Archive for MATH MODELING

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

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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.”

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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.

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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

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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

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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

https://docs.google.com/presentation/d/1B-9xao_S2IAkEg9X_qIpI4kpznbdnO6hUXFNMdFjTpc/edit#slide=id.g1d17d297a8_2_222

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!

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Developing Strategic Competence in Elementary and Middle School

JENNIFER M. SUH AND PADMANABHAN SESHAIYER

Modeling Mathematical Ideas combines current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students’ common misconceptions in investigating and discussing important mathematical ideas related to number sense, computational fluency, algebraic thinking and proportional reasoning. In each chapter, the authors opens with a rich real-world mathematical problem and presents classroom strategies (such as visible thinking strategies & technology integration) and other related problems to develop students’ strategic competence in modeling mathematical ideas.

https://rowman.com/ISBN/9781475817607

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

Tuesday, September 20th, 2016

USA SCIENCE AND ENGINEERING FESTIVAL

April 2016

GMU COMPLETE hosted a booth at the USA Science and Engineering Festival.

Wednesday, March 2nd, 2016

Presentation in Korea-Math Modeling in the Middle Grades

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Barbie and Rescue Hero Bungee Jumping Task

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Footprint problem revealed!

Tuesday, February 16th, 2016

Math Modeling in the News

The September 30 issue of Education Week includes an article titled Math-Modeling PD Takes Teachers Beyond the Common Core that takes an extensive look at George Mason University’s National Science Foundation funded research into the use of advanced problem solving by elementary teachers.

Many experts believe that “introducing modeling to younger students can improve their critical-thinking and application skills in math.”

The article describes the work of Jennifer Suh, an associate professor of mathematics in the College of Education and Human Development, andPadmanabhan Seshaiyer, professor of mathematical sciences in the College of Science.

Their project includes a year-long, university-district partnership with Fairfax County Public Schools. Over the summer, 24 K-6 teachers received professional development on how to teach modeling, a math skill normally not taught until high school (if at all) followed by additional activities throughout the school year.

From the article:

Young children start using physical models in mathematics as soon as they can count. But mathematical modeling is something different and more complex: It’s the process of taking an open-ended, multifaceted situation, often from life or the workplace, and using math to solve it…

Padmanabhan Seshaiyer and Jennifer Suh, both mathematics professors at George Mason, opened the [professional development] session by asking the teachers to brainstorm the kinds of problems they’ve had to solve in their own lives recently…

As they worked, Seshaiyer asked the teachers to identify their “assumptions and constraints,” words typically used in engineering classes, referring to the factors they believe to be true and those that limit their solutions…

Teachers will meet periodically throughout the school year in groups of four or five to do “lesson study”—a collaborative teaching-improvement process with origins in Japan. The groups will choose a modeling problem, devise lesson plans around it, and predict how students will solve the problem, as well as the kinds of mistakes they’ll make. After doing the modeling problem with their classes, the team will meet again to debrief on what worked and didn’t work with students.

“Having all those heads together to anticipate what kids will do will be a benefit,” said Brian Kent, a math-resource teacher at Weyanoke Elementary School in Fairfax who took part in the professional development.

Click here for the full article.
For more information about the project, please see: NSF Grant to Help K-12 Teachers Teach the “Why?” Behind Math.

https://cehd.gmu.edu/news/stories/nsf-grant-to-teach-k12-teachers-why-behind-math

Monday, February 15th, 2016

Math Modeling Tasks