## Archive for MATH MODELING

#### Friday, September 20th, 2019

## Catalyzing Change-position students as being “math strong” with mathematical powers that empowers

Worked with 52 amazing Gr 3-8 VA teachers @VaSCL on using learning progression to position students as being “math strong” with mathematical powers that empowers them-moving away from deficit language to catalyze change in Elem & Middle School and bring #ETP Equitable Teaching Practices in the math class @kmorrowleong @Mathburner @math_rickard @Deb_crawford @nctm

Launched the day with a keynote “Experiencing Wonder, Joy and Empowerment through Modeling with Mathematics “

#### Thursday, August 29th, 2019

## Motivated-COMPUTE Equity

As I begin a new semester with excited new pre-service teachers, I am inspired by Ilana Horn’s book @ilana_horn, Motivated- Designing Math Classrooms Where Students Want to Join In! She identifies five features of a motivational classroom: Students’ sense of **belongingness**, the **meaningfulness** of learning, students’ **competence**, structures for **accountability** and students’ **autonomy**. Dr. Horn shared how the mathematics classrooms are socially risky places and how we need to decrease that social risk to increase student participation and math talk. Thank you to stellar teachers like @pegcagle, Rafranz Davis, Sadie Estrella, Chris Luniak, Fawn Ngyuen, Elizabeth Statmore who open up their practices and routines that motivate student participation. I believe all their effort builds each and every student to have math power. M-power “empower” as I like to call it.

This powerful message aligns with 7 best equitable teaching practices that I call COMPUTE to provide equity in the math classroom that I will share with my pre-service teachers and with teachers I work with Lesson Study.

COMPUTE for Equitable Teaching and Learning in the Math Classroom

**C**aring, celebrating and connecting to cultural diversity, cultural contexts and the world we live in to engage in mathematics.**O**wning the math- Allow students to share their mathematical thinking and author math ideas that builds on collective knowledge**M**otivating student to learn by providing experience that taps into learners curiosity and interest where they find challenge and academic success.**P**roblem Posing and Problem Solving as the core math activities to develop metacognition.**U**nderstanding with competence and confidence that builds students’ math identity**T**argeted feedback to math learning for individual needs and accountable learning**E**motionally supportive learning environment where learners feel safe, valued and cared for where mistakes are embraced as steps to learning.

(See blog connecting COMPUTE Equity with Math Modeling Activities that Connect to Students Lived Experiences http://drjennifersuh.onmason.com/2019/08/20/m-power-through-mathematical-modeling-foregrounding-equity-in-modeling-activities/

#### Saturday, March 9th, 2019

## MSRI 2019-Math Modeling K-16 and beyond

Mathematical Modeling (MM) now has increased visibility in the education system and in the public domain. It appears as a content standard for high school mathematics and a mathematical practice standard across the K-12 curriculum (Common Core Standards; and other states’ standards in mathematics education). Job opportunities are increasing in business, industry and government for those trained in the mathematical sciences. Quantitative reasoning is foundational for civic engagement and decision-making for addressing complex social, economic, and technological issues. Therefore, we must take action to support and sustain a significant increase in the teaching and learning of mathematical modeling from Kindergarten through Graduate School.

Mathematical modeling is an iterative process by which mathematical concepts and structures are used to analyze or gain qualitative and quantitative understanding of real world situations. Through modeling students can make genuine mathematical choices and decisions that take into consideration relevant contexts and experiences.

Mathematical modeling can be a vehicle to accomplish multiple pedagogical and mathematical goals. Modeling can be used to introduce new material, solidify student understanding of previously learned concepts, connect the world to the classroom, make concrete the usefulness (maybe even the advantages) of being mathematically proficient, and provide a rich context to promote awareness of issues of equity, socio-political injustices, and cultural relevance in mathematics.

A critical issue in math education is that although mathematical modeling is part of the K-12 curriculum, the great majority of teachers have little experience with mathematical modeling as learners of mathematics or in their teacher preparation. In some cases, mathematics teacher educators have limited experience with mathematical modeling while being largely responsible for preparing future teachers.

Currently, the knowledge in teaching and learning MM is underdeveloped and underexplored. Very few MM resources seem to reach the K-16 classrooms. Collective efforts to build a cohesive curriculum in MM and exploration of effective teaching practices based on research are necessary to make mathematical modeling accessible to teacher educators, teachers and students.

