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February 25, 2023

Bridging Pre-service to In-service Formative Assessment Skills to Support Early Mathematics

https://bit.ly/cacmathrecovery

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michigan.gov/mistem

diane.owenrogers@kresa.org

ginger.rohwer@gvsu.edu

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Math Recovery Experience

Where are You?

Already Implementing	Somewhat Familiar	New to Me

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Agenda

What is Math Recovery?
Math Recovery Professional Development
Math Recovery Teaching Sample
Math Recovery in Michigan
Math Recovery in Pre-service
Q and A

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Hidden Agenda

What is Math Recovery?
Math Recovery Professional Development
Math Recovery Teaching Sample
Math Recovery in Michigan
Math Recovery in Pre-service
Q and A

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Our Mission:

The mission of the US Math Recovery Council^® is:�- To transform numeracy education�- To connect research with practice�- To empower educators to advance student mathematical thinking and success for all through

Math Recovery^® principles.

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Math Recovery

is

Professional development
Diagnostic, Interview-based Assessment
Curriculum agnostic
Constructivist
Complements CGI well
Flexible Implementation
Transformative & Empowering

is not

Another add-on
A boxed, scripted intervention set
A Curriculum

You may have heard things about Math Recovery before, and it’s important to talk about what it is and what it isn’t.

It isn’t an add-on program that you have to try to fit into your day. It’s also not a boxed program or a scripted intervention system, and it isn’t a curriculum.

It is professional learning for math teachers that focuses on students’ mathematical thinking.

You get this through a series of professional development courses that address student thinking in math in any type of instructional setting.

It is curriculum agnostic, meaning you use the resources you already have in more purposeful ways.

We help teachers get the most out of whatever curriculum has been adopted, and when it is implemented in a systemic approach, Math Recovery has proven to be transformative across very diverse settings.

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A Quick History

Jean Piaget

Lev Vygotsky

Ernst Von Glasersfeld

Les Steffe

Bob Wright

I think it is important to point out that Math Recovery as a professional learning is different from most other PD offerings. I have never been to something like it before. The difference is in what it focuses on.

These courses are founded in decades of research, so I’m going to take you back to your college days by throwing some names at you as I describe this history.

First: I’m sure we remember Piaget and Vygotsky, both Psychologists who studied cognitive development.

Later came Ernst Von Glasersfeld. He built off of their studies and developed a theory of constructivism specifically for learning mathematics.

Les Steffe is a Distinguished research professor who joined Ernst Von Glasersfeld at the University of Georgia and together they began studying the ways that children constructed mathematical knowledge. This was a relatively new way of looking at math instruction, because it focused on the natural development inside a child’s mind, rather than a sequential order of math concepts.

So, Steffe developed models describing how children constructed math knowledge, and he pioneered these new teaching experiments and video methodology in this research.

Finally, there’s Dr. Bob Wright, who was a doctoral student under Les Steffe, and conducted a lot of this research with him.

When Wright completed his doctoral work with Steffe, he returned to Australia and continued his own work in this area, and developed what became known as Math Recovery, which was later brought to the US as the USMRC in 1995.

This research is what I am referring to when I say that student thinking is at the heart of Math Recovery work. In every professional learning course, our focus is on student thinking.

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But Still...What Is It?

Professional Learning
Diagnostic Assessments
Learning Trajectories and Instructional Tasks

And I still haven’t really explained what it is.

Math Recovery is three big things. Professional learning for teachers about how children learn math. If I only had a couple of minutes, I would say that with knowledge of Math Recovery research, you can answer several different questions:

“Why did my student do that?”

“How should I teach this concept?”

“What do I do if they don’t get it?”

Along with that are pedagogical tools that the teacher could use, such as diagnostic assessments, learning trajectories, and instructional tasks.

Diagnostic assessments can be used to clarify a child’s thinking and strategy with a particular concept, such as addition and subtraction.

The learning trajectories describe that development, and the instructional tasks are available for teachers to draw from as they support students’ development of complex mathematical concepts.

The decades of research that I just mentioned is focused on just that topic: How do students think about number?

What is the typical progression that kids experience as they go from not knowing something to knowing something, and what can I do to support that progress?

If, as the teacher, I understand that typical progression, and I can recognize different characteristics when I see them, then I can present more beneficial learning tasks, ask better questions, provide the right kind of scaffolding, and offer the right kind of feedback, so that my students can build strong mathematical knowledge for themselves.

It is empowering to feel that you can teach math to any student, using any curriculum.

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Professional Development

-Add+VantageMR Courses

- Math Recovery Specialist Courses

-Leadership Development

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Add+VantageMR �Courses

Tiers 1 and 2 Instruction

Target Audience:

K-8 classroom Teachers
Special Education Teachers
Title I Teachers
English Learner Teachers
Para-professionals
Instructional Coaches
Administrators

AVMR, which stands for Add+VantageMR, is built from the same research, using the same learning trajectories and assessment models, but is focused on Tier 1 and Tier 2 instruction.

This is traditionally pitched at classroom teachers, but in reality this course is for anyone who is involved in a student’s math education while they are at school.

