6071 M2017-03
The mathematics achievement gap for struggling students is well-documented. Teachers often ask, “What do I do when universal or core instruction is not enough?”
The Center for Teaching and Learning Mathematics at the University of Northern Iowa combined forces with experts in the fields of mathematics and special education to answer this question. This team addressed the need for professional development that supports teachers in closing the achievement gap for struggling students. The resulting professional development, Teaching Mathematics to Struggling Learners (TMSL), builds mathematics content knowledge and increases understanding and implementation of research-supported instructional and assessment strategies, specific to mathematics-intensive intervention.
The Common Core Content Standards and the Common Core Standards for Mathematical Practice provide a firm foundation for universal or core instruction. The TMSL program focuses on intensive instruction when universal or core instruction is not enough.
The TMSL program implements the following Institute of Education Sciences (IES) recommendations:
6071 M2017-03
The mathematics achievement gap for struggling students is well-documented. Teachers often ask, “What do I do when universal or core instruction is not enough?”
The Center for Teaching and Learning Mathematics at the University of Northern Iowa combined forces with experts in the fields of mathematics and special education to answer this question. This team addressed the need for professional development that supports teachers in closing the achievement gap for struggling students. The resulting professional development, Teaching Mathematics to Struggling Learners (TMSL), builds mathematics content knowledge and increases understanding and implementation of research-supported instructional and assessment strategies, specific to mathematics-intensive intervention.
The Common Core Content Standards and the Common Core Standards for Mathematical Practice provide a firm foundation for universal or core instruction. The TMSL program focuses on intensive instruction when universal or core instruction is not enough.
The TMSL program implements the following Institute of Education Sciences (IES) recommendations:
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Vicki Oleson
Director
Thank you for viewing our video!
Teaching Mathematics to Struggling Learners is a four-course professional development series designed to prepare special needs teachers to: first administer and use the results of a high quality diagnostic assessment to accurately place students along a learning progression; second deliver Specially Designed Instruction using high quality intervention materials, and third to intensify Specially Designed Instruction using research based strategies specific to the needs of students with Individual Education Plans.
Teaching Mathematics to Struggling Learners was collaboratively developed by an eight-person team consisting of higher education faculty in both mathematics and special education, mathematics and special education consultants, and special needs teachers. Funding from the Mathematics and Science Partnership and the Iowa Department of Education allowed us to together study research, develop and pilot four, three-credit-hour graduate level courses, and study the impact of the implementation of these four courses by measuring change in teachers’ mathematics content knowledge for teaching, the fidelity with which they implemented assessment and instructional strategies in the classrooms, the degree to which they changed their perception of self-efficacy and the impact of their teaching. In addition, increase in student achievement and change in student attitudes were measured.
We hope you will join us for an exchange about our work. We are interested in your experiences, questions, and ideas:
Share strategies that for worked for you when teaching mathematics to diverse learners
Share your experience if you have been a participant in a Teaching Mathematics to Struggling Learners course
Ask questions about teaching mathematics to struggling learners or the Teaching Mathematics to Struggling Learners professional development program
Marcy Seavey
Hi Vicki and CTLM team. I know that the CTLM has developed many other mathematics professional development programs in the past. Can you share what lead to the development of this program for struggling learners?
Vicki Oleson
Vicki Oleson
Director
Hi Marcy, Thanks for your question. The Teaching Mathematics to Struggling Learners (TMSL) project grew out of an earlier professional development program, Making Sense of Mathematics and Teaching (MSMT). MSMT focused on improving k-8 teachers' mathematics content knowledge for teaching and improving instructional strategies aligned with the Common Core Standards for Mathematical Practice. While working with k-8 teachers in mathematics, we found that struggling students needed additional support. The Teaching Mathematics to Struggling Learners program grew out of the recognition of the need for this additional support. While developing the content of the program, we relied heavily on the Institute for Education Sciences practice guide, Assisting Students Struggling with Mathematics: Response to Intervention for Elementary and Middle Schools. We were really searching for ways to decrease the achievement gap in mathematics between students with Individual Education Plans and those without.
Vicki Oleson
Marcy Seavey
Beth Hulbert
Thanks so much for this video. Your project seems focused on important ideas around equity in math for all students. You should look at our work with learning progressions as it relates to your goals. We are OGAP and also have a video called Formative Assessment Tools to Improve Early Math Learning.
