Math for All is a long-term effort to support teachers in making high-quality math instruction accessible to all students, including those with disabilities. For more than 15 years, Bank Street College of Education and the Education Development Center, Inc. have been collaborating to develop approaches for enhancing the preparation of pre-service and in-service teachers to help all students achieve standards-based learning outcomes in mathematics. Funding from the National Science Foundation has allowed us to develop, pilot-test, and formatively evaluate a multi-media professional development program that has been published by Corwin Press. Currently, we are working with researchers from ICF, Indiana University, and Teachers College, Columbia University, in partnership with Chicago Public Schools, to conduct a large-scale, randomized controlled trial (RCT), funded by the Institute of Education Sciences. The purpose of this study is to assess the efficacy of Math for All for positively affecting teacher and student outcomes. The results we are sharing in our video are from Year 1 of a two-year study.

We hope you will join us for an exchange about our work. Here are some ways in which you can participate:

- Share an anecdote about a child who learns math differently

- Share strategies (for learning math, for teaching math to diverse learners, for professional development, for research) that have worked for you

-Share your experiences as a Math for All participant or facilitator

-Send us your questions about teaching math to diverse learners and the Math for All professional development program and research

-Give us feedback about our work

Every day over the upcoming week, we will post one or two questions for discussion. Please check in frequently to contribute to the various discussion threads. We look forward to your contributions!

Hello and welcome.  Thank you for viewing our video.  We have found some strong benefit to using open-ended tasks in our work.  Please join our conversation by sharing comments about:

*  Which open-ended tasks have you used in your classroom or school and what benefits did you see to using them?

*  What obstacles did you have to plan around in order to implement these tasks?

*  What strategies did you employ to ensure students' access to these tasks?

*  What effects have your use of open ended tasks had on your students' mathematical identity?

Thank you so much.  Looking forward to hearing from you!

Hello everyone! Thanks for your interest in Math for All. Our study is designed as a randomized controlled trial (RCT), and meets the ESSA evidence requirements for Tier 4. 

How are you determining which evidence tiers your professional development or school improvement strategies are at? What are some of the challenges you’re facing?

We'd love to hear your thoughts!

A worthwhile project indeed! Students who learn or approach math differently (or science in my case) make us better teachers:by doing the careful listening and learning to tailor a further challenge or an explanation to meet the individual's need, we have a broader repertoire are better prepared to meet the needs of all students! My own children were fortunate to have math teachers who valued a range of individual solutions to problems and made sure everyone in the class understood a classmate's strategy and rationale. And got to weigh the pros and cons of various solutions. Math was intellectually interesting for young learners. Glad you are doing this work!

Math For All looks like a great projects for teachers. Can you say a little more about the teachers who participate? Are these volunteers? Do regular education and special education teachers from the same school participate together? How long do teachers participate? Do you get any push-back that teachers don't have time to implement Math for All types of tasks or activities?

There is such a deep and methodical body of research and expertise behind this project - it was ahead of its time years ago and it is so exciting to see it continue to move forward. Congratulations to the whole team on this project - Math For All only gets more impressive with time.

Amazing work! The accessibility of a subject is crucial to the learning process, especially at such a young age. Im sure the kids and teachers working with Math For All will both benefit from the experience. It also is so important (and commendable!) to have such dedicated researchers and educators who are willing to expend their energy and time developing programs like this

 This project reminds us all, teachers and developers, that it is incredibly exciting when all children in our classes are able to be mathematicians.  For this to happen we all, teachers, need to let ourselves also be mathematicians.  It is so exciting!!

Math for All has presented many challenges to us as developers, but more importantly to the teachers we have worked with.  The process of working through these classroom challenges are where we see teachers working hard and succeeding.  Teachers move beyond collecting and selecting lessons to thinking with colleagues about how to adapt and plan lessons for a focal child. They are deeply involved with a colleague in developing new instructional strategies using a neuro-developmental lens and a single focal child.  

This planning for a focal child inevitably leads to new instructional strategies for the entire class.  For many this often challenges their assumptions about how they make instructional decisions.

A simple example is when a teacher makes a check list for a child who has sequencing problems and has receptive language strengths.  S/he planned the lesson with her MFA partner and they decide to make the check list available to the entire class.  They reviewed student work samples and saw that several of the children had followed the check list.  The strategy was shared with colleagues who also used it successfully.  

The instructional decisions were made based on the neuro-developmental needs of a single focal child. 

How do you make instructional decisions?  Can you share a simple example with us?

It would be GREAT if a few of you could share how instructional decisions are made in your school and give an example of how an adaptation has lead to increased student learning.  