Since this is built from the same research, and uses the same learning trajectories, math recovery specialists, from the previous slide, and AVMR teachers, can have a deep discussion of math teaching and learning because they both speak the same language.

Imagine a child study meeting where a second grade teacher, a paraprofessional, the EL teacher, the interventionist, and the assistant principal all agree on, and understand a student’s thinking strategy for adding and subtracting, and they all understand what advancing student thinking looks like in that area?

That is a system that is going to have an impact on student learning.

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Add+VantageMR Courses (AVMR)

Courses

AVMR 1

K- 2 Numeracy Standards

Addition and Subtraction
Structuring

AVMR 2

Multiplication and Division
Addition and Subtraction to 100 with Conceptual Place Value

AVMR Fractions

Fraction Concepts
Units coordination

Course Components

Course kits included
Diagnostic assessment tools
Research based learning trajectories
Exemplary teaching settings
Synchronous and Asynchronous learning
Online support resources

There are three AVMR courses. These are less intense than the specialist courses, but equally rigorous in content and pedagogy.

AVMR 1 – Early Numeracy, which focuses on addition and subtraction strands, as well as structuring, and number words and numerals

AVMR 2 extends that content, and adds into it multiplication and division, as well as conceptual place value.

And AVMR Fractions, which is exactly what it sounds like.

Each of these is a stand alone course, but they blend together beautifully, again because they come from common research, based on common principles.

Each course contains developmental models, assessments, instructional resources and learning trajectories, just like the specialist courses do.

Remember, this is not an add-on or a curriculum, and it is not a scripted intervention set. It is professional knowledge of the highest kind, and guidance to help you decide how to use it.

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Add+VantageMR Classroom Implementation Video

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What is Math Recovery?

Select a box and type your idea(s)

[Insert Thought Here]

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��Math Recovery Specialist Courses�

INTENSIVE INTERVENTION

Tier 2 and Tier 3

Target Audience:

Intervention Teachers
Teachers that work with students who are not meeting grade-level standards
Instructional Coaches
Leaders directly supporting mathematics instruction

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Math Recovery Specialist (MRSp)

Math Recovery Specialist Part 1

Early Intervention
Number Sequences
Number Structure
Early Addition & Subtraction

Math Recovery Specialist Part 2

Intermediate Grades Intervention
Advanced Addition & Subtraction
Multiplication & Division
Place Value

Year-long intensive professional development course with targeted on-going support

Course kits included
Diagnostic assessment tools
Research based learning trajectories
Exemplary teaching settings
Synchronous and Asynchronous learning
Online support resources

Courses

Course Components

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Math Recovery Course Summary

Shared elements in a system:

Common diagnostic assessments
Common expectations of numeracy development
Common professional vocabulary among all participants
Common professional knowledge essential to numeracy development
Empowered teachers

4:29-4:33

Diane

There are very few programs or approaches out there that provide supports across all three tiers. Most math curriculum are focused on Tier 1 and leave any Tier 2 or 3 supports up to the teacher. This creates a misaligned or chaotic math support system. In our experience, Math Recovery can be a unifying system that enhances Tier 1 in support of your current curriculum and then adds a system for Tier 2 and 3 instruction. This creates a stronger system across all three Tiers as educators develop a toolkit to approach quality math instruction.

Educators carry with them diagnostic skills as well as instructional activities that apply across Tiers as teachers seek to support students’ development of mathematical understanding. As you can see on the slide, common assessments, common expectations, common vocabulary, common PD.. all empower teachers to have the efficacy to support students.

As we said earlier, results are better when everyone is on board.

By, eventually, developing people in all three types of courses, a school or district can reshape the system of math instruction.

Again, imagine that child study meeting, or any conversation for that matter, where mathematics is the topic.

The more common understanding and mutual foundation of research your staff are working from, the better the work will flow and the more empowered your teachers will feel

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Pathways to Local Leadership

AVMR Champions

Facilitate Add+VantageMR Courses (Tiers 1 and 2)

AVMR 1
AVMR 2
AVMR Fractions

Support classroom and school implementation of AVMR
Become trusted, local leaders

Math Recovery Leaders

Facilitate Math Recovery Specialist Courses (Tier 2 and 3)

MRSp 1
MRSp 2

Support math instruction and Math Recovery implementation
Become trusted, local leaders

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The third type of course is in the area of Leadership- people who can support specialists and AVMR teachers because they have the same level of expertise, and because they are positioned to drive the system if needed.

Those leaders are the course facilitators. There are a lot of ways you can attend a Math Recovery course. You can attend a course sponsored by the Council, or one that is offered by your local RESA or ISD. You can also become a course facilitator yourself, and build the system from within.

There are two different types of course facilitators

Those who facilitate the AVMR courses are called AVMR Champions.

Those who facilitate specialist courses are called MR Leaders.

If you have ever met a Champion or Leader, then you know that Math Recovery is not something that they can simply “turn off.” Math Recovery research and developmental terminology is embedded in nearly every conversation they have; its one of the reasons we call them Champions.

These are people who want to connect teachers to research and help them open doors for every student, everywhere.

