RME Conference Morning Breakout Summaries

Our RME Conference was held at the end of February. Below are summaries of the morning breakout sessions.

Morning Breakout 1 – Solving Word Problems Using Schemas

Presented by Dr. Sarah Powell and facilitated by Cassandra Hatfield

In this session, Dr. Sarah Powell, presented problem solving strategies teachers can use to help
elementary students organize their thinking when approaching word problems. Dr. Powell emphasized the importance of teaching students to recognize schemas, specifically additive and multiplicative problem types. The example word problems used in Dr. Powell’s presentation highlight the importance of teachers moving beyond problem solving strategies that place emphasis on the identification of “key words”, and suggested students should instead focus on understanding the context and meaning of the language used in word problems. Dr. Powell also suggested students should have a strategic plan for solving word problems that is used regardless of the problem type. In order to ensure all students are familiar with the same problem solving processes, Dr. Powell suggests educators adopt a problem solving strategy for their entire school.

• Students need an “attack strategy” anytime they solve a word problem. Regardless of the problem type, students should know what process they will use to solve a given word problem. Many attack strategies involve reading the word problem, paraphrasing the question, developing a hypothesis, using a diagram or equation to represent a process, estimating or computing an answer, and checking your work. These strategies could be considered an algorithm for solving a word problem. Examples include R.I.D.G.E.S., S.T.A.R., D.R.A.W., S.I.G.N.S., and S.O.L.V.E.
• Students should not be encouraged to identify “key words” as a strategy for solving word problems. Students should understand the context and meaning of all language within a word problem.
• When using strategies, it is important to help students identify the three problem types for addition/subtraction (additive schemas) and four problem types for multiplication/division (multiplicative schemas). Additive schemas include part-part whole, difference, and change (join/separate). Multiplicative schemas include

Morning Breakout 2 – Mathematical Problem Solving in Real World Situations

Presented by Dr. Candace Walkington and facilitated by Megan Hancock

At the 2015 RME conference, Dr. Walkington spoke about personalization matters! Specifically in mathematics, it is important that students feel personally connected to what they are studying. This is central to helping some students feel more comfortable and be more successful. Personalization means that instruction is tailored to the specific interests of different learners and problems are introduced using different topics that can be implemented efficiently through technology systems. Students have rich engagement with their interest areas. It is important that instructors incorporate students’ passions into what they are learning.

Personalization interventions should seek to include depth, grain size, ownership, and richness. Depth means to make deep meaningful connections to the ways students’ use quantitative reasoning. Grain size refers to knowing the interests of individual learners. Ownership allows students to control the connections made to their interests. Lastly, richness means to balance rich problem solving with explicit connections to abstractions afterwards. If instructors can implement these important personalization interventions in their mathematics teaching, students will feel more connected to their learning and likely be more successful as well.

• The TEKS Process Standards should be interpreted through real-world situations. Students should be introduced to a topic they can relate to, then, the specific mathematics topics should be brought in after they have a firm understanding of the context.
• Studies show that students learn best from concrete thinking to abstract thinking. The teacher teaches the content using concrete scenarios and then moves to abstract thinking after the students understand the math content.
• When mathematics is connected to students’ interests, they can gain a better understanding of the content being taught. Students with little exposure to algebra can reason about and write a linear function in the context of their interests without realizing they are using algebra. This peaks their interest, then the teacher can follow up with the concrete mathematics topics.

Morning Breakout 3 – Fostering Small-Group, Student-to-Student Discourse: Discoveries from a Practitioner Action Research Project

Presented by Dr. Sarah Quebec Fuentes and facilitated by Becky Brown

This session focused on the use of small group peer discussions to increase student understanding with an emphasis on communication. Three of the math process standards include communication, quality communication with reasoning, explaining, and justifying. By asking the students to communicate, you are effectively changing the way they approach mathematics. When you put kids into a group they will communicate but the communication is not always of quality. The teacher’s role is to facilitate the discussion, not to set a rubric or tell them exactly what to do. Students gain process help through their peer interaction, which aids their problem solving abilities by increasing their adaptive qualities. This type of meaningful communication is achieved
through the Action Research Cycle: planning, acting, observing, and reflecting.

• You can improve student communication in your own classrooms in three phases. Stage 1 is to evaluate student communication and just get them to communication. Stage 2 is to evaluate group communication. Which point on the action cycle is this group? Stage 3 is to evaluate your communication. Are you effectively facilitating meaningful discussion? Lastly Stage 4 is to try a customized intervention.
• There is no blanket intervention strategy because each team interacts differently and operates in different phases of the action cycle.
• This practice can be scaled to an entire math department as long as it is scaled down and adjusted for the time needs of the professional.

