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Mathematics Problem Solving

Mathematics has a language of its own based on the number system, but it is also based on students begin able to see patterns in number, and in data, and then solve problems that are based in real life contexts. The research in this section is anchored by the research by a middle school teacher (and Christa McAuliff scholar) who systematically used Thinking Maps with her underachieving students. In addition, Kathy Ernst, a national leader in mathematics instruction describes in detail and shows how she uses Thinking Maps to coach and mentor math teachers. We strongly suggest you look into her book co-written with Sarah Ryan: Success from the Start: Your First Years Teaching Elementary Mathematics” published by the National Council of Teachers of Mathematics.

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Student Successes With Thinking Maps®
David Hyerle and Larry Alper coeditors Corwin Press, Second Edition, January 2011, Thousand Oaks, California

Chapter 8: Meeting the Challenge of High Stakes Testing in Middle School Mathematics
Janie B. MacIntyre, M.Ed.

Thinking Maps allow you to see where you have made your mistake, and how to show your math in words that make sense’ - Student

The statistics indicate considerable growth in mathematical achievement, so how and why does applying thinking maps in math instruction improve math ability as measured on these tests?

Key sections from the chapter The Challenge of High Stakes Testing in Middle School Mathematics with excerpts above include:

  • Facing Myself and My Students

  • Beyond Intuition

  • Results: Gains in Developmental Growth

  • Thinking Maps: A Bridge to Success

  • Beyond Test Scores



Janie B. MacIntyre, M.Ed. is a middle school teacher, researcher, and educational consultant who was named as a USA Today Teacher Team member and a Christa McAuliffe Scholar.

An Evaluation of Students’ Perception of Thinking Maps® in the Middle School Mathematics Classroom
By Heather A. Mors, Kennesaw State University, Atlanta, United States. 2015

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The findings of this research indicate that students are using Thinking Maps® for knowledge acquisition, namely in the form of note taking.  In addition, Thinking Maps® provide a bridge between prior knowledge and targeted knowledge by breaking problems down into parts that the students can understand.  Finally, students report that Thinking Maps® helped them answer complex math problems by breaking the problems into smaller parts and showing the steps to solve problems. The findings of this research should be used to guide teacher practices.  Regardless of their feelings, most of the students perceived the benefits of using Thinking Maps®.  Students recognized that Thinking Maps® helped them solve math problems, break problems down and make problems easier to understand.  The data from the survey is consistent with the interview data with 54.4% of students agreeing or strongly agreeing that Thinking Maps® is beneficial for solving math problems and 64.9% of the students agreeing or strongly agreeing that Thinking Maps® are beneficial for answering critical thinking questions.  Additionally, students were very interested in the electronic platform of Thinking Maps that allows the students to focus less on the map construction. 

The Relationship Between Thinking Maps® and Florida Comprehensive Assesment Test® Reading and Mathematics Scores in Two Urban Middle Schools
By Ana Delgado Diaz, University of Central Florida, Orlando, United States. 2010

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Statistical analysis did not result in significant differences in the use of Thinking Maps® as measured by FCAT but there were percentage differences that may indicate educational significance for Hispanic, economically disadvantaged and English language learners in FCAT Reading and for white, black and students with disabilities in FCAT Mathematics. Results of this study should not discourage the implementation of Thinking Maps® instruction as visual tools for learning. FCAT may not be an appropriate instrument to measure if an instructional visual tool such as Thinking Maps® makes a difference in student achievement. A better measurement tool would be for teachers to develop rubrics that can be used to assess student generated Thinking Maps® or use rubrics provided in the Thinking Maps ®: A Language for Learning (Hyerle & Yeager, 2007) training manual. 

Student Successes With Thinking Maps®
David Hyerle and Larry Alper coeditors Corwin Press, Second Edition, January 2011, Thousand Oaks, California

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Chapter 17: Mentoring Mathematics Teaching and Learning
Kathy Ernst, M.S.

“So many people have come into my classroom with vague advice and comments that have just made things worse. This is the first time anyone’s given me concrete suggestions about what I can do. This has been really helpful—thank you.”
Teacher (after Kathy and colleague used the Flow and Multi-Flow Maps in post-conference supervision conversation)

Key sections from the chapter Mentoring Mathematics Teaching and Learning with excerpts above include:

  • Tools For Focused Observation and Reflection

  • Tools For Explicit Coaching In Model Lessons

  • Part 1: Lesson Planning/Orientation

  • Part 2: Lesson Observation

  • Part 3 Reflective Conversation

  • Imagining the Possibilities


Kathy Ernst, M.S. has spent 30 years teaching children and teachers in elementary and middle schools and has served on the faculty of the Leadership in Mathematics Education Program at Bank Street College of Education. She has facilitated the implementation of standards-based mathematics curricula in schools, working with teachers to support children’s construction of mathematical ideas.

2004 Final Report Thinking Maps North Carolina School Study
By Nancy Cook Smith, Ph.D., North Carolina, United States, 2005

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This study compares the gains in standardized test scores made by North Carolina schools that adopted Thinking Maps after 1997 and before 2002 and those gains made by comparable schools that did not adopt the intervention. North Carolina state assessment data from 1997 to 2002 were evaluated to ascertain the percentage of students at four performance levels for each school. Schools that adopted Thinking Maps showed statistically significant gains in students in the proficient performance level and parallel significant drops in the percent of students performing at the lowest performance level. The two groups of schools were comparable in geographic location and percent of students at the lowest socio-economic level (eligible for free or reduced lunch).

Thinking About Learning
By Jacqueline Grennon Brooks, Hofstra University, New York, United States.

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It is widely recog- nized that what students learn in school is rarely generalized into applications, theories and principles subject to further investigation. Therefore, deep understanding is often absent and, with it, a basis for reasoning and explanation (Schoenfeld, 1988). In order to further educational practice targeted at promoting pattern recognition and also generate a research approach that studies learners’ pattern recognition and conceptual change, the Thinking Maps® language (Hyerle, 1996) is a useful tool.

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