Friday, October 1, 2010

Mathematical Learning Inventory

Boy, it's been hard to find time to write lately.  Hopefully I can get a teaching and a more mathy post up today.

I was first exposed to the Mathematical Learning Styles Inventory last year at Math in Action, our local math education conference.  (It's the end of registration season for that - if you're close to Grand Rapids, MI give it a thought if you could come present!  Fillable pdf speaker form.)  The teaching center folks from Central Michigan University presented it, and had us take it and discuss.  An interesting bit for me was having a group of my students there.  When they had us move to tables based on our strongest style, all my students were seated at my lowest style!  Hmmm - was I providing them with appropriate work and activity.
Photo by michaelcardus@flickr
I know learning styles are a controversial topic in some arenas.  But I think of them as preferences and predilections.  I do not see them as exclusive or predetermined or limiting.  As with most assessments, they provide data about what your students prefer or think they prefer.  They might indicate areas where I need to provide more or more explicit support for my students.  Hopefully they indicate areas where students can become stronger with more experience and application.

Strong, Silver and Perrini do a good job at laying out their inventory in the 2001 ED Leadership article, Understanding Student Differences.  One of the things they describe are five great suggestions from their research:
  • Have simple, deep standards 
  • Differentiate
  • Increase the role of assessment and feedback
  • Start writing curriculum that appeals to students
  • Collaborate with colleague
They have examples and exposition of all five points in their article.  They introduce their learning styles in the section on differentiation.  A basic break down follows from a Silver, Strong, Perrini and Tuculescu article, The Thoughtful Classroom:Making Students as Important as Standards.
  • Mastery learners want to learn practical information and procedures (what)
  • Interpersonal learners want to dialogue and collaborate (how)
  • Self-expressive learners want to use their imagination to explore (how)
  • Understanding learners want to learn why things work (what)
I dislike their names for the styles, but what can you do.  Notice that two are really about what objectives you're shooting for, and two are about how you reach them, although all four styles have elements of both.  Their inventory is 25-ish multiple choice questions with an option for each style, that you give 5, 3, 1 or 0 points.  (How do they calibrate these?)  Their subsequent research has shown some strong validity to the types, and correllated academic struggle with instruction mismatch with learner type.  In particular, how learners that struggle in mastery classrooms are often remanded to remediation with an even stronger mastery-style.  Turns out that is ineffective.

I reworked the inventory for an inservice with middle school teachers because I thought that most secondary students would see it as repetitive and onerous.  Especially if they have to score their own inventory.  Also, people often complained about hard choices and having to choose between equally weighted (to them) options.  I thought about just giving nine points to distribute among the choices, but that would take even longer for students. (Although I like the elegance.)  So ultimately I decided to break up the questions and have students indicate strong, partial or dis- agreement by giving items 2,1 or 0 points.  That turns this into an informal assessment vs. a research-based inventory.  Sorry!  But I can share:

Math Learning Inventory (Adapted)

I gave it to my preservice K-8 teachers, and they had interesting results.  The different structure seemed to lead to more balanced styles numbers, though still indicating a preference.  It sounds like some of the middle school teachers are going to give it to their students, and I'll share their feedback on the assessment if they do.

Of course, if you try it with your students, I would love to hear how it goes!

I also made an easy data recording sheet to get a glimpse of your students' results quickly. (Plus bonus line plot lesson!)  Out of my cold-depleted class, I had strongest traits as follows: 7 mastery, 9 Inter-personal, 0 Understanding and 10 Self-expressive.  (Ties I counted in both categories.) I expected more mastery learners, as that's what most math teachers tend to be.  I personally have high scores in everything but mastery, so you can see why I worry that my preferences keep me from seeing my students.  But even more interesting (and relevant for planning) to me were the distributions.

The relatively high interpersonal scores fit with the engagement level during discussions, and the relatively low understanding scores fit with the lack of engagement when more formal reasoning is the topic.  The split on self-expressive seems to fit my crazier assignments, where some dive in and some ... do not.  I tend to struggle with what to do for mastery learners, as that doesn't fit my view of mathematics well.

I do want to reiterate what I put on the assessment: This shows the ways you are comfortable to learn math now. People can learn new ways to learn math and try ways that other people like. Everyone can learn to do math better.

In other words, remember the importance of a growth mindset.

PS> I've added a new post describing my use of this inventory and the results from a group of preservice teachers.


  1. Love the inventory, but I have a mental block. How do I plot my totals onto the coordinate plane? Waiting to hear from you. Thank you for your time.

  2. I just stumbled across this inventory and like the simplicity of the statements and score values. Thanks for posting it!

    Gina, the author may correct me if I'm deducing incorrectly, but here is how I am graphing it: *Using a totaled score of M 12, I 7, U 8, and S 9

    My 4 coordinate pairs would be:
    (-8, 12) (7, 12) (-8, -9) (7, -9)
    And unless I'm overlooking something, all results would be rectangles of varying length/width/position among quadrants.

  3. I like that, JB!

    I had students mark their total on each axis and then draw in a spider chart (make the quadrilateral with those 4 vertices). But I think JB's suggestion is a better visualization.

  4. Why are the scores for understanding and self-expressive counted as negative?

  5. John,

    I’m a pre service high school math teacher, and I found this post really intriguing. Although any inventory, survey, or standardized assessment that aims to sort all learners into a finite number of categories has its limitations, I see potential in the four categories that are used in this inventory. What I really like about your post is the suggestion that the students score the inventories themselves. This is a promising exercise in metacognition, especially if the students are asked to reflect upon the results of their own inventories. I think that it’s as important for students to understand themselves as learners as it is for their teachers to understand them. Perhaps a one-on-one discussion or debriefing, if you will, between the teacher and each student would add even more benefit to the process.

    One question that came up as I was reading your post was what to do as a teacher once the results of the inventory have been tabulated. More specifically, how do you adjust your instruction in a classroom with a mix of mastery, interpersonal, self-expressive, and understanding learners? This seems to relate to the practice of differentiated instruction, which is something that I am struggling to understand in a way that lends me concrete ideas and strategies to use in the classroom. I’d be interested in your thoughts and experiences on this matter.


  6. I don't think of this as learning styles, that limit how the student can learn, but rather as preferences. This is what (they think!) they like.

    The group I have this semester really identifies as self-expressive. So I've been trying to connect activities with that aspect. I also try to be cognizant of providing more structure and/or modeling when doing something that's uncomfortable. The oreo story would be an example of that, for what it's worth.

    The biggest benefit is almost intangible - it just helps me know them better. My teaching is at its best when I'm planning for these students in particular instead of designing an activity.

  7. is this learning style inventory has been published anywhere? or validated? thanks

  8. There have been a couple questions about the source - it's linked in the post above. I haven't published this anywhere, and certainly haven't validated it - it's an informal tool to me. The research in the original article is solid, though. Especially for use with preservice teachers, one of its functions is to get them thinking about the variety of ways to engage with mathematics, in comparison to their mostly monotone experiences up to this point.

    For this particular course, it's the last or 2nd last math course they will ever have - so time is running out. They need positive, diverse math experiences now!

  9. dear john, i've email you a request to use your instrument..