Vicki Oleson
Marcy Seavey
Vicki Oleson
Director
I just viewed your video with great interest! Formative assessment and progress monitoring are important tools in supporting struggling learners. While our work included some lower elementary teachers, for the MSP grant, we mainly focused on grades 3-5 and special needs teachers. The focus of our work does align with OGAP, and I will be looking more closely at your website soon. Thank you for reaching out!
Vicki Oleson
Marcy Seavey
Connie Terry
Math Consultant
Beth-
Thanks for viewing! Yes, we agree on the importance of teachers understanding student learning progressions. Without this type of tool, teachers can feel lost. They can struggle to hone in on where students are and how to move forward. When they are equipped with knowledge and tools, teachers feel empowered to design instruction targeted to student needs.
Vicki Oleson
Beth Hulbert
Thank you for your thoughtful and productive work in this area. In OGAP we have grade 3-5 learning progressions and I would love to talk with you about how these 2 projects are similar and could benefit perhaps by each other. We see our learning progressions as tools for equity. I think your work is so important because, as a former special educator, I know there are just not many resources, supports and training for people who work with the most struggling learners in math. I hope we will have an opportunity to talk in the future.
Connie Terry
Vicki Oleson
Marcy Seavey
Vicki Oleson
Director
Beth, We would be interested in connecting with you and learning more about your learning progressions tool. Let's plan to set up a virtual meeting soon.
Vicki Oleson
Beth Hulbert
Yes...let's do that. It seems to me we have a lot in common and it would be really interesting just to talk about it.
Vicki Oleson
Nadine Bonda
Assistant Professor
Working with special needs teachers is so important in order to catch these students up if they are behind. Can you talk specifically about the techniques you are recommending that teachers use that are different from what you would teach to a regular ed teacher? Thank you.
Vicki Oleson
Vicki Oleson
Director
Thank you for asking, Nadine!
Our professional development courses really honed in on three techniques: use of diagnostic assessment (we utilized the cognition-based assessment work of Michael Battista), implementation of effective intervention materials (we used both Marilyn Burn's Do the Math and Bridges Intervention Materials), and building special needs teachers' mathematics content knowledge and their confidence or sense of self-efficacy as effective teachers of mathematics. Our instructional focus was on the students' 30 minute intervention time.
This professional development is based on the researched recommendations put forth by the Institute for Education Sciences practice guide, Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools., and specifically focuses on Recommendation 3 Instruction during the intervention should be explicit and systematic; Recommendation 4 Interventions should include instruction on solving word problems that is based on common underlying structures; and Recommendation 5 Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas.
Vicki Oleson
Nancy McGowan
Marcy Seavey
Connie Terry
Math Consultant
While we don't make recommendations around universal instruction in this coursework, we do explain that intervention should be more explicit and systematic. Much time was spent in development in deciding exactly what was meant by Explicit Instruction. We believe it is critical that explicit instruction verbalizes thinking, illuminates decisions and makes connections between representations and strategies explicit to the student.
Vicki Oleson
Marcy Seavey
Sarah
Having been on the receiving end of the great work, I am appreciative of the learning that our teachers got from participating in these classes. When I am out working in the classrooms I can see the teachers using the information that they gained from these classes and the growth and confidence in their students math understanding is tremendous.
Vicki Oleson
Marcy Seavey
Vicki Oleson
Director
Thank you, Sarah. This TMSL project was a team effort, and we all learned together. The Waterloo Community School District teachers and coaches provided valuable feedback along the way, and the administration learned more about the work and supported the it in the classroom.
Vicki Oleson
Karen Economopoulos
Co-Director, Investigations Center for Curriculum and Professional Development
Thank you for your work in this area. All students deserve to understand the mathematics that they are doing. So often work with students who learn differently or at a rate different from their grade level peers, is focused on rote and procedural skills, through direct instruction, rather than on understanding. Your work with special educators around understanding not only the math they are teaching but also how students learn this math is central to supporting students in meaningful and effective ways so that they can progress along the continuum. I am curious about whether or not your project looks at special ed teachers' initial stance and perspective about the type of instruction "these students" need (pre-PD) and then how these perspectives shift and to what degree?