This research is so important.  I think that professional development that brings teachers together to talk about their craft, try new things, and reflect back on how things went is the most effective.  Teachers in Japan have been doing it for years.  I hope it catches on in this country.

One of the potent aspects of the Math for All work has been the collaborative planning opportunities that grade-level special education and general education teachers have had to talk about their work with children in a safe space and with a supportive professional learning community.  This was made possible by providing teachers with a neuro-developmental framework via which they could speak objectively, respectfully and constructively about how to refine, enhance and retool their instructional approaches in order to celebrate students' strengths while addressing their areas of struggle with strategies and tools that are aligned to their students' unique learning profiles.  Worthy of commendation are principals who embrace the merits of these strategic planning and reflective opportunities by creating the time for teachers to engage in this collaborative discourse. Needless to say, principal buy-in is crucial.  Albeit, teachers, too, need to be highly invested in the process as active participants who are learning and growing together in their role as educational practitioners.

Such an interesting project and discussion! Your example of a teacher creating a resource for a target student that then becomes useful for others is an important finding I think. Along the same lines I'm wondering if you've found that encouraging teachers to focus on the learning of an individual student leads the teacher to pay more attention in general to individual students. In other words, when teachers are learning to teach in ways that are responsive to a student have you noticing if they come to apply that approach to students in the classroom overall?

Miriam, you ask a great question.  Data is being collected ( both qualitative and quantitative) which may well give us more on this but anecdotally in some instances we believe there is transfer to all teaching and sort of a 'tuning in' on how diverse learners make meaning .  I remember filming a lesson planning meeting in a school in NYC with special and general ed teachers and a math coach .  It was so enlightening  to hear Frances saying at the end summation discussion " You know Jordan hasn't  changed.  He's being more successful because we have changed ." She gave us all a lot to think about. What do you think she might mean by that?

This is a wonderful initiative, and I am so glad that you all have been able to continue to educate teachers about how they can better serve their students. I think Hal made a very important point, that when utilizing the strategies that Math for All teaches, the students aren't changing, but we as educators are changing. We can reach our students in a more meaningful way. I am just curious, over all the time Math for All has been around, about how many teachers do you think you have educated further on how to help students reach their math potential and a deeper conceptual understanding?

A hearty welcome to one and all!  Did the video pique your interest in learning more about differentiated instructional strategies for math tasks? How are you making math more accessible to diverse learners? 

In our Math for All professional development training, we recently had the opportunity to watch teachers adapt the Measuring Up Problem of the Month Levels A and B math lesson (that is based on the story, Stone Soup) to support their students in ways that tapped into their students' neuro-developmental strengths and other aspects of their learning profiles.  Here are some examples of how students with different abilities approached this math task in different ways. Some students figured out the solutions to the problem via a table with horizontally-aligned pictures that represented each ingredient (2 carrots, 3 green onions, 5 chunks of meat) and vertically-aligned numbers to represent the number of people for whom the soup will be made.  Others used manipulatives such as colored tiles or colored post-its to figure out the ingredients needed to make soup for different numbers of people. (The tiles and post-its matched the color of the ingredients.)  Some students placed the appropriate number of colored tiles in a pot to make the soup for different numbers of people.  Other students drew circles on chart paper or in notebooks and then drew pictures of the ingredients inside the circles.  (Each circle indicated one person's portion of each ingredient.)  One student had plates that denoted a person; on each plate was placed square tiles that portrayed the person's portion of soup ingredients. 

I'm eager for you to share examples of how you created opportunities for students to access math lessons/tasks using different approaches that utilized their affinities/interests, strengths and other aspects of their learning profile. 

A central theme of Math for All: demands of mathematical tasks. As teachers plan lessons we ask them to do the problem themselves and then to consider what they needed to do as they explored it. For example, the demands that were considered in a problem they were planning about three children in a heal-to-toe race with different shoe sizes anda different track lengths. Teachers noted these demands: reading the problem, remembering the directions, keeping track of the size of the shoes and track lengths associated with each child, talking to their partner, measuring and cutting shoes, staying focused, understanding what “each” refers to… You will notice that there were many demands that didn’t have to do with the “math.”  As they became aware of the demands, teachers came to see their extended role in supporting children in math learning. They came to understand what got in the way for children – it was much more than remembering their multiplication facts. We find that simple adaptations go a long way: acting out the problem, using manipulatives, simplifying the wording of the problem, using see-through rulers, using sentence starters…

As we do this work with teachers they come to understand that math lessons have aspects that include: memory, motor skills, psycho-social skills, attention, language and of course others that are more like the ones that we usually associate with math: like higher order thinking, special ordering and sequential ordering.

