NSF Awards: 1625215

*The video presents activities and outcomes for an online professional short-course for college instructors who were new to teaching mathematics for future elementary school teachers. Participants in the short-course included graduate student, part-time, and full-time instructors from 2- and 4-year colleges. Research examined **participants' knowledge of mathematics for teaching and that of their students. Participating instructors and their students completed pre- and post-semester questionnaires about the specialized knowledge used for teaching mathematics. Continuing research will examine instructors' contributions in online text-based discussions and individual interviews. Questions driving the research: What did instructor-learners find challenging? Valuable? How did the short-course influence their perspectives related to equitable teaching and learning? How did they use what they learned? Why that way? What did their students -- prospective elementary school teachers -- learn related to equitable teaching and learning of rigorous mathematics?*

## Shandy Hauk

Lead PresenterAssociate Professor

Greetings from Shandy, Jenq Jong, and Billy,

Welcome to our corner of the showcase for

Professional Resources and Inquiry into Mathematics Education (PRIMED) for K-8 Teacher Education. Given the complex and multi-cultural environments for today’s public school teachers, the project sought to understand and support the growth of two things: (a) college instructors’ mathematical knowledge for teaching and (b) their attention to inter/cross-cultural aspects of teaching.We welcome your contributions to the conversation thread!Now nearing the end of our project, we are particularly interested in feedback on these points:What is your sense of the skills that a college mathematics faculty member brings to teaching prospective elementary school teachers? What skills do they need to develop?

What are others using as evidence of inter/cross-cultural development?

Learning Mathematics for Teaching(LMT) questionnaire. Greater student gains happened in classes where instructors used a course package of locally tested instructional materials, sometimes called a “course notebook.” If we create a library for mathematics faculty:What things might be important to highlight about such instructional materials? Why those things?Thank you for your contributions!

## Hollylynne Lee

Hi Shandy!

What an important and ambitious project! I'd like to further discuss the questions you raised in your #1 above. Your project seems to be addressing K-8 mathematics, which is a pretty broad set of mathematical concepts. Of course, we know that different states do licensure for different grade bands, and thus universities design their elementary teacher preparation differently as well.

SO I have two wonderings:

1. What may be the best way to organize your materials so as to be able to help college faculty develop their matheamtical knowledge for teaching across different domains/topics in K-8? Have you all done anything to distinguish between mathematics topics? It seems that having a deep understanding of how the different topics are developed across the K-8 grade band and how they are interconnected would be important---and too much for a faculty "short course".

2. Related to important skills, you mentioned in the video that college faculty like to engage with videos rather than read, and to talk rather than listen. Thus, I wonder how these may translate into skills they need to develop as mathematics teacher educators to provide meaningful experiences for their college students (preservice teachers). Ultimately these college faculty will need to be designing leanring experiences for their classrooms of preservice teachers. So while this may seem more pedagogical in nature, is there a way to help faculty connect this to their developing of MKT?

## Shandy Hauk

Lead PresenterAssociate Professor

Whoo hoo! On #1, your thinking goes with ours -- we have already begun collecting activities for a PRIMED 201 (as opposed to 101) short-course. Several activities were pruned during the test-bed of the short-course. We took things out to maintain responsiveness to the faculty needs for those participating in the course. The short-course is designed for NOVICES -- folk who have taught the course once or twice only.

On #2, that's why we are interested in starting a base of curated materials developed by people who are experienced -- to give novices insight into what effective design looks like. That would be another PRIMED 201 topic, more on how to design tasks (there was one Lesson Experiment in PRIMED 101 that did a bit of that).

## Hollylynne Lee

Looking forward to seeing how your 201 course will develop!

If you are interested in seeing some online teacher education materials we developed for learning to teach statistics, see our ESTEEM project and materials (an IUSE-funded project). We have many faculty who implement our Foundations in Statistics Teaching module into courses for elementary preservice teachers.

## Shandy Hauk

Lead PresenterAssociate Professor

More information for researchers and developers can be found in our paper in the current issue of

The Mathematics Enthusiast:Jackson, B., Hauk, S., Tsay, J.J., & Ramirez, A. (2020). Professional development for mathematics teacher education faculty: Need and design.

