Curriculum+and+Related+Factors++
TURKISH 8 TH GRADERS’ MATHEMATICS SUCCESS ON TIMSS IN RELATION TO NATIONAL HIGH SCHOOL PLACEMENT TESTS
Musa Sadak Indiana University [email protected] Keywords: Assessment and Evaluation
This study examined the mathematics items in two national assessments conducted in Turkey, namely the OKS 2007 (Assessment of Secondary Educational Institutions) and the SBS 2011 (Secondary Education Placement Test), in terms of content and cognitive domains. The main focus was to interpret the gains in Turkish 8th graders’ mathematics scores on TIMSS between 2007 and 2011 in terms of the OKS 2007 and SBS 2011 assessments.
The data for this study was derived from the Turkish 8th graders’ mathematics scores in TIMSS 2007 and 2011 (Martin, Fullis, & Foy, 2008; Mullis, Martin, Foy, & Arora, 2012) and the
mathematics questions in OKS 2007 and SBS 2011 assessments. For this study, the questions in OKS 2007 and SBS 2011 assessments were categorized into one of four content domains (numbers,
algebra, data & chance, and geometry) and one of three cognitive domains (knowing, applying, and reasoning) according to the TIMSS 2011 framework.
Although Turkish 8th graders’ overall average mathematics score increased from 432 to 452 from 2007 to 2011 in TIMSS assessment, there was no significant difference between given years in numbers content (Mullis et al., 2012). On the other hand, performance improved on the other content domains, especially geometry (Mullis et al., 2012) where the score increased 43 points (Mullis et al., 2012).
One of the likely reasons for the lack of improvement on the numbers domain of TIMSS is that the percentage of content items in number decreased from 39% to 20% between OKS 2007 and SBS 2011. Along with this decrease, there is evidence that teachers decreased emphasis in the area. In contrast, the percentage of geometry items increased from 35% in 2007 to 50% in 2011. Thus the change in focus of the Turkish assessments in relation to TIMSS, where the emphasis on each of the content domains was constant, is likely a major reason for the increase in geometry performance relative to number.
With respect to the cognitive domains in the assessments, it was found that there was an increase in the percentage of items in the knowing domain (28% to 55%) and a decrease in the percentage of items in the other two domains between the OKS 2007 and SBS 2011. Relative to PISA, TIMSS is more of a factual and knowing-based assessment (Kloosterman, Roach, & Pérez, in press) and thus emphasis on the knowing domain in the Turkish assessments could also have impacted the strong gains of Turkish students on TIMSS.
References
Kloosterman, P., Roach, M., & Pérez, A. (in press). International assessment results. In P. Kloosterman, D. Mohr,
& C. Walcott (Eds), What mathematics do students know and how is that changing? Evidence from the National Assessment of Educational Progress. Charlotte, NC: Information Age.
Martin, M. O., Mullis, I. V., & Foy, P. (2008). TIMSS 2007 international mathematics report: Findings from IEA's Trends in International Mathematics and Science Study at the Fourth and Eighth Grades. Chestnut Hill, MA:
TIMSS & PIRLS International Study Center, Boston College.
Mullis, I. S., Martin, M. O., Foy, P., Arora, A. (2012). TIMSS 2011 International Results in Mathematics. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.
Bartell,!T.!G.,!Bieda,!K.!N.,!Putnam,!R.!T.,!Bradfield,!K.,!&!Dominguez,!H.!(Eds.).!(2015).!Proceedings+of+the+37th+
RE-EXAMINING THE VALIDITY OF WORD PROBLEM TAXONOMIES IN THE COMMON CORE ERA
Robert C. Schoen Florida State University
Zachary Champagne Florida State University [email protected]
Ian Whitacre Florida State University
[email protected] Keywords: Curriculum; Curriculum Analysis; Early Childhood Education; Standards
Background and Research Questions
Through studies conducted in the latter half of the twentieth century across many different languages and cultural norms, the semantic structure of word problems has been found to influence problem difficulty for young children, and word problems have been organized into taxonomies based on semantic structure and difficulty (Fuson, 1992; Verschaffel, Greer, & DeCorte, 2007). In the current era, the Common Core State Standards for Mathematics (CCSSI, 2010) explicitly incorporate the full range of word problems found in the established taxonomies.
This change in the standards presents an interesting opportunity to explore questions of whether there is a fundamental way that children think about word problem types that makes some problem types inherently more difficult than others, or whether the differences in difficulty are manufactured by relative amounts of exposure and opportunities to learn.
Using data generated from interviews and written assessments involving more than 2,000
students during the 2013–2014 school year, our investigation is driven by the following two research questions:
• With respect to the semantic structure of word problems, do the textbooks used in classrooms of students in our sample afford different opportunities to learn than the textbooks used in classrooms of students in the samples of students in the 1970s and 1980s?
• Do the previously identified patterns in relative problem difficulty based upon the semantic structure of word problems continue to be valid for first grade students?
