Spatial Temporal Mathematics at Scale

1. Spatial Temporal Mathematics at Scale An Innovative and Fully Developed Paradigm to Boost Math Achievement Among All Learners

2. Traditional Instruction in Mathematics • Traditional math education relies heavily on symbolic notation in the form of numerals, operations, and equations, as well as on technical terminology.

3. A Spatial-Temporal Approach • Instead, mathematical patterns can be represented as images or transformations of images. • Pattern-finding, experienced as mental imagery, is a natural ability of the human mind and its underlying neural circuitry.

4. An Exciting Possibility • Spatial-temporal (ST) reasoning may be a highly intuitive way of learning fundamental math concepts. • ST-based mathematics offers the potential for effective learning among students who experience frustration with traditional ways of teaching math. • ST Math may be a gateway to far larger numbers of students gaining high levels of mathematical proficiency, opening a pipeline of future scientists, engineers, and medical professionals.

5. ST Math Software • Designed to develop deep intuitive understandings of fundamental mathematical concepts: • Fractions, proportions, symmetries, and functions • Video game metaphor • Universally motivating • Games With a Purpose (GWAP) • Activities challenge children to apply their spatial-temporal skills to solve problems

6. Prior Research Results • ST Math has produced substantial gains in mathematics achievement in comparison to control group students. • Learning advantages tend to grow each year. • Effects have been found on standardized tests of broad mathematics achievement, not only on ST concepts. Martinez, M. E., Peterson, M., Bodner, M. Coulson, A., Vuong, S., Hu, W., Earl, T., & Shaw G. L. (2008). Music training and mathematics achievement: A multiyear iterative project designed to enhance students’ learning. In A. E. Kelly, R. A. Lesh, & J. Y. Baek (Eds.), Handbook of design research methods in education: Innovations in science, technology, engineering, and mathematics learning and teaching (pp. 396-409). New York: Routledge.

7. Magnitude of Impact • The impact of the program on standardized test scores has been as high as two sigma • Gains translated into standard deviation equivalents • Two sigma is historically considered to be the maximum effect achievable by an educational intervention

8. Findings From Previous Research • Our research findings imply that a large segment of students, perhaps most, can benefit from an approach to learning math that uses spatial-temporal reasoning • Spatial-temporal reasoning and representations might hold special promise for English language learners • By de-emphasizing mathematical terms and explanations expressed in English

9. But Open Questions Remain • Causality: Will ST Math produce learning gains when subjected to a rigorous evaluation using a true experimental design? • With treatment and control groups • With random assignment • Subgroups: Will particular subgroups of students enjoy heightened benefits from the ST approach? • English language learners • Students who initially show low confidence or aptitude • Durability: Will ST Math convey benefits that last for years beyond the ST experience?

10. A New Project: ST Math At Scale • An Innovative and Fully Developed Paradigm to Boost Math Achievement Among All Learners • Funding • US Department of Education, Institute of Education Sciences (IES) • Four years (2009-2013) • Participating Schools • Approximately 50 elementary schools in Orange County • Allied with the Orange County Math Initiative

11. The Collaborating Institutions

12. Study Design • Schools Are Randomly Assigned (Gold Std.) • “A” Schools initially implement at grades 2 and 3 • And “B” Schools are controls at these grades • “B” Schools initially implement at grades 4 and 5 • And “A” Schools are controls at these grades • In this way, all schools receive ST Math, but initially only at particular grade levels • Schools must be willing to be assigned to either “A” or “B”

13. Measurement Tools • Standardized Tests of Math Achievement • Attitude Scales: Students and Teachers • Spatial and Mathematical Ability • Use of Games • Online Data Feedback System • Keystroke/clickstream for every student • On-Site Fidelity of Implementation • Professional Development • Teacher and Student Surveys

14. What To Expect • Students: Individualized Testing • Every school (52 in all) • Most 2nd, 3rd, 4th, and 5th grade classrooms • As many classrooms as possible • No more than 4 students per classroom • About 20 minutes per student • Teachers • Surveys, focus groups, observations • Plans still in formation

15. Research Question 1:Superior Learning of Mathematics • Does ST Math Improve Student Achievement in Mathematics? • Standardized test scores are the most credible evidence of broad impacts on learning • Favored by Mind Research Institute for ten years • Primary instrument: California Standards Test • In Addition, Conceptual Understanding and Mathematical Problem Solving • Woodcock-Johnson subscales

16. Research Question 2:Effects of Multi-Year Participation • Does participation in ST Math for multiple years offer enhanced benefit to achievement in mathematics? • Varying participation: 1, 2, or 3 years

17. Research Question 3:Interactions With Student Characteristics • Do learning gains associated with ST Math interact with student background? • Gender • English language learners • Special needs • Economically disadvantaged • Prior mathematical proficiency • Initial aptitude in spatial reasoning

18. Research Question 4:What Implementation Factors Moderate Gains? • Time Spent on ST Math • Teachers’ Use of Diagnostic Information • Administrative Support • Teacher Behavior • Pedagogical Integration • Linking software activities to traditional math curriculum

19. Research Question 5:Do Attitudes Toward Math Moderate Gains? • Teachers’ Attitudes Toward Mathematics • Do teachers’ attitudes toward math change? • Students’ Attitudes Toward Mathematics • Do students’ attitudes toward math change?

20. Research Question 6:Does Professional Development Moderate Gains? • What is the influence of teacher professional development on ST software and curricular integration? • If professional development moderates gains, then does the influence vary by the type and amount of training?

21. A New Paradigm • Prior research shows that a spatial-temporal (ST) approach to mathematics learning can open the gateways to STEM learning • Now it’s time to put this exciting possibility to a rigorous test • To understand the nature and magnitude of causal effects through a large-scale randomized experiment • To understand whether ST Math offers particular advantages to specific subgroups of learners • To understand what implementation factors moderate the effects of ST math on student learning

22. Addressing Critical Needs • The U.S. faces a crucial need for elevated achievement in math and, more broadly, STEM fields • To close the achievement gap • And to increase the potential pool of highly-trained scientists and engineers • Resulting in heightened international competitiveness • These are longstanding valued goals • Now we need fresh thinking to achieve them