NSF Awards: 1503486

Collaborative Math is a professional development model that addresses the whole teacher -- knowledge, attitudes, and practice. In the first year of our randomized control trial, we discovered we made significant differences in early childhood teachers' confidence in their own ability to help young children explore math.

Research indicates that teacher attitudes are an important factor in math learning among children. In particular, it has been shown that female teachers who are anxious about mathematics can engender a similar attitude in their female students. Finding ways to make positive shifts in the thinking of teachers of young children about mathematics and its teaching may be an important key to altering children's math-related attitudes and subsequently, their math achievement.

Collaborative Math emphasizes a community approach to the enrichment of young children's math learning. At early childhood centers, teachers, assistant teachers, aids, and instructional leaders are all involved in learning together about foundational mathematical thinking. An intensive site-based component that includes coaching and extra supports for instructional leaders helps teachers and caregivers make and maintain the kind of changes in both their thinking and their practice that make math a rich and fun experience that both teachers and children look forward to.

This video describes the intensive, multi-pronged intervention model that has made this difference and documents the profound shifts teachers have experienced in their math teaching as a result of their experience in Collaborative Math.

## Jeanine Brownell

Co-PresenterThank you for your interest in preschool mathematics teaching and learning!

Collaborative Math is a professional development program designed to create sustainable excellence in math teaching in Head Start centers. In this video we highlight two activities we routinely use for professional development: 1. engaging adult learners in rigorous math tasks, and 2. role playing adult-child interactions around preschool math. In combination, these activities help teachers and instructional leaders participate in parallel processing--reflecting on their own experiences as learners and anticipating how to respond to the thinking of young children. As a result, we have found that Head Start teachers feel more confident in their ability to teach mathematics--an important and necessary shift for improved child outcomes.

Our findings did not show a shift in attitudes about mathematics in general, however. We are interested to know what other approaches people use when working with early childhood educators to build content knowledge, instructional practices, and positive mathematical mindsets. How do you address the particular needs of this workforce?

We look forward to the discussion and sharing of ideas!

## Nancy Gaumer

Watching the video gave me an idea for how I might have my online students "practice" teaching math to children. I'm thinking I can have them try out the practice with a friend or colleague to have them gain some confidence before trying it out with "live children". Just thinking about what to say and what materials they could use should help them or just encourage them to want to use this with children.

## Jeanine Brownell

Co-PresenterNancy,

I'm glad that you might try asking your online students to role play a teacher-child interaction. We have found that it's important to have the adults talk as if they were teaching--e.g. "I'm wondering which of these shapes might fit together" versus "I would ask the children to put the shapes together." Moving into the active voice forces teachers to think precisely about word choice and how to phrase questions. In addition, for our teachers who instruct in other language, we encourage them to practice in that language. Teachers feel more prepared this way, and that confidence boosts their ability to be responsive to children in the moment.

## Nadine Bonda

Resiliency is such an important concept in math teaching and learning. As you begin to build confidence in teachers about their ability to teach mathematics, what do you think you will need to do to also help early childhood teachers shift their attitudes toward mathematics? How are you helping them to send the message to children that math is fun, interesting, and challenging in a positive way?

## Jeanine Brownell

Co-PresenterThanks for the great question!

One hypothesis we have is that shifting teachers' confidence in teaching mathematics can begin a virtuous cycle of positive feedback that will, over time, repair and rebuild early childhood teachers' relationships to mathematics in general.

When teachers improve their instruction, the children are given more opportunities to reveal their natural curiosity about and enthusiasm for math. Many teachers have that "ah-ha" moment when they realize that young children actually enjoy mathematics! That discovery can open them up to see mathematics in a whole new light--as a sense-making, creative pursuit. But, this takes time. We must account for this when we plan for teacher development.

## Lynn Rule

Teachers with math anxiety cannot be effective math instructors, they need to be submerged in mathematical experiences, conversations and research to empower their teaching and in turn their students' understanding of math. Thank you Erikson for all you do!

Lynn

MathRack

## Jennifer McCray

Lead PresenterJeanine is right, Nadine--great question! To me, this finding that confidence for teaching mathematics can be shifted even when general attitudes about math remain relatively untouched, is extremely important. The way we assess these things is obviously key here.

Our ABC-EM measure frames "attitude" as how teachers feel about math in their own lives. Do they like math puzzles? Are they good at estimating the height of objects? Does the word "math" make them nervous? The answers to these questions have proved very difficult to shift through our professional development work, both in this current NSF study and in Innovations, our previous i3 work.

In both cases, however, confidence in math teaching was readily increased, sometimes with an effect size as high as .71. They way we frame this confidence is through agreement with statements such as "I am good at anticipating when my students might be confused with a certain math concept," and "Engaging students in math thinking is easy for me."

