# A Short Overview of The Poincaré Institute Impact on Teaching and Learning

**Please go to the end of this report for a list of downloadable published papers.**

The Poincaré Institute courses started in 2011 and have served, across four cohorts of teachers, over 240 educators and their students in ten partner school districts across New England. Research reveals the positive impact of the program on classroom teaching and learning, and on student results on standardized tests.

## Teaching and Student Engagement

External evaluation by the Intercultural Center for Research in Education (INCRE) documented changes in instruction over time using the Reformed Teaching Observation Protocol (RTOP, Arizona State University) and the INCRE analytical observation tool.

RTOP mean scores for cohort 1 (see Figure 1) show that, after participating in the three Poincaré Institute courses, teachers significantly used more representations to explore mathematical topics and were more effective in their math classes, leading to more engagement from students. Also, students in classes of teachers who had taken Poincaré courses significantly more often used multiple representations, solved more complex problems, explained their ideas, and connected math to real-world phenomena. Observations of a sub-sample of teachers showed that these gains continued six months and a year after they had completed the program.

Figure 1: Mean RTOP scores for the first cohort at beginning and end of courses, and for a sub-group of 23 teachers, six months and a year later (source: INCRE, External Evaluation).

## Improved Test Scores

The Massachusetts Comprehensive Assessment System test, MCAS, is the standard for assessing student proficiency throughout the state of Massachusetts. We compared MCAS results in terms of percentage of proficient and advanced students from grades 5 to 8, in each of the five Massachusetts partner school districts in the first three cohorts, to all state results, and to results of students from matched districts.

The criteria for matched school districts were number of students, demographic variables, and MCAS performance for the school year 2010-2011. Each Poincaré District was compared to the average of five matched districts.

When the courses were first offered (spring of 2011), the proficiency in mathematics (% students at the Proficient and Advanced levels) according to MCAS results was below the levels for the state of Massachusetts, but very close to the matched districts (see Figure 2).

Figure 2: Percent of students at the MCAS test Advanced and Proficient levels.

Three years later, the situation had significantly changed. The Poincaré districts had narrowed the performance gap with regard to the state of Massachusetts from 7.1 to 4.5 percentage points. Furthermore, the students in the Poincaré districts had surpassed the matched districts by 5.1 percentage points. Changes for students in Poincaré districts were significantly higher than those in matched districts after the teachers had participated in the Poincaré program.

Note that these results underestimate the impact of the program on students, given that Poincaré district results included all of the students, even if their teachers had not taken part in the Poincaré program. In fact, the Poincaré school districts varied in the percentage of teachers who had taken the three Poincaré courses. This allowed investigation of whether performance differences between Poincaré and matched districts varied as a function of the districts’ percentage of teachers who had completed the Poincaré program.

This analysis showed that the greater the percentage of Poincaré teachers in a district, the greater the advantage in MCAS scores of Poincaré districts over matched districts (see Figure 3). This advantage was significantly correlated with the number of teachers who had taken the courses (Spearman’s r =.54, p=.007). This provides additional evidence that performance differences between Poincaré districts and matched districts was due to participation in the Poincaré courses.

Figure 3: Target districts’ advantage in 2014 over similar districts, as a function of percentage of teachers who completed the program. Each point represents one of four grade levels in five different districts (two points are hidden by other points).

The preponderance of data points in quadrant I of Figure 3 highlights the advantage of Poincaré districts. The regression line shows that the advantage was, overall, directly proportional to the percentage of teachers in each grade level and in each district who had completed the three Poincaré courses.

## In Summary

Classroom observations by the external evaluator showed substantial and significant improvement in classroom practices.

The positive impact of the program was also found across grades 5 to 8 on a state mandated assessment of proficiency on all content areas of the middle school mathematics curriculum.

## Published Papers

* The documents distributed here have been provided as a means to ensure timely dissemination of scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author’s copyright. These works may not be reposted without the explicit permission of the copyright holder.*

### 2017

Liu, C. & Carraher, D. (2017). Teachers’ Interpretations of a Linear Equation Regarding Physical Quantities. NCTM Research Conference, San Antonio, TX, April 3-5.

