We recognize that we could have measured many, many habits of mind. Focusing on three habits has allowed us to create an assessment that is not too burdensome to use. We started with a list of 40 mathematical habits of mind, gathered from the field (including the CCSS SMP), from advisors, and from our own experience of mathematics, and first thought about which of those habits we could measure using a paper and pencil assessment. We then used a process suggested by our methodologist to determine which of those were most “central” habits.

We then parsed the habits for measurement purposes – for example, the two processes of seeking structure and using structure in SMP7 look different when people actually do them, so we are studying them separately. We also chose the habits that we felt we could capture in paper and pencil format. (Fee free to contact us for more details on the methodological process used come up with our current list of habits.) After multiple rounds of field testing of the assessment, we did carry out some analysis to investigate the relative contribution of each of the three habits we were measuring.

The rubric was built from teacher data – our assessment advisors predicted that the data from completed teacher assessments would “clump” around particular responses, and indeed, that happened. We then used those clumps as the basis for exemplars for a scoring rubric, and invited a collection of nationally esteemed mathematicians (all of whom are deeply immersed in education) to choose the scores for each exemplar/clump.

For information about the assessment and the rubric, please see: Sword, S., Matsuura, R., Gates, M., Kang, J., Cuoco, A., & Stevens, G. (2015). Secondary Teachers’ Mathematical Habits of Mind: A Paper and Pencil Assessment. In C. Suurtamm (Ed.), Annual Perspectives in Mathematics Education: Assessment to Enhance Learning and Teaching (pp. 109–118). Reston, VA: NCTM.

Hi Mary – if you’re asking about assessment items, just shoot me an email and I can send them. If you’re asking about actual PROMYS-like problems, there are lots of places to find that kind of content. One example is the recent AMS collection of PCMI-SSTP books: http://bookstore.ams.org/SSTP. We also have content from a number of EDC seminars that have been developed over the years but are not yet in published form – we can get those to you if you’re interested. Thanks for the question!

Hi Brian, thanks for asking. We often do discuss the assessments with the teachers who have taken it. In the early days of development, those conversations had a pretty big impact on the development process. Now that it’s being used as a pre-post assessment, we don’t usually talk about it after the pre, but if project time allows, we do discuss the items and the assessment as a whole after the post. As you predicted, those conversations are pretty interesting. It’s a concrete way into starting a conversation about the Standards for Mathematical Practice, for example.

And teachers have been involved in other ways. For example, teachers at Lawrence High piloted some of the early drafts, and some teachers in PROMYS spent some afternoons coding responses from a pre-test.

It would depend on how much of teachers’ thinking we can capture in a computer-based assessment. As described in the video, we’re interested in how teachers approach each item, not necessarily the solutions that they obtain. Early in the project, we tried using multiple-choice items, but this wasn’t helpful in capturing their thinking/approach.

So, coding does take some time—-but our rubrics have been refined to the point where most teacher solutions tend to fall into one of the codes, and we can identify this pretty quickly.

Hi Ale –
Thanks for writing. It might be worth trying the measures out with your next cohort. The assessment works better with teachers who have experience teaching algebra (or are comfortable with it) because of the content – although it’s not a content test, the items are rooted in algebra content. One of the things that may be useful is that it’s possible disaggregate the scores by language, structure, and experimentation – so in one of the pre-post field tests, teachers’ scores improved overall, but their “structure” scores improved the most. That was handy, because the course focused on algebraic structure. (We weren’t the instructors, by the way.) So even if the whole assessment isn’t a fit, some component may be. Shoot me an email if you’d like to take a look at the assessment. ssword@edc.org. Thanks again!

Thanks Sarah for the explanation and the alternatives to the measures. I will contact you to obtain the assessment. Besos!