At the undergraduate level, mathematical modeling has traditionally been reserved for university courses for students in STEM majors beyond their sophomore year. Many of these courses introduce models but limit the students’ experience to using models that were developed by others rather than giving students the opportunity to generate their own models as is common in everyday life, in modeling competitions and in industry.

The CIME workshop on MM will bring together mathematicians, teacher educators, K-12 teachers, faculty and people in STEM disciplines. As partners we can address ways to realize mathematical modeling in the K-12 classrooms, teacher preparation, and lower and upper division coursework at universities. The content and pedagogy associated with teaching mathematical modeling needs special attention due to the nature of modeling as a process and as a body of content knowledge.

**Overarching critical issue of the 2019 CIME Workshop:** How can we individually and collectively advance the teaching and learning of mathematical modeling in K-16?

**The following questions will frame the structure of the CIME 2019 Workshop:**

1. CRITICALLY EXAMINE CURRENT MM EDUCATIONAL POLICIES AND PRACTICES:

**What is the current state of mathematical modeling (MM) education and why isn’t it a central part of mathematics education from K-16?**

- What
**policies**bring MM into the curriculum and which have presented obstacles? What has been the impact of Common Core Mathematical Practice Standard 4: Model with mathematics? What is the role of MM with respect to quantitative literacy? - What
**curricular resources**exist? How do teachers access them? How are they understood by teachers? How are they enacted in classrooms? What is needed? - Which
**professional development**approaches are effective for teachers? - How does MM appear in current
**assessments**? How have current assessment development processes and test items supported or created barriers for MM education? - What current MM
**teaching practices**support equitable classroom environments in which student thinking is valued and respectfully considered? - How does the way we teach mathematics connect with the
**workplace**?

2. DEVELOP A VISION FOR MATHEMATICAL MODELING EDUCATION:

**How can we coordinate and increase efforts to infuse K-16 classrooms with equitable teaching practices through mathematical modeling (MM) education?**

**Student Learning in Equitable and Collaborative Environments**

How can research inform learning trajectories for math modeling elementary, secondary and undergraduate education? What are key competencies to develop for students to be successful modelers? What are the relationships between mathematical modeling and statistical modeling? How do teachers assess their students’ modeling proficiency?

What are the affordances and challenges of MM with respect to providing a more equitable, just, and humanizing mathematics education? How can MM be taught through effective, equitable and collaborative group work?**Experiential Learning and Community Engagement**

How can modeling tasks be tied to community/cultural contexts? How can students use their lived experiences and cultural knowledge along with their mathematical tools and reasoning, to engage in MM? How might MM engage students, especially those who may be marginalized from mathematics?**Policy**

How do we convince policymakers and stakeholders of the need for MM in K-16? What are the benefits and challenges of including MM in standards, textbooks and assessments? How might MM be included in state/national teacher certification as a competency/domain? What kind of policy changes would need to happen in order to make MM central in K-16?**Professional Preparation and Development: Teachers, teacher educators, mathematicians**

What MM experiences/competencies/support do**teachers**and**teacher educators**need to in MM teaching practices and pedagogy? As they teach MM, how can**teachers**get ongoing support to meet the challenges associated with acquiring mathematical and computational content knowledge as well as contextual information?**Career Preparation and Readiness**

How do we position MM as a critical element of workforce preparation in similar ways to computing and engineering? How might we use public awareness of data science (including the positive and negative associations) to help people see the value of MM education? How do we educate policy makers, admissions officers, recruiters, and career counselors about the value of MM in businesses, industry and government agencies?

3. TAKE ACTION BEYOND CIME:

**What will you do after the CIME Workshop to contribute to MM in K-16?**

- What can mathematicians, mathematics teacher educators, teachers, and professionals in industry do to bring more mathematical modeling into the K-16 classrooms?
- What is the
**role**of each of the constituencies in realizing the vision for mathematical modeling in education? - How can the mathematics and mathematics education
**research communities**come together to offer solutions? - What innovative ideas are there to provide professional development to teachers at a global scale?
- How can we use the new
**Math Modeling Hub**platform to create**professional communities and resources**and sustain these efforts so that they continue to be accessible and useful?