Liu, C., Schliemann, A.D., Carraher, D.W. & Teixidor-i-Bigas, M. (2017). How Teachers Interpret Equations and Graphs in terms of Situations. NCTM Research Conference, San Antonio, TX, April 3-5.

Schliemann, A.D., Liu, C. Carraher,D.W., & Teixidor-i-Bigas (2017). Understanding Operations on Quantities. NCTM Research Conference, San Antonio, TX, April 3-5.

### 2016

Caddle, M., Bautista, A., Brizuela, B. M., & Sharpe, S. (2016). Evaluating mathematics teachers’ professional development motivations and needs. *Journal of Research in Mathematics Education/Revista de Investigación en Didáctica de las Matemáticas* (REDIMAT), 5(2), 112-134. doi:10.4471/redimat.2016.2093

Hotomski, M. & Schliemann, A.D. (2016). Teacher Development and the Achievement Gap.

Liu, C., Teixidor-i-Bigas, M., & Schliemann, A.D. (2016). Teachers’ Quantitative Reasoning When Using Graphs.

Schliemann, A.D., Carraher, D.W., & Teixidor-i-Bigas, M (2016). Teacher Development and Student Learning. Invited Presentation. 13th International Congress on Mathematical Education. Hamburg, Germany, July, 25-30.

Sharpe, S., & Schliemann, A. (in press). Teacher Development and 7th Graders’ Learning of Algebra. *The Mathematics Enthusiast, 14(1)*.

Wilkerson-Jerde, M., Bautista, A., Tobin, R., Brizuela, B. M., & Cao, Y. (2016). More than Meets the Eye: Patterns and Shifts in Middle School Mathematics Teachers’ Descriptions of Models. *Journal of Mathematics Teacher Education*, *19(2-3)*.

### 2015

Bautista, A., Cañadas, M. C., Brizuela, B. M., & Schliemann, A. D. (2015). Examining How Teachers Use Graphs to Teach Mathematics in a Professional Development Program. *Journal of Education and Training Studies, 3(2)*, 91-106

Sharpe, S., & Schliemann, A. (2015). Algebra Notation for Functions in Grades 5 through 9. In Bartell, T. G., Bieda, K. N., Putnam, R. T., Bradfield, K., & Dominguez, H. (Eds.). (2015). *Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education*. East Lansing, MI: Michigan State University.

### 2014

Bautista, A., Brizuela, B. M., Glennie, C., & Caddle, M. (2014). Mathematics teachers attending and responding to students’ thinking: Diverse paths across diverse assignments. *International Journal for Mathematics Teaching and Learning*. July Volume (28 pages). Retrieved from http://www.cimt.plymouth.ac.uk/journal/bautista.pdf

Bautista, A., Wilkerson-Jerde, M. H., Tobin, R. G., & Brizuela, B. M. (2014). Mathematics teachers’ ideas about mathematical models: A diverse landscape. *PNA, 9(1)*, 1-28.

Sharpe, S., & Schliemann, A. (2014). The Impact of a Teacher Development Program on 7th Graders’ Learning of Algebra. In Nicol, C., Oesterle, S., Liljedahl, P., & Allan, D. (Eds.) *Proceedings of the Joint Meeting 5 – 161 of PME 38 and PME-NA 36,Vol. 5*, pp. 161-168. Vancouver, Canada: PME.

### 2013

Bautista, A., Brizuela, B. M., & Ko, Y.-Y. (2013). Middle school mathematics teachers’ implicit conceptions about multiple representations for functions. In D. Halkias (Ed.), *Psychology and the Search for Certainty in Everyday Life* (pp. 31-48). Athens: ATINER.

Bautista, A., Wilkerson-Jerde, M. H., Tobin, R., & Brizuela, B. M. (2013). Diversity In Middle School Mathematics Teachers’ Ideas About Mathematical Models: The Role Of Educational Background. In B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds.), *Proceedings of the 8th Congress of the European Society for Research in Mathematics Education* [CERME] (pp. 960-969). Ankara, Turkey: Middle East Technical University.

Teixidor-i-Bigas, M., Carraher, D. W. & Schliemann, A. D. (2013). Integrating Disciplinary Perspectives: The Poincaré Institute for Mathematics Education. *The Mathematics Enthusiast,* 10(3).

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