We’re hoping to hear your examples of doing math activities hands-on when planning and adapting lessons for children.

Hello everyone,

We are so glad to see that many of you have taken an interest in our work. We are also interested in your work, and would love to engage in dialogue about it.  One of the defining pieces of our project is intentionally bringing together both general ed and special ed teachers to plan lessons.  We find that planning by looking through the lenses of both mathematics and learning needs helps us pay attention to how we can make adjustments to the structure of a lesson that maintains high level mathematics and yet makes it accessible to all children.

Have you had any experience collaborating on math with general and special ed teachers? 

-how have you in your school been able to foster collaboration

-what benefits have you observed in co-planning and co-teaching

Excellent video Babette, and a great program! Taking a strengths-based approach to instruction is an excellent way to support all students, but especially those with special needs. We are using that approach on an ITEST project that supports students on the autism spectrum, and typical peers, who engage in maker activities. Math is definitely a subject that requires multiple strategies to make sense to diverse learners. What are some strategies that you or your teachers have come up with that have been particularly effective?

This is masterful work in terms of the development of good practice and powerful curricular experiences for all- not just for the students, which is key. In my own work with teachers, the richest explorations happen when we work through more open ended problems and focus on multiple entry points, when we work to monitor the type of tasks we are asking of our students, and when we are able to remove to some degree our own assumptions about a student's ability to process, which can only happen through thoughtful planning and a commitment to learn along side the student. 

From Barbara Dubitsky's comment above: "As we do this work with teachers they come to understand that math lessons have aspects that include: memory, motor skills, psycho-social skills, attention, language and of course others that are more like the ones that we usually associate with math: like higher order thinking, special ordering and sequential ordering."

For me, this is one of the most interesting points to come up in this project. I think neuro-typical people often assume that those of us who learn differently have just one, obvious challenge—e.g., a dyslexic is dealing "only" with decoding or reading comprehension. But like ripples in a pond, the effects of a processing problem can radiate out and influence many other areas of life.

Do you think the teaching strategies that educators learn to apply in this project could somehow be "reverse engineered" so that a student who learns to have success with math learning would be able to build on that experience of success to increase their confidence or help them in some other way than just academically? 

Hi all – I’ve enjoyed reading the correspondence and have a new question. The Every Student Succeeds Act is now of course the law of the land.  It shifts federal accountability to the states but still highlights the need for evidence-based practices. Hence, it seems there remains a need for randomized controlled trials and other forms of strong evaluation designs. So to my question: do others think that RCTs remain important? And do these designs by themselves generate the kind of evidence that we need to inform mathematics instruction?

Hi Bronwyn Taggart, concerting the question you asked:

“Do you think the teaching strategies that educators learn to apply in this project could somehow be "reverse engineered" so that a student who learns to have success with math learning would be able to build on that experience of success to increase their confidence or help them in some other way than just academically?”

We find that people who meet with success in mathematics, especially when they have had problems with it, may gain a sense of power.  This feeling of power can permeate other aspects of their life.  When teachers find successful adaptations for children when demands of mathematical tasks are getting in way they are more likely to succeed in those mathematical tasks.

What feelings are kicked up when you 'do' the math of the lesson?

Each Math for All PD session incorporates a video case study of a math lesson. In these video case lessons, we see children “doing” math. We hold the view that the way you learn math is by doing math, not just talking about the math. We have found if we expect teachers to really appreciate the multi- demands required of each task they themselves also have to do the math. At each session, before viewing the video tapes of children, teachers, in groups, are found using materials in deep conversation with each other working on the same task they will see children doing. Interesting conversations arise as groups of teachers unearth what they themselves know or are confused by. We hear some teachers admitting that they only learned rules or tricks (eg. they know the procedures) but have no clue about how operational concepts are connected to each other. For example they may not know that a ‘naked’ division problem can be better solved by some kids by thinking about it as a multiplication problem or maybe as a subtraction problem or even as a repeated addition problem. And we find, even though Common Core clearly affirms the use of models in math, too few teachers are well versed in how to help  8 / 9 year old students  to visually represent multiplication using an open array model  (and seldom do they know how that model lays a strong algebraic foundation for multiplying polynomials in middle school!! ). For the child with a strong visual spatial sense that may be their only ‘way in’ to understanding and remembering how to multiply 523 X 21. Some teachers share how hard it is for them to think flexibly in math since they have never been taught flexibly. Some even reveal their antipathy towards math ; sometimes referred to as math anxiety.
We have tried in each of the five sessions to help teachers play with big ideas in math and open up their minds to the multiple pathways one might explore any one math idea. Different learners can access big important math ideas as long as we find their ‘way in’. Often we find it's the same for teachers. Math for All provides access points for teachers as well as children. Teachers deserve to have that ‘ah hah’ experience they aim to provide their children. Math for All aims to provide some of that for teachers as needed.