#### Tuesday, July 10th, 2018

## Tapping into the Sense of Wonder in Math

Sense of Wonder and curiosity is innately wired in human beings.

http://www.5280math.com/noticing-and-wondering/

http://robertkaplinsky.com/lessons/

There are a number of resources available as sources of great, engaging mathematics tasks.

Michigan-developed MAISA CCSSI Units (Michigan Association of Intermediate School Administrators – Common Core State Standards Initiative)

Grades: kindergarten through high school

The MAISA project has taken the CCSS-M and CCSS-ELA standards and placed them in units of study for all grades K-11. The mathematics units include a unit plan, a detailed model lesson from the unit, one or more formative assessment tasks, and a wealth of other resources. The units are made available through MAISA’s Atlas curriculum management software’s public site.

Jerry Burkhart’s “Creative Math Prompts” provide visual prompts for exploring “What do you wonder?” “What do you know?” See also his “Problems That Never End”.

Jo Boaler and her youcubed team at Stanford University have created and gathered a number of tasks across all grade levels. Since fall 2015, the team has also created a “Week of Inspirational Math” with the idea of kicking off the school year with highly engaging rich mathematics tasks.

Grades: kindergarten through high school

MathHooks.com – intriguing “hooks” for each of the grades 7 and 8 mathematics standards to help teachers kick off lessons through inquiry.

EMATHS – Excellent Michigan-produced tasks and units for Algebra 1, Geometry, and Algebra 2. The professional learning is also great, and along with the tasks, can change teaching and learning to enrich mathematical understanding and competence.

Mathematics Assessment Project – from MARS (Mathematics Assessment Resources Service)

Grades: Mainly 6-8 and high school

See the Index of Classroom Challenges for 100 lessons in total. See the Index of Summative Tasks for middle and high school novice, apprentice, and expert tasks.

A 1993 NSF funded mathematics assessment project, Balanced Assessment included teams from Harvard, the University of California, Michigan State University, and the University of Nottingham. It was ahead of its time in creating tasks (rather than “problems”) for students to engage in, explore, and develop and provide evidence of deep understanding. Tasks are available at all grade levels, and have since been published by Corwin Press and by Teachers’ College Press.

Grades: kindergarten through high school

NRICH – Enriching Mathematics – from the University of Cambridge

Grades: kindergarten through high school; Select the “Teachers” menu option and choose from Early Years, Primary, or Secondary.

Inside Mathematics – Includes “Problems of the Month” and “Performance Assessment Tasks”, along with other helpful resources for teachers and professional learning providers.

Graphing Stories: Fifteen seconds at a time A collection of short video clips illustrating various types of change for students to graph. Not a “rich task” in itself, but the site takes the “heavy lifting” of providing suitable edited video clips for teachers to use as part of a task.

Grades: Middle school and high school

101 Questions provides a wealth of photos and video clips to inspire asking great mathematical and statistical questions. These graphics can help kick off a rich investigation.

Grades: mainly middle and high school; some suitable for upper elementary.

National Science Digital Library – Includes mathematics tasks. Choose MATHEMATICS as the “subject” and the grade level you are interested in viewing.

National Council of Supervisors of Mathematics – NCSM has published a new version of its “Great Tasks for Mathematics” (original set of problems released in the 1990s). Two books.

Grades: K-5 (“NCSM Great Tasks for Mathematics K-5”) and 6-12 (“NCSM Great Tasks for Mathematics 6-12”)

Dan Meyer’s Three-Act Math Tasks – For background on using Three-Act Mathematical Stories, read Dan’s blog here.

3-Act Math Problems – Inspired by Dan Meyer. An innovative way of approaching and enriching mathematics problems; many sites are noted in this LiveBinder.

Grades: Mainly middle school and high school.

Achieve the Core – Includes mathematical tasks along with other resources of interest to teachers.

Emergent Math – Includes CCSS Problem-Based Curriculum Units, along with links to the mathematical tasks within the units.

(Fee-based) Mathalicious has a number of tasks tagged to standards. They have now organized some tasks into units to assist teachers with embedding rich tasks into lessons throughout the course.

Grade levels: Grade 6 through High School

PBS provides over 1900 math-related itemsto spark ideas for rich tasks. Most of the entries here are not fully-developed tasks, but inspirations or launches for tasks. Use the filter provided to explore what’s available for your grade(s).

