## Barbara Kinach

## Biography

Dr. Kinach is a mathematics teacher educator whose research centers on the tasks of mathematics teacher preparation and their impact on pre-service teachers’ mathematical understanding and teaching practice. Through design research, she studies the role of physical manipulatives and other visual representations in transforming prospective teachers' procedural views of mathematics and preferences for direct instruction. Known for her content-specific pedagogical innnovations, her cognitive strategy (IACTS) develops preservice teachers' pedagogical content knowledge through a teaching routine based on a depth of knowledge framework that improves teaching practice by asking preservice teachers to consider *what *they are teaching (rote skills, memorized vocabulary words, rich concepts, problem-solving strategies, ways for students to justify their thinking). Through design research she also is developing tasks related to generalizing figural sequences to assist teachers in facilitating the transition to symbolization that all early algebra students undergo. Currently, she is exploring the potential of semiotics and Peircean diagrammatic reasoning for teaching teachers how to sequence mathematical learning tasks logically from concrete to pictorial to symbolic forms of representation to foster deep learning.

## Education

- Ed.D. Harvard University 1992, Teaching Curriculum & Learning Environments
- M.A. University of California-Berkeley 1998, History and History of Science
- M.S.T. Boston College 1972, Mathematics Education
- B.A. SUNY College-Cortland 1970, Mathematics/Secondary Education

## Research Interests

- What role do manipulative, inquiry-based mathematics-methods course tasks play in developing pre-service teachers (1) understanding of abstract mathematical concepts and processes and (2) mindset toward mathematics and their ability to do and teach it in meaningful ways?
- What tasks and pedagogy support preservice teachers process of learning to teach inquiry-based mathematics generally?
- What role might learning trajectories play in preservice teacher learning-to-teach specific mathematical domains such as introductory algebra, integer concepts/operations, and proof?

## Publications

Ali, H., Kinach, B. M., & Lande, M. (2019). Innovating scaffolded prototyping for design education: toward a conceptual framework derived from mathematics pedagogy. Paper to be presented at the International Group for the Psychology Of Mathematics Education – North American Chapter. St. Louis, Mo. November 14-17, 2019.

Ali, H., Lande, M., & Kinach, B. M. (2019). Learning through stuff: Scaffolded prototyping with manipulatives as a means to effectively learn engineering design by navigating from the concrete to the abstract. Paper presented at the Clive L. Dym Mudd Design Workshop XI. Design Education & Practice “How Process Matters,” Harvey Mudd College, 30 May – 1 June.

Kinach, B.M. (2019). Inquiry-based mathematics teaching: Does it really take too much time? *OnCore: Journal of the Arizona Association of Teachers of Mathematics 1*(1): 15 – 21.

Kinach, B.M. (2018). Progressive visualization tasks and semiotic chaining for mathematics teacher preparation: Towards a conceptual framework. In Presmeg, N., Radford, L., Roth, W.-M., and Kadunz, G., *Signs of signification: Semiotics in mathematics education research *(235-255)*. *Heidelberg, Germany: Springer Verlag.

Kinach, B. M., Bismarck, S., & Salem, W. (2018). Activities and a cognitive pedagogy for fostering prospective teachers’ concept‐development practices in mathematics methods courses. In Kastberg, S. E., Tyminski, A. M., Lischka, A. E., and Sanchez, W. B. (Eds.) *Building Support For Scholarly Practices In Mathematics Methods. A Volume in the **Association of Mathematics Teacher Educators Professional Book Series.* Charlotte, NC: Information Age Publishing and Association of Mathematics Teacher Educators.

Merritt, J. D., Lee, M. Y., Rillero, P., & Kinach, B. M. (2017). Problem-Based Learning in K–8 Mathematics and Science Education: A Literature Review. *Interdisciplinary Journal of Problem-Based Learning, 11*(2).

Available at: https://doi.org/10.7771/1541-5015.1674

Kinach, B. M., Polasky, S., & Darwin, M. (2017). ASU Brings a STEM Focus to Elementary Teacher Preparation. 100kin10 Website https://grandchallenges.100kin10.org/progress/asu-brings-a-stem-focus-to-elementary-teacher-preparation

Kinach, B. M. (2014). Generalizing: The core of algebraic thinking. *Mathematics Teacher 107*(6): 432-439.