Supporting English Learners in the Mathematics Classroom

By Dr. Deni Basaraba, RME Assessment Coordinator

The number of English Learners (ELs) in the United States is growing at an unprecedented rate that shows no signs of slowing. As of 2013, for example, over 60.6 million people (21%) spoke a language other than English in the home and, of those, 37.6 million (62%) spoke Spanish in the home (Ryan, 2013). Moreover, the National Center for Educational Statistics (2011) reported that the number of ELs attending public schools has increased in the last three decades, from 4.7 million to 11.2 million. In Texas specifically, the percentage of students classified as ELs increased from 15.3% to 17.5% from 2003 to 2013 and the percentage of students receiving bilingual or English as a second language services grew from 14% to 17.1% (Texas Education Agency [TEA], 2014). This steady increase in the number of ELs attending our schools, combined with a persistent achievement gap in mathematics on both state and national assessments on which ELs exhibit consistently lower levels of proficiency than their non-EL peers, (NCES, 2013), underscore the need to ensure that our mathematics instruction incorporates evidence-based principles of instructional design and delivery to support the development of ELs mathematics understanding and proficiency.

Listed below are three research-based recommendations for supporting ELs mathematics understanding and proficiency.

Situate mathematics problems in contexts that are familiar to students. One of the primary goals of education is to provide students with instruction and practice in skills that they can generalize outside of the classroom to real-world contexts. Consequently, situating mathematics problems for students to solve in contexts that are familiar to them is important not only because it increases their likelihood of engaging in meaning-making actions that rely on conceptual understanding (as opposed to carrying out rote procedures) (Domínguez, 2011) but also because it increases students’ engagement in the problem-solving process (Brenner, 2002; Domínguez, LópezLeiva, & Khisty, 2014). Examples might include: grocery shopping, preparing meals, playing video games, reading books aloud to siblings and/or adults, or eating meals in the school cafeteria.

Focus explicitly on mathematical vocabulary. Although proficiency in mathematics requires students to think in terms of abstract ideas, concepts, and symbols that may be similar across languages, this does not support the common misconception that mathematics is “culture free” (Garrison & Mora, 1999). Rather, it could be argued that explicit instruction of mathematics vocabulary may be critical for some ELs because some mathematical words such as odd, times, table, or line may have specific mathematical definitions that are different than their meaning in everyday conversation (Fang, 2012; Garrison & Mora, 1999; Schleppegrell, 2007)

Strategically incorporate visual representations and manipulatives. One means of fulfilling the recommendation for developmental mathematics instruction put forth by the National Council of Teachers of Mathematics (NCTM, 2000) is to scaffold students’ understanding of abstract mathematical concepts with concrete and visual representations. Concrete representations, or manipulatives such as tangrams, for example, can be used to provide students with tangible experience with mathematical concepts such as greater than and less than, larger and smaller, or concepts of size (e.g., small, smaller, smallest) (Garrison & Mora, 1999). Visual representations, such as graphs or tables, may be useful methods for helping ELs to communicate their preliminary understanding of complex mathematical concepts such as multiplication or division that can be represented graphically more easily than they can verbally or with written words. Not only do these representations provide ELs with opportunity to see and touch while simultaneously being exposed to new mathematical vocabulary, but they also provide ELs with access to the key mathematical concepts in formats that don’t require dependence on language (Cirillo, Bruna, & Herbel-Eisenmann, 2010).

References

Brenner, M. (2002). Everyday problem solving and curriculum implementation: An invitation to try pizza. In M. E. Brenner & J. N. Moschkovich (Eds.) Journal for research in mathematics education. Monograph (Vol. 11): Everyday and academic mathematics in the classroom (pp. 63-92). Reston, VA: National Council of Teachers of Mathematics.

Cirillo, M., Bruna, K. R., & Herbel-Eisenmann, B. (2010). Acquisition of mathematical language: Suggestions and activities for English language learners. Multicultural Perspectives, 12, 34-41.

Domínguez, H., LópezLeiva, C. A., & Khisty, L. L. (2014). Relational engagement: Proportional reasoning with bilingual Latino/a students. Educational Studies in Mathematics, 85, 143-160.

Domínguez, H. (2011). Using what matters to students in bilingual mathematics problems. Educational Studies in Mathematics, 76, 305-328.

Fang, Z. (2012). Language correlates of disciplinary literacy. Topics in Language Disorders, 32, 19-34.

Garrison, L., & Mora, J. K. (1999). Adapting mathematics instruction for English-language learners: The language-concept connection. Changing the Faces of Mathematics: Perspectives on Latinos, 35-48.