We consider this study to be an important preliminary investigation into a larger question concerning the influence of semantic structure and opportunities to learn on the relative difficulty of word problems for young learners of mathematics.
Acknowledgements
The research reported here was supported by funding from the Institute of Education Sciences, U.S. Department of Education, through Grant # R305A120781 to Florida State University. The opinions expressed here are those of the authors and do not represent views of the Institute or the U.S. Department of Education.
References
Common Core State Standards Initiative (CCSSI) (2010). “Common Core State Standards for Mathematics”
Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. Retrieved from http://corestandards.org
Fuson, K. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.),Handbook of research on mathematics teaching and learning. Reston, VA: National Council of Teachers of Mathematics.
Verschaffel, L., Greer, B., & DeCorte, E. (2007) Whole numbers concepts and operations. In F.K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning. Reston, VA: National Council of Teachers of Mathematics.
TEACHERS’ PERCEPTIONS OF MATHEMATICS STANDARDS: A COMPARISON OF PSSM AND CCSSM
Jonathan Thomas Northern Kentucky University
Sarah Kasten
Northern Kentucky University [email protected]
Christa Jackson Iowa State University [email protected] Keywords: Standards; Teacher Knowledge; Teacher Beliefs; Middle School Education
Introduction and Method
In this study, we engaged middle grades mathematics teachers in a comparative study of national and quasi-national standards documents, the CCSSM and the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (PSSM). Findings indicate tensions exist between what teachers’ desire in standards documents and what standards authors provide. Nine middle grades teachers who were part of an existing professional development community that focused on increasing mathematical knowledge for teaching, participated in a focus group that reviewed and compared the PSSM and CCSSM. The focus group was conducted near the end of the academic year in which CCSSM was adopted by the state. The teachers were randomly divided into two focus groups, and were presented with three blinded sets of parallel excerpts from each standards document that represented similar content and foci. The excerpts included a topic from the algebra and geometry content standards, and the Problem Solving Process Standard from PSSM and the Standard for Mathematical Practice (SMP)Make Sense of Problems and Persevere in Solving Them from CCSSM. During the focus groups, the teachers were asked to compare the relative clarity and usefulness of the blinded excerpts. The discussions were video recorded and transcribed for inductive analysis. Open coding (Ryan & Bernard, 2000) was used to identify themes. All discrepancies in coding were discussed until consensus was reached. The data were then analyzed for similarities and differences (Charmaz, 2006) using a constant comparative method.
Findings and Implications
Based on teacher responses, the following findings were organized by three broad themes: 1) formatting, 2) implementation of standards, and 3) characteristics of ideal standards. The documents examined by the teachers in this study represent the intended curriculum; however, teachers’
indicated expectations of support that are traditionally found in a written curriculum (Reys & Reys, 2010). The ideas expressed by teachers in these groups suggest that practitioner consensus regarding features of standards has yet to be conceived which manifests as tension between desired
characteristics that, at times, appear in conflict with one another.
References
Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. Thousand Oaks, CA: Sage Publications.
Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for Mathematics.
Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20 Standards.pdf
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Reys, B.J., & Reys, R.E. (2010). Preface. In Mathematics curriculum: Issues, trends, and future directions (pp. ix- xiv). Reston, VA: National Council of Teachers of Mathematics.
Ryan, G. W., & Bernard, H. R. (2000). Data management and analyses methods. In N. K. Denzin & Y. S. Lincoln (Eds.), Handbook of qualitative research, 2nd Edition (pp. 769-802). London: Sage.
Bartell,!T.!G.,!Bieda,!K.!N.,!Putnam,!R.!T.,!Bradfield,!K.,!&!Dominguez,!H.!(Eds.).!(2015).!Proceedings+of+the+37th+
THE EFFECTS OF VISUAL REPRESENTATIONS AND INTEREST-BASED PERSONALIZATION ON SOLVING MATHEMATICS STORY PROBLEMS
Candace Walkington Southern Methodist University
Jennifer Cooper Wesleyan University [email protected] Mitchell J. Nathan
University of Wisconsin-Madison [email protected]
Martha W. Alibali
University of Wisconsin-Madison [email protected] Keywords: Curriculum; Learning Theory; Middle School Education
This study examined how (1) visual representations including illustrations and diagrams and (2) personalization to students’ out-of-school interests, affects 7th grade students’ performance on and perceptions of math story problems. Considerable research shows that learners benefit from visual representations, and effectively using visual representations is one way in which to improve problem solving. Research also suggests that even shallow attempts to personalize problem contexts to student interests in areas like sports or shopping can promote learning and interest. In prior research we found no effect for personalization or decorative illustrations for 7th graders solving percent problems, but diagrams with mathematical information were associated with higher performance.
Here, we seek to replicate the results for a new content area and examine student perceptions of easiness and interestingness for the problems they solve.
