Instruments

Distinguishing features of our instruments:

• A focus on MHoM—the methods and ways of thinking through which mathematics is created—rather than on specific results. It’s impossible, even in three or four years of high school mathematics aligned with the Common Core, to equip students with all of the facts they’ll need for college and career readiness. But learning to think in characteristically mathematical ways is a ticket to success in fields ranging from business, finance, STEM-related disciplines, and even building trades.
• The core involvement, at every level, of mathematicians who have thought deeply about the implications of their own MHoM for precollege mathematics curricula, teaching, and learning.
• The items are designed to be accessible. We are not measuring teachers’ content knowledge per se; we are measuring what tools they choose to use to solve problems.

Our instruments are therefore aimed at discerning the extent to which secondary classrooms are centered on the practice of doing mathematics rather than on the special-purpose methods that often plague secondary curricula. In our work with teachers over the past decades, we’ve seen how expert teachers use core mathematical habits of mind in their profession—in class, in lesson planning, and in curricular sequencing. And, as the Common Core becomes the nationally accepted definition of school mathematics, teachers will be expected to make the development of mathematical habits an explicit part of their teaching and learning agenda. Our work will therefore make a unique contribution to the field’s increasing level of attention to secondary mathematics teaching.
 
The Paper and Pencil Assessment
The assessment aims to measure teachers’ use of MHoM when doing mathematics for themselves. The items are rooted in familiar secondary mathematics and are accessible, meaning most secondary teachers can solve them, or at least begin to solve them. This instrument is for use for research purposes only—it is not designed to be used to measure individual teachers’ knowledge or for teacher evaluation.
 
Classroom Observation Framework
During classroom observations, we identify classroom episodes in which teachers provide students with opportunities to develop MHoM. We also use teacher interviews to study the bridge factors between teachers' own MHoM and their use of these habits in the classroom.
 
Commitment to Equitable Practices
We are committed to equitable practices in our assessment. Some elements in particular support this commitment: first, the assessment is concerned with choices teachers make in their solutions, rather than what solutions were obtained, consistent with equitable practices  outlined in the literature (Steele, 2010). Second, we recognize that teachers choices in a given moment may reflect something they just taught, or there may be other influences on those choices. Thus, we do not allow use of our assessment for individual teacher evaluation; rather, the assessment gives a picture of the habits of mind of a group of teacher. Third, we ask that any and all survey/research/demographic data be collected after the assessment is administered to mitigate the effects of stereotype threat on the assessment itself.