Grade levels: Pre-K through High school

Illustrative Mathematics has released an excellent mathematics curriculum resource for grades 6 through 8. It has received a nearly perfect score from EdReports.org. See also the other rich tasks at the website.

Math Landing: Resources and Tools for Elementary Math Specialists and Teachers. Grades: K-5. Check out the Classroom Collections. Grouped by Standard of Mathematical Practice.

Estimation 180 provides photos which teachers can use a prompts for estimating and developing number sense. Many of these photos could serve as prompts for Number Talks or Math Talks. The site provides lessons, other activities, and other resources.

Grade Levels: kindergarten through high school

CIC Task Library (Complex Instruction Consortium) – Tasks for High School – You may need to sign in with a Google account. Once in the site, click on CONSORTIUM, and then on TASK LIBRARY.

East Midlands (U.K.) Math Tasks – A collection of tasks along with teacher guides.

Grade levels: kindergarten through high school

North Carolina has developed a number of tasks as part of their Department of Education curriculum support. They are posted by grade level. Look under the “Compiled Documents”.

Click on the grade level to visit:

kindergarten 1st grade 2nd grade

K-2 Formative Tasks Overview

3rd grade 4th grade 5th grade

Grades 3-5 Formative Tasks Overview

6th grade 7th grade 8th grade

Grades 6-8 Middle Grades Overview

North Carolina High School Resources – “Math Resources for Instruction” documents provide or link a suggested task for each standard. Look in the purple “Instructional Resources” box of the table.

Rich learning tasks from New Zealand. See also their “Counting Collections” resources.

**Resources to help plan for and implement these great math tasks for teaching and learning:**

Thinking Through a Lesson Protocol (TTLP)

The Thinking Through a Lesson Protocol

For a number of “math in real life” resources (not necessarily rich tasks), visit Math in Daily Life from Annenberg (Learner.org)

#### Wednesday, November 22nd, 2017

## Mathematical Literacy

Math Literacy, according to the PISA’s Math Framework (2015), places the emphasis on the math modeling process and describe it as the “ability of students to analyze, reason and communicate ideas effectively as they pose, formulate, solve and interpret mathematical problems in a variety of situations. The PISA mathematics assessment focuses on real-world problems, moving beyond the kinds of situations and problems typically encountered in school classrooms. In real-world settings, citizens routinely face situations in which the use of quantitative or spatial reasoning or other cognitive mathematical competencies would help clarify, formulate or solve a problem. Such situations include shopping, traveling, cooking, dealing with personal finances, judging political issues, etc. Such uses of mathematics are based on the skills learned and practiced through the kinds of problems that typically appear in school textbooks and classrooms. However, they also demand the ability to apply those skills in a less structured context, where the directions are not so clear, and where the student must make decisions about what knowledge may be relevant and how it might be usefully applied.” PISA 2015 Math literacy document

They continue to state that “Citizens in every country are increasingly confronted with a myriad of tasks involving quantitative, spatial, probabilistic and other mathematical concepts. For example, media outlets (newspapers, magazines, television and the Internet) are filled with information in the form of tables, charts and graphs about subjects such as weather, climate change, economics, population growth, medicine and sports, to name a few. Citizens are also confronted with the need to read forms, interpret bus and train timetables, successfully carry out transactions involving money, determine the best buy at the market, and so on. The PISA mathematics assessment focuses on the capacity of 15-year-old students (the age when many students are completing their formal compulsory mathematics learning) to use their mathematical knowledge and understanding to help make sense of these issues and carry out the resulting tasks. PISA defines mathematical literacy as: …an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned and reflective citizen. Some explanatory remarks may help to further clarify this domain definition: • The term mathematical literacy emphasises mathematical knowledge put to functional use in a multitude of different situations in varied, reflective and insight-based ways. Of course, for such use to be possible and viable, many fundamental mathematical knowledge and skills are needed. Literacy in the linguistic sense presupposes, but cannot be reduced to, a rich vocabulary and substantial knowledge of grammatical rules, phonetics, orthography, etc. To communicate, humans combine these elements in creative ways in response to each real-world situation encountered. In the same way, mathematical literacy presupposes, but cannot be reduced to, knowledge of mathematical terminology, facts and procedures, as well as skills in performing certain operations and carrying out certain methods. It involves the creative combination of these elements in response to the demands imposed by external situations.”

