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.
Tuesday, January 20, 2015
Tuesday, December 16, 2014
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
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
Thursday, November 20, 2014
Analyzing Assessment Items
By Dr. Pooja Shivraj, RME Educational Assessment Researcher
Much of the work we do at Research in Mathematics Education involves the development of assessments used by educators to identify students who may be struggling with algebra-readiness knowledge and skills, so that teachers can provide additional instructional support. The research process we use is rigorous and begins with an assessment blueprint, then item writing, internal reviews and external expert reviews, followed by a pilot test and finally the development of the test forms. The pilot test is given to a large number of students in order to determine the validity of the assessment items. Our researchers receive the results of the pilot and perform an extensive statistical analysis to determine if an item is good, psychometrically speaking.
The point of obtaining item statistics is to develop a pool of items that function well from which future tests can be designed. There are two kinds of analyses that can be performed: a Classical Test Theory (CTT) analysis, which is sample-dependent and non-model based, or an Item Response Theory (IRT) analysis, which is sample-independent and model-based. Regardless of the type of analysis performed, three primary statistics are used to determine if an item is psychometrically good. The ranges listed below are the acceptable norms found in the literature.
(1) The item should have a strong correlation between each item score and the total score. In other words, the correlation should show that the test-takers choosing the correct answer on the item are likely to receive a higher score. This statistic is measured by the point-biserial correlation (CTT) or the point-measure correlation (IRT). A good item would have a point-biserial correlation of >0.2 or a point-measure correlation of >0.25.
(2) The difficulty of the item, measured by the proportion of students answering the item correctly (CTT), should be between 30% to 80% of the test-takers. In IRT, the difficulty parameter, b, should be between -4 and +4.
(3) The discrimination of the item, also measured by the point-biserial correlation (CTT) should be higher for the correct response than the distractors. In IRT, the discrimination parameter, a, should be between 0.5 and 1.5. The greater the discrimination, the better the item discriminates between lower ability and higher ability students.
What can you do with items that don't function well? For the items that don't function well, reviewing the data would be the first step. Are the items functioning poorly because the majority of students are choosing the correct answer? Is one distractor not being chosen at all? Are the majority of students choosing a single distractor more often than other options? These data would all be red flags. The next step would be to review the content of all the items that don't function well, especially the items that were flagged in the previous step. What about the content led students to choose or not choose a particular response choice?
Using this process of analyzing data, reviewing items, and adjusting the content of the items, a pool of items that function well can be developed for use in the future.
Note: Many other statistics (e.g., fit statistics in IRT like Chi square, infit, outfit, etc.) could be used to determine if an item functions well in addition to the ones described above that could also provide information at the test level. Please feel free to email me if you would like more information at pshivraj@smu.edu.
Much of the work we do at Research in Mathematics Education involves the development of assessments used by educators to identify students who may be struggling with algebra-readiness knowledge and skills, so that teachers can provide additional instructional support. The research process we use is rigorous and begins with an assessment blueprint, then item writing, internal reviews and external expert reviews, followed by a pilot test and finally the development of the test forms. The pilot test is given to a large number of students in order to determine the validity of the assessment items. Our researchers receive the results of the pilot and perform an extensive statistical analysis to determine if an item is good, psychometrically speaking.
The point of obtaining item statistics is to develop a pool of items that function well from which future tests can be designed. There are two kinds of analyses that can be performed: a Classical Test Theory (CTT) analysis, which is sample-dependent and non-model based, or an Item Response Theory (IRT) analysis, which is sample-independent and model-based. Regardless of the type of analysis performed, three primary statistics are used to determine if an item is psychometrically good. The ranges listed below are the acceptable norms found in the literature.
(1) The item should have a strong correlation between each item score and the total score. In other words, the correlation should show that the test-takers choosing the correct answer on the item are likely to receive a higher score. This statistic is measured by the point-biserial correlation (CTT) or the point-measure correlation (IRT). A good item would have a point-biserial correlation of >0.2 or a point-measure correlation of >0.25.
(2) The difficulty of the item, measured by the proportion of students answering the item correctly (CTT), should be between 30% to 80% of the test-takers. In IRT, the difficulty parameter, b, should be between -4 and +4.
 |
| An item characteristic curve depicting the discrimination parameter (a) and the difficulty parameter (b) in an IRT model |
What can you do with items that don't function well? For the items that don't function well, reviewing the data would be the first step. Are the items functioning poorly because the majority of students are choosing the correct answer? Is one distractor not being chosen at all? Are the majority of students choosing a single distractor more often than other options? These data would all be red flags. The next step would be to review the content of all the items that don't function well, especially the items that were flagged in the previous step. What about the content led students to choose or not choose a particular response choice?
Using this process of analyzing data, reviewing items, and adjusting the content of the items, a pool of items that function well can be developed for use in the future.
Note: Many other statistics (e.g., fit statistics in IRT like Chi square, infit, outfit, etc.) could be used to determine if an item functions well in addition to the ones described above that could also provide information at the test level. Please feel free to email me if you would like more information at pshivraj@smu.edu.
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