How have you found to help teachers become facile , flexible, open thinkers about underlying math concepts? Have you ever encountered a teacher who has expressed their own fears or negative views about mathematics themselves? What supports work well?

Megan and Ashley, thanks for your input on RCTs and evidence. I fully agree that RCTs should be seen as one tool, albeit an important one. Others may have heard that RCTs are the "gold standard of research." I disagree. I do however think that these class of designs represent a gold standard in causal research (there might be a higher platinum standard) as long as it is understood that there are many important issues around implementation, acceptability, etc. that are best explored with other design-types. Ashley, involving teachers more is critical. I've spent some time worrying about the research-to-practice gap, but lately have become interested in the practice-to-research gap, wherein teacher innovations need to be understood by researchers. Megan, I suspect we're going to have some compelling evidence around mediators and moderators in the MFA study, but it will be hard to analyze these with standard statistical approaches given the power that is needed.  But I personally hope we will be able to describe these issues using exploratory and qualitative methods since it is better to think of a portfolio of research rather than single studies.

Our research shows that engaging teachers in sustained collaborative lesson planning holds great promise for enhancing the instructional and emotional support teachers provide when teaching mathematics, and students' engagement when learning mathematics. We have found that for teachers to engage in this ongoing lesson planning and professional learning, the engagement of and support from school leaders is essential.

We are interested to hear from school leaders:

**  How do you support ongoing, professional collaboration and learning among your teachers?

**  What supports have been helpful to you in having teachers work in this way?

We are also interested to hear from other projects that have utilized teacher collaboration as a strategy for improving practice:

**  How are you involving school leaders in your work?

**  What practices have you found promising for supporting ongoing, collaborative professional learning at the school level?

Thanks in advance for your input!

Following the discussion above regarding RCTs, the overall design for  the Math for All (MFA) project also includes the collection of qualitative data to better understand the work from the perspective of the teachers and principals.  We have interviewed them in both the control and experimental schools, giving us a better understanding of the overall context for the MFA work in the Chicago schools.  By including qualitative data in this mixed RCT research design, we are able to include the voices of those most directly involved and affected by the project.  What are your thoughts about mixed RCT designs?  Should qualitative data have a role to play?

I think that the range, the focus, and the quality of the research on this project has provided the PD team with invaluable ongoing feedback that has informed the work we have been doing.  

Sorry to be somewhat late to the discussion here, but if I understand it correctly your current PD model is to do meetings with teachers in day-long face-to-face sessions.  Have you investigated the feasibility of conducting your sessions remotely?  Is that a direction in which you would like to move, or are you seeing potential drawbacks in online delivery?  This is quite the compelling project.

This is an excellent video explaining an important project. The depth of knowledge, experience, and wisdom of the Math For All team is unique. I've observed the project develop over the years and its commitment to reaching these students and the teachers who serve them is impressive and inspiring. My Congratulations on the work so far and may it continue to grow

Thanks for your question, John. We have done some of our PD on line – we did a course for people who were learning to be MFA facilitators, totally on-line. We have also worked on line with teachers who need a catch up session because they had joined us late. We have thought a lot about how to conduct the PD on line. We would certainly want to do them live. We might have some hurdles to deal with -- creating a sense of community, needing to have many shorter sessions rather than the six-hour ones we have face-to-face, making sure there are a variety of manipulative and other materials at every site…

Looking into the future, we are very interested in scaling up our program to widen its reach. Scaling up can happen at many different levels. It could mean spreading and deepening our intervention at the schools that we are already working with. It could also mean bringing it to a wider range of geographic locations and settings. We are interested in hearing from other programs to learn what strategies and practices you have found promising for scale-up.

And if you are part of a school district that is interested in enhancing its capacity to make high quality math instruction more accessible to diverse learners please let us know. We would love to partner with you!

Thank you for watching our video and for contributing to the discussion! While the live discussion concludes today, we are eager to continue the conversation about Math for All and making mathematics accessible to all students. Please contact us directly with other questions, comments, or suggestions. You can also visit us at mathforall.cct.edc.org for more information, resources, and updates on our research.