Other social science research tends to bear out that some ideas are so deeply rooted, it may be nearly impossible to shift them, and we believe that may be the case regarding some of these teachers' attitudes about mathematics in general. The same research also shows, however, that behaviors can be shifted regardless of whether or not attitudes change -- a very encouraging finding!

Within the year, we will have coded teacher observation data from the same sample of teachers that can tell us whether our improvements in teaching confidence are accompanied by positive shifts in teaching behavior or not. For now, I am hopeful that teachers who are more confident about teaching mathematics--and certainly trying not to convey any negative math-related attitudes they may have to children--might be providing that positive math experience that can help us break the cycle.

## Karen Economopoulos

Such important work with the teachers of our youngest learners! I'm curious about whether or not you collected data about teachers' perceptions of what math is and what math preschool age children should be learning? Did you see a broadening of teachers' perceptions of the mathematical opportunities that exist in children's play at the sand or water table or in the block area or on the playground?

## Jennifer McCray

Lead PresenterAnother great question! In our earlier version of our teacher survey, we did try to assess teachers' perceptions of what math is and how developmentally appropriate it is, but when we conducted factor analysis on the measure, we did not see these kinds of ideas hanging together the way they should. This is something we would love to know more about.

On the other hand, we use a measure of teacher knowledge change that is heavily influenced by Shulman's construct of pedagogical content knowledge. We felt that existing tools for this--designed for elementary school teachers--were somewhat focused on teachers' ability to analyze student's written work and to provide useful real-world examples that would help to make written equations meaningful. These are not the pedagogical tasks of the preschool teacher, who, as you say, must be alert to mathematical opportunities that exist in children's play.

Our interview, PM-PCK (Preschool Math - Pedagogical Content Knowledge), presents two play scenarios to teachers and asks them to analyze opportunities for thinking mathematically within that play. It produces a quantitative score, and we have decent inter-rater reliability and construct validity, and very nice variability among teachers in the results. It's not an easy tool to share since we are still working out training, but there have been adaptations of the work by others. And yes, we have seen such shifts in teacher knowledge.

We also focus our PD on Big Ideas rather than activities. That is, we try to prepare teachers to enact truly emergent math teaching by helping them develop familiarity with key concepts and experiences that can be highlighted for children. For example, using the kinds of natural organizational questions that come up during classroom clean-up time to point out that we can always sort a set of objects in more than one way can support the development of logico-mathematical thinking. By the same token, when children are on the older side, it can be useful to meet with the whole group to sort out the lost-and-found box when it is full of hats, mittens, and scarves. We find this focus on the concepts children need to grapple with and the kinds of experiences that foster such grappling to be very effective. Whether it changes what they think math is--that is another question, but I kind of hope so!

## Nancy McGowan

Your project brings about a very unique perspective that has not been considered. I love that you are building the confidence of those who work with young children! Roughly how much time went into the face to face professioal development in order to see the shift in confidence by the adults ?

## Jeanine Brownell

Co-PresenterThe Collaborative Math model is built around learning cycles. There are six cycles in a school year. A cycle involves 1. 3.5 hour Learning Lab with teachers and instructional leaders; 2. 4 hour Leadership Academy for instructional leaders; and 3. onsite coaching of teacher teams and building site-based coaching practices of the instructional leader (approximately 2 days on site). It's an intensive program by design.

## Jennifer McCray

Lead PresenterI appreciate the feedback, Nancy! The evidence keeps piling up that how teachers feel about the math they are teaching is an important factor in children's learning, and we're certain that these early years matter.

It's an intensive program, for sure. Teachers, assistant teachers, aides, and instructional leaders from Head Start sites all attended 6 "Learning Labs" that were 3.5 hours long. Instructional leaders (e.g., site directors, educational coordinators) attended 6 additional "Leadership Academy" meetings, also 3.5 hours long. Each Head Start site had a coach, and each 3-5-year-old classroom teaching team received one complete "Coaching Cycle" (planning, observation, reflection) between Labs, for a total of 5 cycles. Instructional leaders received on-site consultation from their site's coach around some center-wide initiatives, and they also shadowed coaches as they coached classrooms. We can estimate a coaching cycle as a total of 2 hours, or perhaps 2.5. Amounts of consultation to instructional leaders varied a bit by site, depending upon need and availability. Overall, the program focuses more time and energy on the instructional leader than the teachers. We hope this will lead to greater sustainability for what is learned.

All of this, as you can imagine, is expensive. Right now, we are gathering data to determine whether centers that had this experience last year are able to maintain the new teaching practices they developed with us. We are also implementing a slightly revised version of the model under a new contract with the City of Chicago, so we will continue to see how this goes. These teachers are our heroes, so it's great work for us!

Further posting is closed as the showcase has ended.