Participants were 179 7th grade students attending a suburban middle school; they solved a worksheet containing 8 story problems on which diagrams, illustrations, or personalization were manipulated. Students were significantly more likely to get a problem correct if it had a diagram alone than if it had no visuals (Odds = 1.66, p = 0.014). Students were not more likely to get a problem correct if it contained an illustration (p = 0.225) or a diagram with an illustration (p = 0.378) compared to no visuals, and students were not more likely to correctly solve personalized problems than non-personalized problems (p = 0.526). In the models predicting students’ ratings of easiness (1- 5 scale), problems with a diagram alone were rated as significantly easier compared to: no visuals (B
= 0.17, SE = 0.07, p = 0.013), illustration alone (B = 0.19, SE = 0.07, p = 0.006), and a diagram with an illustration (B = 0.20, SE = 0.07, p = 0.006). Problems with an illustration were rated as
significantly harder than problems without an illustration (B = 0.11, SE = 0.05, p = 0.029).
Personalization was not related to easiness (p = 0.53). In the models predicting students’ ratings of interestingness (1-5 scale), problems with a diagram alone were rated significantly less interesting compared to: no visuals (B = -0.16, SE = 0.07, p = 0.017), illustration alone (B = -0.20, SE = 0.07, p
= 0.002), and a diagram with an illustration (B = -0.27, SE = 0.07, p < .001). Personalized problems were significantly more interesting than non-personalized problems (B = 0.46, SE = 0.05, p< .001).
In both this study and our prior study, performance was highest on problems that had
personalization, a diagram, and no illustration. The combination of personalization and diagrams may be ideal to promote engagement while scaffolding performance for struggling learners. We found that diagrams improved performance and made problems seem easier but students found them boring. Personalization did not affect performance or easiness, but made problems more interesting.
Illustrations did not impact performance, but students felt they made problems harder. This study provides guidance to inform curriculum design in math education.
DEVELOPING EFFECTIVE CURRICULUM MATERIALS FOR PROFESSIONAL DEVELOPMENT
Zhaoyun Wang University of Toronto [email protected]
Douglas McDougall University at Toronto [email protected] Keywords: Teacher Education-Inservice; Curriculum
This study examined the effectiveness of the curriculum materials for a series of grade 8 mathematics teacher workshops. In recent decades, educational researchers have tried to find effective ways to improve teachers’ professional knowledge (Desimone, 2009). Educational “field has acknowledged a need for more empirically valid methods of studying professional development”
(p. 181). The development of computer information communication technology (ICT) provides an informal and integral tool for teaching and learning.
The objectives of the materials were to integrate technology, mathematics content, pedagogical content knowledge and teaching resources in a collaborative environment of learning. The core features in this grade 8 mathematics program concentrate on Ten Dimensions (McDougall, 2004) for teachers’ professional development. The Ten Dimensions are: (1) program scope and planning, (2) meeting individual needs, (3) learning environment, (4) student tasks, (5) constructing knowledge, (6) communicating with parents, (7) manipulatives and technology, (8) students’ mathematical communication, (9) assessment, and (10) teacher’s attitude towards and comfort with mathematics.
The research questions are: (1) how do curriculum materials meet the needs of participants? And (2) how do workshops in mathematics content, use of technology and pedagogical strategies affect teacher’s attitudes and beliefs about mathematics teaching?
The participants were 29 middle school teachers and 8 principals from an urban school district.
The teachers took part in four full day workshops and were provided teaching materials through a two-way website. The participants selected five dimensions as core objectives for the workshops.
The curricula materials and delivery for this teacher program identified a few key factors: teachers’
needs based on former research, their feedback after each workshop, curriculum content selection, style of content delivery, and when and how to distribute workshops. The participants were interviewed individually and completed two surveys at the beginning and end of project in the academic year. This survey is a Likert-like six scale with 20 questions (McDougall, 2004). A paired T-test was employed to test significance for each of 20 questions to see the effects. Finally, the quantitative results were confirmed by the qualitative study.
The results showed that the tailored curriculum material designed by focusing on the Ten Dimensions framework is an effective approach for in-service teacher programs. The participants increased their knowledge in their targeted objectives of this program. The participants changed their beliefs about their scope and planning skills, their ability to design interesting students’ tasks, their ability to communicate with parents and peer teachers, and the effective use of manipulatives and technology in classes. The participants were satisfied with the materials of mathematics content, use of technology for teaching and communication, and assessment activities conducted in the program.
The findings of this program for design of curriculum content can be used in the similar educational contexts.
References
Desimone, L. (2009). Improving Impact Studies of Teachers’ Professional Development: Toward Better Conceptualizations and Measures. Educational Researcher, 38(3), 181–199.
McDougall, D. (2004). School Mathematics Improvement Leadership Handbook. Thomson Nelson.
Bartell,!T.!G.,!Bieda,!K.!N.,!Putnam,!R.!T.,!Bradfield,!K.,!&!Dominguez,!H.!(Eds.).!(2015).!Proceedings+of+the+37th+