The Mathematics Enthusiast, 17(2&3), 537-582. Link to PDF of the article [opens in new window].## Jamie Mikeska

Can you say more about what these modules include and how they are set up to support math teacher educators in developing their MKT? I also like your idea to create a library for faculty. What kind of materials do you think would be most beneficial to include in such a library?

## Billy Jackson

Hi --

So thanks for the questions. The modules include topics such as

(1) task-based learning in K-8 classrooms and courses for teachers,

(2) an introduction to teaching and learning theories such as Bruner and constructivism,

(3) readings on MKT and research pieces on various goals and strategies employed in the courses by experienced teacher educators

(4) an introduction to Schoenfeld's Teaching for Robust Understanding framework as a lens for helping faculty understand issues such as equity and access in the math classroom

(5) introduction to policy and standards documents such as the Common Core and AMTE standards

In response to your second question, we envision including tasks with annotation from experienced teacher educators that can help guide faculty enacting the tasks for the first time as they construct their own anticipatory knowledge. Materials would also include discussion about task alignment with policy and standards documents in helping future teachers learn about MKT.

## Shandy Hauk

Lead PresenterAssociate Professor

Hi Jamie,

As an example, I've included a link to the current version of the one-page Module 1 roadmap [click here, *should* open in new window...].

Given the sample "course notebooks" we have seen, and informed by work by Sandra Laursen in the CoMInDS project, we are considering possible layers to include for each library entry:

(1) a checklist that summarizes/highlights content of the materials based on a set of policy/recommendations (perhaps AMTE, or the synthesis of recommendations such as can be found in Zhang et al., 2020);

(2) a profile of the particular context/program in which the materials are used (generated by interviewing folk who have developed/use the materials locally);

(3) the actual digital files and organization provided by the department that has generated the course notebook.

## Ann Cavallo

It would be helpful to know more, perhaps with some brief examples, on how the project addressed this goal: b) their attention to inter/cross-cultural aspects of teaching. How was this measured and what were results indicating gains in this area? Thanks!

## Billy Jackson

Hi Ann--

Thanks for stopping by : hopefully things are going well for you and James there at UTA. So in response to your post, intercultural competence often times has to start with recognition of similarity and differences: i.e. faculty have to develop a sense of "other" from "self". One of my favorite tasks that we had the faculty engage in was reading a piece Shandy had written several years ago that examines differences in math autobiographies among various student subpopulations, including future elementary teachers. The reading highlights the many different experiences that future elementary teachers have had in math and ask we asked the faculty to compare/contrast the teachers' experiences with their own. In fact, if you look at our 2014 paper on PCK, we have long claimed that intercultural awareness and responsiveness is an integral part of MKT. This has been long accepted in the science ed community as they have continually argued that orientations towards science and its teaching are an integral part of disciplinary knowledge for teaching-- the math ed community overall has been slower to accept this I believe.

But the task I just described gets the faculty in that reflective mode to notice difference. Intercultural competence was also highlighted in module 2 on the TRU framework-- during the synchronous session discussion, Shandy and I (as the facilitators) made conscious efforts to have the faculty engage with the challenges that intercultural competence can bring in instruction. For instance, agency can often times be challenging to balance with things like cognitive demand.

Another task in Module has the participants read a case as described by an experienced math teacher educator in working with her future teachers on having them reflect upon their beliefs about working with English language learners. The piece is so perfect I believe because it deals with the culturally embedded aspects of discourse. We have the participant go back and reread the piece and replace ELLs with future elementary teachers and let them discuss the parallels between the two groups.

