Teacher Outcomes

Transition to Algebra: A Habits of Mind Approach

This research and development project provides resources for ninth-grade mathematics students and teachers by developing, piloting, and field-testing intervention modules designed as supplementary materials for Algebra 1 classes (e.g., double-period algebra). Rather than developing isolated skills and reviewing particular topics, these materials aim to foster the development of mathematical habits of mind—in particular, the algebraic habit of abstracting from calculations, a key unifying idea in the transition from arithmetic to algebra.

Project Email: 
Award Number: 
0917958
Funding Period: 
Tue, 09/01/2009 to Sat, 08/31/2013
Project Evaluator: 
Jim Hammerman, TERC
Full Description: 

Transition to Algebra, A Habits of Mind Approach, is aimed at very quickly giving students the mathematical knowledge, skill, and confidence to succeed in algebra, and showing them that they can be good at things they believed they couldn't do. The students were all smart and intrepid when they were six. Even now, they are better and more persevering than we are about figuring out their smartphones and video games. Transition to Algebra aims to tap that smart, intrepid, persevering spirit of puzzling things out and making sense of them by presenting mathematics based in common sense, not arbitrary rules.

This project is developing a collection of modules introducing key ideas of algebra in ways that complement the core curriculum when a school is offering double period algebra. The key habit of mind being developed is abstracting from calculation. Modules deal with the transition from arithmetic to algebra, rational numbers, expressions/equations/word problems, graphs and equations, geometry of algebra, and proportional reasoning. The target population is students in urban high poverty schools with a significant ELL sector.

Our hypothesis is that instructional materials focused on developing conceptual understanding and mathematical habits of mind can complement traditional skill-focused algebra instruction in ways that are engaging to students. Furthermore, they argue that using materials with such meta-cognitive aims will actually strengthen the learning of core algebraic concepts and skills.

The supplementary algebra modules are being developed by a form of design research. Concurrent with development and field test of the student and teacher materials, the investigators are addressing four research questions. The first two questions are focused on the effects of the intervention in developing student habits of mind and in improving their competence and confidence in algebra. The other two address the feasibility of implementing the new approach to double-period algebra in a variety of school settings. A small-scale quasi-experimental field test is being used to give preliminary estimates of the effectiveness of the instructional materials and the implementation guidelines. The core purpose of these research activities is to inform development and refinement of the student and teacher instructional materials.

Products of this development effort will be a valuable resource to schools as they devise strategies for helping all students master the essentials of elementary algebra.

Supporting Staff Developers in the Implementation of Professional Development Programs to Improve Mathematics Education for Students with Disabilities

This project is (1) conducting a qualitative study on the way facilitators use Math for All (MFA), an NSF-supported set of professional development materials for teachers who teach elementary school students with disabilities; (2) developing resources based on that study for teacher leaders and other facilitators of professional development; and (3) conducting fieldtests of the resources to examine their usefulness and impact.

Award Number: 
0822313
Funding Period: 
Mon, 09/01/2008 to Fri, 08/31/2012
Project Evaluator: 
Teresa Duncan
Full Description: 

 

Target Inquiry: Investigating the Teacher and Student Effects of a New Model in Chemistry Teacher Professional Development

This five-year research project has as its central aim the testing of the Target Inquiry (TI) model of teacher professional development with secondary school chemistry teachers. This model emphasizes the importance of the inquiry process in teaching and learning science by combining a research experience for teachers (RET) with curriculum adaptation and action research.

Partner Organization(s): 
Award Number: 
0553215
Funding Period: 
Mon, 05/01/2006 to Sat, 04/30/2011
Full Description: 

Inquiry is the foundation of teaching and learning and is therefore at the center of the TI model.  The features of the TI model are designed to encourage and improve inquiry instruction by impacting teachers’ beliefs and attitudes, and content and pedagogical knowledge, as well as providing adequate resources and materials.  The model integrates the core experiences (research experience for teachers (RET), materials adaptation, action research) with the central characteristics of high-quality PD programs (duration, cohort participation, active learning, coherence, and content-focus (Garet, et al., 2001)) in alignment with the National Science Education Professional Development Standards (NRC, 1996) (see TI model on website).

Although many teachers associate inquiry with research scientists, the underlying habits of mind by which one actively acquires new knowledge are the same for a scientist in a research laboratory, a student in a science classroom, or a teacher assessing student understanding (Llewellyn, 2005; AAAS, 1993).  The RET will allow teachers to further develop habits of mind central to inquiry such as curiosity, persistence, reflection, skepticism, and creativity while gaining firsthand experience in how chemistry research is conducted.  However, research has shown that affecting instructional change requires clear connections to classroom practices (Gess-Newsome, 2001), and many teachers have difficulty translating the laboratory research experience to classroom instruction that promotes inquiry habits of mind.  Thus, the other core experiences and supporting features of TI are designed to build upon the RET, facilitating connections between the research laboratory and classroom practices, so that teachers can effectively engage their students in authentic inquiry activities. 

At GVSU, the TI model has been translated into seven graduate chemistry education courses to be taken over three years, with a majority of work to be carried out over three summers.  A five year study of the program, consisting of data from two cohorts shows that teachers beliefs about science inquiry become more aligned with those of practicing scientists following the RET experience; both the RET and materials adaptation experiences are required for significant gains in reformed teaching practices as measured by the RTOP instrument; teachers feel they have developed the skills to help them continue to reform their teaching practices; teachers believe that the use of inquiry instruction engages more of their students and results in better student confidence and retention; and student outcome measures show overall improvement in student content gains as teachers progress through the program.

Investigating the Effect of Professional Development, Mathematical Knowledge for Teaching, and Instruction on Student Outcomes

To meet College and Career-Ready standards in mathematics, classroom instruction must change dramatically.  As in past reform efforts, many look to professional development as a major force to propel this transformation, yet not enough is known about mathematics professional development programs that operate at scale in the United States. In this project, we evaluated one such program.

Lead Organization(s): 
Award Number: 
0918383
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2012
Full Description: 

To meet College and Career-Ready standards in mathematics, classroom instruction must change dramatically.  As in past reform efforts, many look to professional development as a major force to propel this transformation, yet not enough is known about mathematics professional development programs that operate at scale in the United States. In this project, we evaluated one such program by randomly assigning 105 teachers to either an “as is” control group or to receive professional development designed to a) improve mathematical knowledge for teaching and b) help teachers revise their instruction to be more cognitively demanding and student-centered. We found positive impacts on teachers’ mathematical knowledge for teaching, but no effects on teaching or student outcomes, suggesting that a modest increment in mathematical knowledge may not by itself be sufficient to improve instruction or student outcomes.

Helping Teachers to Use and Students To Learn From Contrasting Examples: A Scale-up Study in Algebra I

Several small-scale experimental classroom studies Star and Rittle-Johnson demonstrate the value of comparison in mathematics learning: Students who learned by comparing and contrasting alternative solution methods made greater gains in conceptual knowledge, procedural knowledge, and flexibility than those who studied the same solution methods one at a time. This study will extend that prior work by developing, piloting, and then evaluating the impact of comparison on students' learning of mathematics in a full-year algebra course.

Lead Organization(s): 
Award Number: 
0814571
Funding Period: 
Mon, 09/15/2008 to Tue, 08/31/2010

Pages

Subscribe to Teacher Outcomes