply what I’ve learned from lurking and eavesdropping. Here’s what I have so far. Your help could make it all the better.

Students will be paired and will receive this Number Properties Partner Password game that has been cut in half hotdog style. Partner A begins by reading problem 1. Partner B does what his partner says in the space provided.


Only one student who took the pre-test could provide an example of any of the properties so I know nearly all my students will have difficulty coming up with the terms commutative, associative, etc. Originally my resource card for commutative referred to passenger trains that move people to and from work, but that’s beyond my kids’ vocabulary, so I resorted to hangman as the resource card.


Now it’s Partner B’s turn for round 2. The partners alternate until the game is finished.


The directions also include using precise math vocabulary. My hope is students will use sum, product, the quantity, etc along with identifying the property in their sentences. I may end up saving that for another lesson because the primary focus is on number properties.

After debriefing, and time permitting, I’ll reinforce with a number talk, maybe start small with 16 x 5 and see where that takes us. Then, when doing number talks, I can make connections to the number properties.

This activity is better than the blank page I started from several days ago, but I truly welcome suggestions.

Others blogging about their 3 – 2 – 1 summary can be found by clicking the link below.