Vicki Oleson
Marcy Seavey
Vicki Oleson
Director
While we did not study change in perspectives related to the type of instruction students need specifically, but I am glad you asked about change in the teachers' perspectives, which was one of the most interesting findings of our evaluation. We used the Mathematics Teaching Efficacy Beliefs Instrument to measure change in teachers' beliefs about the effect of good instruction on student outcomes and on their own sense of self-efficacy. As Connie mentioned below, both of these measures indicated growth when compared to a control group. Interestingly, the teachers sense of self-efficacy shifted much earlier than their belief that improving instruction would impact student outcomes. That surprised me. Here's a link to the evaluation brief for the TMSL project: https://tinyurl.com/ycqk5q64
Vicki Oleson
Connie Terry
Math Consultant
We spent quite a bit of time in development trying to clearly articulate the differences be direct instruction and explicit instruction for this reason. We did not want students forced into direct instruction situations that would not benefit their understanding of mathematics. To some mathematics educators, direct instruction and explicit instruction are the same. We disagree. Explicit instruction should give students a chance to hear and see a proficient problem solver as they make decisions and notice connections. This hearing and seeing of strategies should be followed by students attempting the use of similar thinking. Over time, students are able to become more comfortable in the strategy and can be given opportunities to employ that strategy in unique situations that require the transfer of the learning.
We did not study the change in teacher's perspective of the type of instruction, but we did measure their self-efficacy as teachers of mathematics and also their student outcome expectancy. Both of these measures showed growth when compared to a control group. Results are shown in the attach evaluation brief.
Thanks for the question!
Vicki Oleson
Marcy Seavey
I'm wondering what I would/might see and hear when a Teaching Mathematics to Struggling Learners Educator is working one on one with a student.
Vicki Oleson
Connie Terry
Math Consultant
You might see...
Teachers stating the expected learning of the lesson.
Teachers modeling proficient problem solving by verbalizing their thought process with a Teacher Think Aloud.
Students attempting to use the same thinking in pairs while they share that thinking with a Student Think Aloud.
Students attempting to use that same thinking independently while teachers provide corrective feedback.
Teachers using concrete, representational, and abstract models that help conceptualize the thinking process.
Student using those same models as their solve problems.
Teachers asking questions that help students generalize the learning past the specific problems they worked on so that students begin to transfer the learning.
Vicki Oleson
Vicki Oleson
Director
For a look into the classroom, and a demonstration of Explicit and Systematic Instruction, specifically IES Guide recommendations 3 and 5, read the description below and then check out portions of this video.
Mrs. Colflesh demonstrates explicit and systematic instruction. Throughout the entire video she models verbalization of thought processes whil solving addition problems, and expects her students to do the same (IES Recommendation 3) Watch this at about minute 16:15
She helps students make sense of the mathematics through two different visual representations, the hundred-chard and open number line, and is working towards the abstract representation of a numeric equation (IES Recommendation 5). Watch at about 2:40 to see her helping students make sense of the problem on an open number line.
Vicki Oleson
Nicole Kee
Hello Vicki and CTLM Team,
I teach 8th grade math Geometry, Pre-Algebra and Algebra and have been challenged over the last 6 years with my struggling learners. I often deal with students that are struggling learners especially with algebra content and teaching to the demands of the common core standards can often be challenging especially to students who may have low self-confidence in the area of math. I often see that students have shut down the second day of school because they already have pre-determined that they hate math and just can't get it. Teaching concepts to students that require higher level and abstract thinking about graphing linear equations always appears to be a daunting task. I reflect every year and try to improve on my instruction to make connections to my struggling learners to help them create the same passion that I have found in math and to help build their confidence back up.
I see myself as a reflective teacher and continually find myself trying to help the student with low self confidence in their mathematical abilities build this self esteem up by the time they leave my classroom. However, in a large class size this can sometimes feel very defeating as the year comes to an end. I implement a lot of differentiated instruction in my classroom when it comes to practice time but do you have any specific advice on the best way to deliver direct instruction in a whole group setting to students that may feel defeated and ultimately not engaged in a content area that they struggle?
Vicki Oleson
Connie Terry
Math Consultant
Nicole-
Thanks so much for the post. I started my career as a middle school and high school teacher so it's great to hear from you!
This is difficult work. What we found and research supported is that teachers need quality materials, quality professional development and onsite support.