The Intercultural Development Inventory (IDI) was administered at the start of the program for both instructors and their students. This well established reliable instrument has been shown to validly measure a person's orientation towards intercultural difference and similarity. The students and instructors also took the Learning Math for Teaching assessment pre and post. We found that the students who scored lowest initially and showed the greatest gains from pre to post were in the classrooms where their instructors had more intercultural development as measured by the IDI. Interestingly enough, we reaffirmed what we have seen in our prior work over the years. The students are generally in a stage of development where they are polarized (i.e. they notice difference but see it as "us" compared to "them"): the instructors by and large tend to be in a stage of development where they notice difference but they tend to minimize those differences in favor of similarity as a means of "finding common ground" by stressing how we are all alike. Note that there exceptions to this -- some instructors were in different stages. We actually are looking to hypothesize in coming work that professional development and learning for math faculty and K-12 teachers can be most effective when learning opportunities are differentiated by the development stages of the participants.

Hope this long (my apologies) response helps!

Billy

Ann Cavallo

## Ann Cavallo

Hi Billy! Yes we are fine here in Texas - I sent James the link to participate in this event so hope he stops by! Great explanation of how you implement inter/cross-cultural aspects of teaching. We are working with university faculty as well as our K-12 preservice and inservice teachers incorporate cultural responsive pedagogy in teaching. The IDI might be something we should explore using. Thanks!

## Luella

In the presentation, my experience agreed so strongly with the idea that college educators don't usually know what is being taught in elementary school. I often think about common core and how the little I know about it comes from friends who are parents or K-12 teachers! I think it's helpful to understand how students learn to add/subject/multiply/divide etc in order to understand how to continue to teach them. When I went to elementary school, we memorized the multiplication table. From my limited understanding, that's not the focus now for multiplication? This might be part of a larger trend to teach away from formulas. If that is true, then if a student started to see a lot of formulas in college that they just have to memorize, it might be especially difficult to transition. So then perhaps at the college level, it is helpful to consider how to teach in a way more similar to what students grew up with or at least somehow make use of how they have been learning? I am not sure if this is practical; it is just a thought.

## Kathryn Kozak

Did you do a presentation at this years AMTE conference?

## Billy Jackson

Co-PresenterHi Kathryn--

Unfortunately no. AMTE and RUME both have their conferences in February and I like others generally end up having to choose one or the other for compensation purposes. I am hoping that if our supplement request is approved that I will be able to have funds to go to both since Shandy and I are members of both organizations. It's a real shame because there is a significant proportion of people who are members of both as teacher education is considered a part of RUME, and as such, a large portion of RUME research comes from teacher education.

## Kathryn Kozak

I am sorry to ask. I thought I saw your presentation on this at AMTE. Actually, it is more that I think I have met Sandy somewhere. Is she a member of AMATYC? I know I have met her and I am just trying to figure out where. I am the president of AMATYC and I meet many people at many places.

## Billy Jackson

Co-PresenterNo problem. Yes if you have met Shandy, it is probably in connection with AMATYC. She does a lot of work with 2 year institutions on her various projects, especially in California. In fact, she did the leg work with working the IRBs on this project. She has a wealth of experience in working with 2 year institutions and is certainly someone who can offer useful advice for those projects looking to use 2 year institutions as primary data sources. She also presented on PRIMED at AMATYC recently I believe. I also did a local AMATYC presentation on the project here in Kentucky last year.

## Kathryn Kozak

So I finally remembered how I know Sandy. I was one of the main authors on the AMATYC IMPACT document. She helped write the chapter on research. Sandy, you do great work. I am sure that this project was well done. When we start teaching Math for elementary school teachers again, I will suggest that we look at this project.

## Beth Sappe

This is such a key component to supporting our future teachers. We spend a lot of time working with our local colleges and our high school teachers to collaborate so the transition from K-12 to higher education is aligned. I am excited to think about this connection for our professors who are supporting our future elementary and middle school teachers. As a math educator for 20 years that gets the opportunity to observe math instruction on a regular basis, I see that some teachers have misconceptions about student’s prior and future learning which causes missed opportunities for connections that can support learning. Are your professors engaging in work aligned to the math progressions as well as how students develop content knowledge from year to year through the aspects of rigor (procedures, conceptual understanding, and application)?