#### Tuesday, November 21st, 2017

## Art of Asking Good Questions

With my work with Mathematical Modeling and Teaching practices, I think hard about the art of asking questions.

Harvard Business School article by Pohlmann and Thomas (2015) write about “Relearning the Art of Asking Questions” https://hbr.org/2015/03/relearning-the-art-of-asking-questions

The curious four-year-old asks a lot of questions — incessant streams of “Why?” and “Why not?” might sound familiar — but as we grow older, our questioning decreases. In a recent poll of more than 200 of our clients, we found that those with children estimated that 70-80% of their kids’ dialogues with others were comprised of questions. But those same clients said that only 15-25% of their own interactions consisted of questions. Why the drop off? They suggest these four types of questions to achieve 4 different goals. Clarifying, adjoining, funneling (or focusing since funneling has a negative connotation with PtA practices) and elevating. It makes me think about the math questions we ask in our math classrooms. Some view of the problem is wide and some narrow- when we are looking for patterns that is trying to look at a set of repeated reasoning or patterns (narrow) then to make a generalization or general rule for cases (wide). Often times, we are clarifying what students are thinking and affirming their thinking and other times we are extending their thinking to discover something new.

**Clarifying questions** help us better understand what has been said. In many conversations, people speak past one another. Asking clarifying questions can help uncover the real intent behind what is said. These help us understand each other better and lead us toward relevant follow-up questions. “Can you tell me more?” and “Why do you say so?” both fall into this category. People often don’t ask these questions, because they tend to make assumptions and complete any missing parts themselves.

**Adjoining questions **are used to explore related aspects of the problem that are ignored in the conversation. Questions such as, “How would this concept apply in a different context?” or “What are the related uses of this technology?” fall into this category. For example, asking “How would these insights apply in Canada?” during a discussion on customer life-time value in the U.S. can open a useful discussion on behavioral differences between customers in the U.S. and Canada. Our laser-like focus on immediate tasks often inhibits our asking more of these exploratory questions, but taking time to ask them can help us gain a broader understanding of something.

**Funneling** **questions **are used to dive deeper. We ask these to understand how an answer was derived, to challenge assumptions, and to understand the root causes of problems. Examples include: “How did you do the analysis?” and “Why did you not include this step?” Funneling can naturally follow the design of an organization and its offerings, such as, “Can we take this analysis of outdoor products and drive it down to a certain brand of lawn furniture?” Most analytical teams – especially those embedded in business operations – do an excellent job of using these questions.

**Elevating** **questions **raise broader issues and highlight the bigger picture. They help you zoom out. Being too immersed in an immediate problem makes it harder to see the overall context behind it. So you can ask, “Taking a step back, what are the larger issues?” or “Are we even addressing the right question?” For example, a discussion on issues like margin decline and decreasing customer satisfaction could turn into a broader discussion of corporate strategy with an elevating question: “Instead of talking about these issues separately, what are the larger trends we should be concerned about? How do they all tie together?” These questions take us to a higher playing field where we can better see connections between individual problems.

#### Sunday, November 5th, 2017

## Sparking a sense of Wonder- Curiosity a Pathway to Learning

## Curiosity

Kids are relentless in their urge to learn and master. As John Medina writes in **Brain Rules**, “This need for explanation is so powerfully stitched into their experience that some scientists describe it as a drive, just as hunger and thirst and sex are drives.” Curiosity is what makes us try something until we can do it, or think about something until we understand it. Great learners retain this childhood drive, or regain it through another application of self-talk. Instead of focusing on and reinforcing initial disinterest in a new subject, they learn to ask themselves “curious questions” about it and follow those questions up with actions. Carol Sansone, a psychology researcher, has found, for example, that people can increase their willingness to tackle necessary tasks by thinking about how they could do the work differently to make it more interesting. In other words, they change their self-talk from *This is boring* to *I wonder if I could…?*

You can employ the same strategy in your working life by noticing the language you use in thinking about things that already interest you—*How…? Why…? I wonder…?*—and drawing on it when you need to become curious. Then take just one step to answer a question you’ve asked yourself: Read an article, query an expert, find a teacher, join a group—whatever feels easiest.