Do you have both diagnostic assessments AND intervention materials? Our work was in grades 3-5, but there are good things available for your grade level too. Would love to talk to you about the materials we have found valuable. If you don't have additional intervention time, you may have to incorporate this things into your Core instruction, but could still be valuable. Just getting really skillful at Teacher Think Alouds can be very powerful for struggling learners. They don't always know how a proficient problem solver makes decisions. They don't always know how to make connections.
Do you have access to professional development focused on struggling learners in mathematics? Although reading is not the same as full PD, these is an IES practice guide that gives recommendations in k-8 that we used and in Algebra. I find these helpful, but would need a colleague to help me put these into practice.
Do you have access to a on site coach? Even if this person isn't a math specialist, their help in engagement and other aspects of instruction can be helpful.
The last thing I would say is that there is really amazing research about Growth Mindset that could really help kids believe in themselves as learners. I want every student to believe that they are capable learners!
Hope something from this post is helpful. I appreciate your effort and perseverance in working through this challenge.
Vicki Oleson
Caroline Ebby
This work sounds very interesting and important. I like the distinction you make between direct instruction and explicit instruction. Is explicit instruction a by-product of having students share their strategies or are there specific practices teachers can engage in to highlight particular strategies for struggling learners?
Vicki Oleson
Connie Terry
Math Consultant
We expect teachers to model specific strategies that they need their students to learn to move forward on a learning progression. To be able to do this, teachers need to have a good idea of the strategy that they student is comfortable using and what strategy would be an achievable next step. Too big of leap leaves the kids behind and encourages the student to try to just mimic what the teacher is doing instead of understanding the strategy. This is why good diagnostic assessment is needed as well as strong teacher understanding of the learning progression.
Vicki Oleson
Vicki Oleson
Director
Caroline,
Fortunately, in order to make the distinction between direct instruction and explicit instruction, we had time to delve into the research. Our MSP grant allowed us to take six months at the beginning of the funding period and really dive into the research as a team. Our development team consisted of mathematics and special education university professors, consultants, coaches and teachers. During the first six months of the project, we read research, and came together (weekly during the summer) to discuss the research, and to plan the PD.
The Institute for Education Sciences practice guide, Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools, defines explicit instruction based upon the findings of the 2008 National Mathematics Advisory Panel Final Report.
We studied, modeled and asked the teacher to implement these specific practices in their classrooms. Here is a short excerpt from page 21 of the IES guide:
The National Mathematics Advisory Panel defines explicit instruction as follows (2008, p. 23):
“Teachers provide clear models for solving a problem type using an array of examples.”
“Students receive extensive practice in use of newly learned strategies and skills.”
“Students are provided with opportunities to think aloud (i.e., talk through the decisions they make and the steps they take).”
“Students are provided with extensive feedback.”
Starting on page 48 of the 2008 National Mathematics Advisory Panel Final Report, you can find more of the foundational ideas upon which the TMSL program based professional development focused on explicit instruction.
Vicki Oleson
Nancy McGowan
Math Instructional Coach
Preparing teachers is a critical part of launching any successful educational endeavor. I am curious to know the length of time you have implemented your program and what method of evaluation you plan to use to measure your success.
Vicki Oleson
Vicki Oleson
Director
Thanks for your question, Nancy. We provided professional development for the TMSL four-course program over 18 months, and teachers were asked to implement during that entire time. They video recorded themselves and received extensive feedback from colleagues, coaches, and facilitators as they implemented. While we typically would like to see three years of support for implementation, the TMSL implementation phase was intensive we were able to see change in practice in that short time frame.
To evaluate the program, the external evaluator used the Concerns Based Adoption Method Levels of Use interviews, the Mathematics Teaching Efficacy Beliefs Instrument, the Learning Mathematics for Teaching (Teacher Knowledge Assessment System, and a course evaluation survey to measure growth in the teachers.
For a quick look at the results, check our our TMSL Evaluation Brief.
Vicki Oleson
Kris Morrissey
Thanks for sharing this project and the information about the evaluation. Good luck!
Vicki Oleson
Vicki Oleson
Director
Thank you, Kris.
Vicki Oleson
Gregory Stefanich
Thank you for posting an insightful summation of your efforts to address the needs of students struggling in mathematics. It is so important in that mathematics is the gateway into essentially all STEM fields. Your efforts in working with students directly to address their learning needs is critical. It is the only way to generate persistent learners that will assume responsibility as a participant in the learning process. We must create within the learner a sense of success through guided instruction and we must work to make them feel important and appreciated. Well done!
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