## Billy Jackson

Co-PresenterHi Beth--

The answer is yes as we do have the faculty examine the Standards of Mathematical Practice in the Common Core. However, our focus in the first short course is mainly on pedagogy. We realize that that approach is not necessarily the norm in professional development. However, we made the choice to do it that way for a few reasons, all mainly to be responsive to our audience. The material you mention in your post is all a part of "content" for teacher educators as for them the content is mathematical knowledge for teaching instead of just mathematical knowledge. So, the reasons for choosing the pedagogy as our primary emphasis in the first course were the following:

(1) in our pilot, we put sessions aimed at building more content knowledge first and this did not go over as well as we had hoped. Participants told us that they wanted more sessions with emphasis on things they could use and take back to their own classrooms. So as you and I know as teacher leaders, the faculty are asking for the same things in their learning as our K-12 teachers do.

(2) Our participants are novices at educating teachers, and as such, many are not aware of the specialized nature of the mathematical knowledge that teachers need to have. In a sense, math faculty who are new to working with K-8 don't know that they generally aren't aware of mathematical ideas and concepts as they are presented in K-8. Those of us who are mathematicians who have worked in math ed and with teachers more specifically like me, Shandy, Sybilla Beckmann, Eric Hsu, Dave Kung, Yvonne Lai, Alan Schoenfeld, Hyman Bass, Jodie Novak, etc. all realize that there is a fundamental knowledge base required in teaching K-12 that math faculty generally don't have. The reason we know is by our experience: we were all trained as mathematicians but came to understand this way of using mathematical knowledge only after we started working in the K-12 realm with teachers. That is not a slight against mathematicians -- they have little need for such knowledge or to use their own knowledge in such ways in their own work since they don't teach children. Instead, I think it says a lot about what we ask of our teachers and that they are truly professionals in that they have a fundamental understanding of K-8 ideas in ways that even mathematicians may not since their jobs require it. Take division for example -- many math faculty are unaware of the two different models of fair share and measurement : like the majority of the population division for them is usually taken in a fair share context. The fair share context is reinforced in their axiomatic ways of thinking about things like groups and fields in abstract algebra where in a sense there really is no division but rather a collection of objects and their multiplicative inverses.

(3) For Shandy, David, and I, a big part of what we do in math ed is devoted to equity and justice in math classrooms. No where is that more important than in courses for future teachers as they will be teaching children later on at some point. If we want our teachers to understand what equitable classrooms look like for their children, then we have to make sure that we are teaching in equitable and just manners in our own courses with them. Hence, it was important for the three of us to have our participants at least begin to reflect and take action upon these dimensions in their own classrooms.

Now, that is not to say that we did not discuss any content: indeed, it is difficult to separate pedagogical issues from the content itself. As a former colleague of mine said about the methods course: it is difficult if not impossible for the teachers to comprehend and implement the methods appropriately if they do not have a firm foundational understanding of the underlying mathematical concepts. We interwove some of the content into some of our discussions and readings that were assigned: for instance, Shandy and I wrote a piece on mathematical knowledge for teaching that introduced the participants to the construct, and as a part of this exposition we included examples as illustrations such as the one for the different models of division.

If we decide to continue with designing a second course for instructors who have more experience with teacher education, we intend for the content of that course to include more learning about and constructing of K-8 MKT itself. I believe our audience for such a short course would be "ready" for such learning opportunities as they are more likely to be receptive to the notion that there is a fundamental knowledge base that they lack when teaching the courses.

## Beth Sappe

Hi Billy,

Thanks for the detailed response. It is amazing to hear all the thought that went into making decisions on how to support the learners.

## Benjamin Starr

Do you include anything that focuses on students with disabilities? My understanding is that SWD benefit most from direct, explicit instruction in math. Discourse is another important factor, we want to get students talking about math. Both responding to questions and asking questions so that misconceptions can be addressed.

## Shandy Hauk

Lead PresenterAssociate Professor

Hi Benjamin,

Excellent question. Research to date indicates direct, explicit, instruction has had varied success when the target of instruction is more complex (i.e., beyond achieving and adhering to behavior or procedural norms deemed valuable by current policies). The short-course touches on a variety of aspects of responsive instruction for school and college teaching. To echo and extend some of Billy Jackson's earlier posts to this thread, the principles and practices for the short-course are rooted in the Teaching for Robust Understanding (Schoenfeld et al., 2016) and Culturally Responsive Mathematics Teaching (Aguirre et al., 2012) frameworks. What benefits a student depends largely on what experiences, skills, and expectations coalesce in a student's learning environment.