So, they don’t just facilitate courses, AVMR Champions and MR Leaders are habitual supporters of math teachers. Every one of them I have ever met will stop what they are doing to talk about math and math instruction; its just part of who we are.

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Overarching Course Components

Diagnostic assessment tools
Learning Framework in Number
Research-based learning trajectories
Exemplary teaching settings
Online data tools

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Learning Framework in Number

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Learning Framework in Number

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Place Value Model

Link

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What do you notice and wonder about the framework?

Conversations Among Colleagues

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Diagnostic Assessment Tool

Link

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What connections might you be making to work you do or aspire to do?

Conversations Among Colleagues

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Intervention Teaching Video

Math Recovery professional development helps teachers understand the critical components needed to develop strong numeracy in all students, as well as, the teacher moves needed for student success. Much of the teaching makes use of common materials. The difference is helping teachers understand how to implement the teaching for the greatest impact and acceleration of learning. As you watch this clip of an intervention group, notice the progression of tasks, the materials and how the teacher provides scaffolds as needed to ensure success.

[Play video]

In the video we saw the teacher begin with materials, and link to a number chart. We then fast forward to an individual check for understanding with the number ladder. The student in the middle needed more support so the teacher brought out the materials again. One of the key ideas we are accomplishing with instruction is to support students making connections with the conceptual and quantitative aspects of number to the symbolic representation, and you can see how this teacher uses their knowledge of student learning trajectories to make on the fly adjustments for each student.

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How will I know when they get there?

Where are they now?

Where do I want them to be?

How will they get there?

Teaching & Learning Cycle

An overarching idea for instruction is the teaching and learning cycle. This approach to instruction is connected to our 9 Guiding Principles of Instruction which is central to Math Recovery teaching. We use this approach in all tiers of assessment and instruction.

The teaching and learning cycle describes the process of making instructional decisions, and with Math Recovery content, we help teachers develop the skills to apply this cycle on a macro level, thinking in short term and long term goals; but they also apply this on a micro level, where they are constantly engaging in these questions and making instructional adjustments. The GELN Early Math Essentials Instructional Practice number 4 asks teachers to engage in formative assessment as a process. For Math Recovery participants this is called “observing the child and fine-tuning instruction.”

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Pre-Service Assignments

Reflection Paper

Activity 1: They watch a video of an MR formative assessment interview on place value and analyze it. They are provided with the interview protocol and the constructs for place value. We do other work in class developing their understanding of place value. Attached are the MR interview protocol, MR constructs, and my Activity 1 paper assignment for the activity.

Math Recovery Leaders

Activity 2: They go out into schools and use MR assessment interview with children. They analyze their findings and we discuss in class. Then they go out a week later to do a teaching episode with children using MR games to target construct/level they are at and help them progress. Attached is the Activity 2 paper I have them write about the teaching episode.

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Evaluation Evidence

mathrecovery.org/research

The Math Recovery website offers a couple of white papers that will allow you to dig more deeply into their efficacy and effectiveness evaluations and their design research underpinnings. I just want to highlight a few details for you.

In the 2015-2016 school year a project funded by the Michigan Math and Science Partnership found that when teachers attended AVMR 1 and AVMR 2, they are better able to support student growth. In this project, 76% of K-5 students met or exceeded their projected NWEA growth.

The project also noted an overall improvement in the mean percentile rank of each grade level K-5 from fall to spring.

As we have said, these courses are professional learning for the teacher first. The study also showed improvement in teacher instructional decision making and increased engagement in professional conversations related to math recovery courses. This is an important data point for administrators, who want to see that their PD investment will last.

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MiSTEM Network

www.michigan.gov/mistem

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Michigan Implementation

Partnership since 2016
Development of statewide regional leadership for sustainable professional development
Pandemic Response – free resources to +3,200 trained teachers
2021- 26 MiSTEM Network Advisory Council Grant Math Action Area – workgroup focused on Foundational math
Included in FY24 Governor’s budget

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Michigan Math Recovery

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All Courses by County 2017-Oct. 2022

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All Courses by MiSTEM Network Region 2017-Oct. 2022

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Math Recovery Connections to Pre-Service

Potential Next Steps:

Attend a Math Recovery course yourself
Integrate content from the MR books into pre-service course material
Pre-service teachers use one assessment to see how the system works, engage with students to develop formative assessment and pedagogical strategies
Connect with MiSTEM Network or ISD/RESA staff so pre-service teachers know where to go for next steps for PD supports over their career

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How To Get Connected:

Mathrecoverymi.org – click on the connect tab
Contact your ISD or RESA
Contact your MiSTEM Regional Director at:

www.michigan.gov/mistem

Contact Math Recovery

www.mathrecovery.org

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I’m interested in Partnering

Tell us what you are interested in partnering on…

[Name, Contact Info]

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I’m interested in Partnering

Tell us what you are interested in partnering on…

[Name, Contact Info]

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Q & A

https://bit.ly/3aH6EWY

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michigan.gov/mistem

diane.owenrogers@kresa.org

ginger.rohwer@gvsu.edu