Changing Your Inner Narrative

#### Wednesday, March 8th, 2017

## COMPLETE MATH at NCTM and VCTM

Suh, J.M., Birkhead, S., Baker, C., Frank, T., Seshaiyer, P. (April, 2017) Examining Coaching Structures that Supported Mathematics Teacher Learning. Presented at National Council of Teachers of Mathematics, San Antonio, TX.

Suh, J.M. & Matson, K. (April, 2017). Mobilizing Teachers as Researchers to Promote an Innovative Classroom Practice of Implementing Mathematical Modeling in the Elementary Grades. Presented at the annual meeting of the American Educational Research Association Conference, San Antonio, TX.

Gallagher, M.A. & Suh, J.M. (April, 2017) Learning to Notice Ambitious Mathematics Instruction Through Cycles of Structured Observation and Reflection. AERA, San Antonio, TX.

** Modeling Mathematics Ideas to Enhance Productive Disposition towards Mathematics- New! – **“Family of Problems” This session will focus on implementing Modeling Mathematics Ideas to develop students’ math understanding and productive disposition towards mathematics. The workshop will engage teachers and math leaders in meaningful mathematical tasks called a “Family of Problems” that focus on algebraic and proportional reasoning, data analysis, and problem solving. Participants will also discuss the important teaching and assessment strategies that are used with this problem-based learning approach. We will share our framework for building Strategic Competence and Productive Dispositions through Modeling Mathematical Ideas including the application of mathematics for 1) problem solving; 2) problem posing; 3) mathematical modeling; 4) the flexible use of representational models, tools, technology and manipulatives to solve problems and communicate mathematical understanding; and 5) the deep understanding of conceptual models critical to understanding a specific mathematics topic. We will also share a series of classroom tested teacher-designed problem tasks called the “Family of Problems” which are rich tasks that have a related mathematics concept. **• Jennifer Suh, jsuh4@gmu.edu, **George Mason University, Fairfax, VA • Padhu Seshaiyer, George Mason University, Fairfax, VA • Patti Freeman • Linda Gillenillen

**Making Instructional Shifts: Targeted Professional Development on Coaching Mathematics **teacher leaders will share their experiences as co-facilitators with George Mason University instructors for lesson study with small teams of K-12 teachers enacting rich mathematics tasks. Participants will draw from the coaches’ challenges and celebrations as they engage in activities to envision instructional shifts in their schools. •** Courtney Baker, cbaker@gmu.edu,** George Mason University, Fairfax, VA • Terrie Galanti, George Mason University, Fairfax, VA • Alyson Eaglen • Jenny Clovis • Bonnie Krajeski • Amy Miknis • Jennifer Suh, jsuh4@gmu.edu, George Mason University, Fairfax, VA • Padmanabhan Seshaiyer, pseshaiy@gmu.edu, George Mason University, Fairfax, VA • Toya Frank, tfrank4@gmu.edu, George Mason University, Fairfax, VA

https://docs.google.com/presentation/d/1yHgwihCqeSzXGdM6HX66euuV6haihvJrUvNNWXbZhSw/edit?usp=sharing

**Broadening Participation for English Learners in Mathematics **We will present an assets-based approach for teaching mathematics to English language learners (ELLs) that was the guiding framework of a summer workshop and follow-up lesson stud for teachers’ grades 5-9 on rational numbers and proportional reasoning. This approach challenges educators to broaden their understanding of what it means to communicate mathematically. It also challenges the idea that vocabulary acquisition must precede deep mathematical thinking. Teachers in the session will have the opportunity to experience instructional scaffolds for ELLs based on contemporary research from experts in ELL and mathematics education. These scaffolds help to reduce cognitive overload while maintaining high cognitive demand as students productively struggle with challenging mathematical tasks. All examples will be presented in the context of rational numbers and proportional reasoning. The faculty, teachers, and coaches from the summer/fall workshop and subsequent lesson study will present how they used this approach in their schools, the instructional shifts they observed, the challenges they faced, and the advantages of teaching mathematics to ELLs using this approach. •** Toya Frank, tfrank4@gmu.edu,** George Mason University, Fairfax, VA • Rachelle Farmer – Fairfax County PS, VA • Abhilasha Tripathi – Prince William County PS, VA • Jennifer Suh, jsuh4@gmu.edu, George Mason University, Fairfax, VA • Courtney Baker, cbaker@gmu.edu, George Mason University, Fairfax, VA • Padmanabhan Seshaiyer, pseshaiy@gmu.edu, George Mason University, Fairfax, VA