National Center for Educational Statistics. (2013). NAEP data explorer [Data file].Washington, DC: U.S. Department of Education. Retreived from http://nces.ed.gov/nationsreportcard/naepdata/report.aspx.

Ryan, C. (2013). Language use in the United States: 2011. American Community Survey report (ACS-22). U.S. Census Bureau; U.S. Department of Commerce. Retrieved 02/26/14 from http://www.census.gov/prod/2013pubs/acs-22.pdf

Schleppegrell, M. J. (2007). Linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23, 139-159.

Texas Education Agency (2014). Enrollment in Texas public schools: 2013-2014. (Document No. GE15 601 03). Austin, TX: Author.

RISD Enterprise City - Tackling Financial Literacy

By Brea Ratliff, RME Secondary Mathematics Coordinator


The revised mathematics TEKS for grades K-8 include a strand addressing financial literacy. The student expectations within this strand were developed to ensure students have a fundamental understanding of economics, and the skills connected to being a consumer and investor (TEA, 2012).

While many schools and school districts are for the first time investigating ways to implement these standards, a program created by the Richardson Independent School District could serve as a prototype for educators looking to cultivate students’ understanding of financial literacy using a real-world model.

Enterprise City is a miniaturized representation of an actual city, and is housed on the campus of Canyon Creek Elementary in Richardson, Texas. Almost 30 years ago, Richardson ISD developed Enterprise City to promote students’ understanding of economics through the development of an innovative interdisciplinary curriculum. While students begin ascertaining the essentials of business and financial literacy through classroom experiences, their knowledge is put into action when given the opportunity to manage the operations of the city for one day.

In addition to gaining an appreciation for the fiscal responsibilities of maintaining a city, students are utilizing critical thinking skills and being engaged citizens as they work collaboratively with other students to support businesses and organizations within the city. I had a chance to interview Jodi Freeman, Enterprise City Program Coordinator, to learn more about the program and how it has impacted their district.

How was the Enterprise City curriculum developed?

In 1983 one of our superintendents visited a program called Exchange City in Kansas City. The curriculum was developed based on that program and has been revised several times since then. It teaches basic economic concepts and personal finance.

Several financial literacy concepts have been embedded within the Enterprise City curriculum since it was established in 1985. How has the adoption of the new mathematics TEKS impacted the curriculum?

Our curriculum has focused on PFL and free enterprise from the start. Students complete job applications, practice money management by using a checkbook, maintain a register and understand the purpose of a debit card. They also formulate advertisements for their business, secure a bank loan, and budget for their business as well as develop an understanding of their role as a good citizen.

How has Enterprise City impacted the community (both RISD and the city of Richardson)?

Our program has won several awards, most recently the Magna Award - a national recognition program that honors innovative programs that advance student learning. Hundreds of businesses have generously donated to our program over the past twenty years, city and state leaders and representatives have visited our facility in support of our program and goal of teaching the free enterprise system and we receive several emails/calls per year from prior “citizens” of Enterprise City who want to participate again as a teacher/parent volunteer or have chosen their career path based on what they learned at Enterprise City as a child.

Does the district provide any programs similar to Enterprise City that are available for students in other grades? How has the district addressed the study of financial literacy and economics in other grade levels?

There isn’t another district-wide program in RISD; Enterprise City is the only program offered for our 6th graders. However, some of our high school business classes have used our facility and revised parts of the curriculum to meet their objectives. We also have our high school LOTE (Languages Other Than English) classes attend. The purpose is to give the students a simulation of life in this environment and to use their language for more than just one class period. The rules of the day in the city require that the students speak only their language at all times. Currently, every RISD 6th grade class attends Enterprise City; however, our district has moved the program over the years from one grade level to another. Teachers in various grade levels at different schools have implemented their own economic activities/programs such as classroom economies. Many students learn how to use check registers, apply for jobs and earn money as incentives.

Can students and teachers outside of RISD participate in the Enterprise City program?

Yes, we offer our program to non-RISD schools for a fee. Currently, we have 8 districts, which send several schools within each district and about 20 private schools that participate.

What advice would you give to teachers and instructional leaders looking to implement a similar program in their district?

Do exactly what we did- secure the funding from their community/school district to build a city and implement a similar program and recruit a core group of teachers to develop the curriculum. Anyone interested is welcome to come visit our facility to see the “best city in Texas” first-hand!

To learn more about Enterprise City, visit http://www.richardson.k12.tx.us/enterprisecity/index2.html

References
(J. Freeman, personal communication, October 23, 2014).

Welcome to Enterprise City. (n.d.). Retrieved November 21, 2014, from http://www.richardson.k12.tx.us/enterprisecity/index2.html