The PRIMED short-course is grounded in the idea of Discourse (big D -- includes talking about math AND the values, life experiences, norms related to orchestrating and engaging in mathematical conversation). The PRIMED short-course mentions the long-time reliance on direct instruction in teaching in the U.S. while also noting the value of small group learning when scaffolded by clear learning goals, including learning goals for peer-support in tasks.

Aguirre, J. M., Zavala, M. D. R., & Katanyoutanant, T. (2012). Developing Robust Forms of Pre-Service Teachers' Pedagogical Content Knowledge through Culturally Responsive Mathematics Teaching Analysis.

Mathematics Teacher Education and Development,14(2), 113-136.Schoenfeld, A. H. (2016). An introduction to the teaching for robust understanding (TRU) framework. Available at http://map.mathshell.org/trumath.php

## Jennifer Carinci

Thanks for your work on this important topic! I will be interested to see your future results and how the intervention translates to more distal outcomes.

## Mitchell Nathan

Shandy, I love your focus on developing mathematical knowledge for teachers. This is so key to promoting STEM education. Thank you for sharing this project!

## Jen Monastra

Hi Billy,

This is an interesting project and I love the idea of providing and studying PD for mathematics faculty! I wanted to follow up on a post you made above related to the modules used in this project. Specifically, you mentioned (3) readings on MKT and research pieces on various goals and strategies employed in the courses by experienced teacher educators. I am also interested in instructors goals and was wondering if you could you share any of the research pieces related to goals and strategies used by teacher educators? Thanks for sharing and keep up the good work!

## Billy Jackson

Co-PresenterHi Jen--

Thanks for stopping by and the encouraging comments. In our work, we have used Castro-Superfine and Li's work in addition to Taylor and Appova. Some of their useful works are below:

Appova, A. and Taylor, C. (2019). Expert mathematics teacher educators’ purposes and practices for providing prospective teachers with opportunities to develop pedagogical content knowledge in content courses. Journal of Mathematics Teacher Education, 22, 179-204.

Castro Superfine, A., & Li, W. (2014a). Developing mathematical knowledge for teaching teachers: A model for the professional development of teacher educators. Issues in Teacher Education, 23(1), 113-132.

Castro Superfine, A., & Li, W. (2014b). Exploring the mathematical knowledge needed for teaching teachers. Journal of Teacher Education,65(4), 303-314.

Taylor, C.E., & Appova, A. (2015). Mathematics teacher educators’ purposes for K-8 content courses. In Beswick, K., Muir, T., & Wells, J. (Eds.). Proceedings of the 39th Psychology of Mathematics Education conference, vol 4, (pp. 241-248). Hobart, Australia: PME.

Earlier work on the nature on the knowledge used by teacher educators comes from Olanoff and Zopf:

Olanoff, D.E. (2011). Mathematical knowledge for teaching teachers: The case of multiplication and division of fractions (Doctoral dissertation). Syracuse University, Syracuse, NY.

Retrieved from http://surface.syr.edu/cgi/viewcontent.cgiartic...

Zopf, D. (2010). Mathematical knowledge for teaching teachers: The mathematical work of and knowledge entailed by teacher education (Unpublished doctoral dissertation). Universityof Michigan, Ann Arbor, MI. Retrieved from

http://deepblue.lib.umich.edu/bitstream/2027.42...

If you are looking for more on our conceptualization of mathematical knowledge for teaching future teachers (MKT-FT) , you can check out our recent paper:

Jackson, B., Hauk, S., Tsay, J.J., & Ramirez, A. (2020). Professional development for mathematics teacher education faculty: Need and design.

The Mathematics Enthusiast, 17(2&3), 537-582. Link to PDF of the article [opens in new window].Hope this helps!

## Jen Monastra

Wow thanks so much Billy! Look forward to reading over these.

## Jen Monastra

Wow thanks so much Billy! Look forward to reading over these.

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