Ducks & Sheep to Minotaurs & Pegasi: Algebraic Thinking Grades 2-11 Participants in this session will have the opportunity to look at how a single problem was modified and implemented across grades 2 through 11 to promote students’ understanding of algebraic reasoning. Presenters will be classroom teachers who collaborated to modify the task for use at each grade level and who implemented the problem in diverse settings. The vertical nature of this rich task will provide participants the opportunity to see how this task fits into their grade-level content. We will look at teachers’ implementation, students’ strategies, as well as the vertical articulation of content acquisition within the Patterns, Functions, and Algebra strand. Participants will have the opportunity to experience several versions of the task presented at multiple grade levels and analyze the progression of student work in algebraic reasoning. Presenters will also share online resources that we call “Family of Problems” with rich tasks at all grade levels. • **Padmanabhan Seshaiyer, pseshaiy@gmu.edu, George Mason University, Fairfax, VA** • Jennifer Suh, jsuh4@gmu.edu, George Mason University, Fairfax, VA • Courtney Baker, cbaker@gmu.edu, George Mason University, Fairfax, VA • Toya Frank, tfrank4@gmu.edu, George Mason University, Fairfax, VA • Sara Birkhead, George Mason University, Fairfax, VA • Terrie Galanti, George Mason University, Fairfax, VA • Emily Burrell, Fairfax County Public Schools, Fairfax, VA • Liz Taylor, evtaylor1@fcps.edu, Fairfax County PS, VA • Brain Wiseman, Fairfax County PS, VA

https://docs.google.com/presentation/d/1g5JT5lskwkwQefDVuqekIDn_rxxjwKZnSm-7MNVzqcM/edit?usp=sharing

Mathematical Modeling in General Education and Advanced Academic Classrooms Is Mathematical Modeling (MM) equally successful in General Education and Advanced Academic settings? Elementary teachers designed and implemented a MM task engaging students in authentic problem posing and solving while addressing grade-level standards. We compare student responses and strategies and the development of 21st century skills. •** Kathleen Matson, kmatson@masonlive.gmu.edu, George Mason University, Fairfax, VA **• Jennifer Suh, jsuh4@gmu.edu, George Mason University, Fairfax, VA • Kim Fair – George Mason University, Fairfax, VA • Samara Green – Fairfax County PS, VA • Christine Onide – Fairfax County PS, VA • Atifa Kuraishi – Fairfax County PS, VA • Spencer Jamieson, spencer.jamieson@fcps.edu, Fairfax County PS, VA • Carol Cockerill, Fairfax County PS, VA • LyndaLea Furtado, Fairfax County PS, VA • Padhu Seshaiyer, George Mason University, Fairfax, VA

Mathematical Modeling Inspiring our Students to Love Math Mathematical modeling is an important topic of study and mathematical practice in grades K-12. This session will engage the participants in considering Mathematical Modeling tasks in the early grades. Teachers and university collaborators will share Math Modeling Units taught in 3-6th grades and share how MM enhanced the teaching and learning of mathematics by bringing in the real world context to students and enriched the learning environment. We will launch the task called “America in a Day” to inspire the audience with the authentic MM task of designing a family outing for their summer vacation and two 6th grade lessons called “Food for Thought” and “Running a School Store” that bring in number sense, algebra and data analysis .** • Liz Taylor, evtaylor1@fcps.edu, Fairfax County PS, VA • MaryAnne Rossbach, Fairfax County PS**, VA • Spencer Jamieson, spencer.jamieson@fcps.edu, Fairfax County PS, VA • Kathleen Matson, kmatson@masonlive.gmu.edu, George Mason University, Fairfax, VA • Padhu Seshaiyer, George Mason University, Fairfax, VA • Jennifer Suh, jsuh4@gmu.edu, George Mason University, Fairfax, VA

#### Thursday, January 5th, 2017

## Modeling Mathematical Ideas- Published in 2017!

https://rowman.com/ISBN/9781475817607

https://www.amazon.com/Modeling-Mathematical-Ideas-Developing-Competence/dp/1475817592