Kinach, B. M., Coulson, A., & Luther, D. (2014). Visualization as learning tool: What should prospective teachers know and teacher educators teach? In P. Liljedahl & C. Nicols (Eds.). *Proceedings of the International Group for the Psychology of Mathematics Education* (26)*. *Vancouver, Canada: University of British Columbia.

Kinach, B. M. (2013). Discovery activity design. *On Core: Journal of the Arizona Association of Teachers of Mathematics 1*(1): 40 – 48.

Kinach, B. M. (2011). Transformative tasks in algebra teacher preparation. In T. Lamburg, (Ed.). *Proceedings of the International Group for the Psychology of Mathematics Education North American** Chapter* (1416-1423). Reno, NV: University of Nevada.

Kinach, B. M. (2011). Fostering spatial thinking in geometry teaching. *Mathematics Teacher*, ** 105(**7): 534-540.

Kinach, B. M. (2010). How the brain learns mathematics, by D. A. Sousa. *The Journal of Educational Research*, ** 103**(05), 368-369.

Kinach, B. M. (2002). Understanding and learning-to-explain by representing mathematics: Epistemological dilemmas facing teacher educators in the secondary mathematics "methods" course. *Journal of Mathematics Teacher Education 5*(2): 1-34.

Kinach, B. M. (2002). A cognitive strategy for developing prospective teachers' pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. *Teaching and Teacher Education 18*(1): 51-71.

Kinach, B. M. (2001). Teaching critical thinking through cultural perspective taking: Potential insights for the Asian critical thinking movement from multicultural education reform in the United States. *Manusya: Journal of Humanities 1*(2): 181-204.

Kinach, B. M. (2001). Case studies of subject-matter preparation reform in U.S. preservice teacher education. *The Alberta Journal of Educational Research XLVII*(1): 87-90.

Kinach, B. M. (2001). Assessing, challenging, and developing prospective teachers' pedagogical content knowledge and beliefs: A role for instructional explanations. In Tamar Ariav, Anat Keinan, & Ruth Zuzovsky (Eds.), *The Ongoing Development of Teacher Education: Exchange of Ideas. *Tel Aviv, Israel: The Mofet Institute..

Kinach, B. M. (1996). Logical trick or mathematical explanation? Re-negotiating the epistemological stumbling blocks of preservice teachers in the secondary mathematics methods course. *Proceedings of the Eighteenth Annual Meeting North American Chapter of the International Group for the Psychology of Mathematics Education, Volume 2 *(414-420)*. *Columbus, OH: Ohio State University.

Kinach, B. M. (1995). Grounded theory as scientific method: A response to Haig on educational research methodology. *Philosophy of Education 1995*. Urbana, IL: University of Illinois Urbana Champaign.

Kinach, B. M. (1993). Solving linear equations physically. In Christian R. Hirsch & A. Robert Laing (Eds.), *Activities for active learning and teaching: Selections from the Mathematics Teacher. *Reston, VA: National Council of Teachers of Mathematics.

Kinach, B. M., & Moore, C. A. (1992). Teacher education: An integrative and interdisciplinary model for linking the liberal arts and the profession (Special issue: Creative Visions of Teacher Education). *Action in Teacher Education XIV*(1): 26-34.

Kinach, B. M., & Moore, C. A. (1991). Science: A pedagogical tool for developing critical thinking. *Inquiry: Critical Thinking Across the Disciplines,* 5-7,13.

Kinach, B. M., & Moore, C. A. (1994). Knowledge and the curriculum: Epistemological considerations for teacher education reform. *International Network of Philosophers of Education Papers of the Fourth Biennial Conference: Identity, Culture and Education, 17-20 August 1994, Leuven, Belgium, *396-397.

Kinach, B. M., & Moore, C. A. (1990). Linking the liberal arts and the professions: An integrative and interdisciplinary approach. In Sally J. Reithlingshoefer, (Ed.), *What If the University Took Learning Seriously: Selected Papers from the Eighth Annual Conference on Non-Traditional and Interdisciplinary Programs. *Virginia: George Mason University, 204-209.

Kinach, B. M., & Phillips, C., French, D., Goldring, N., Ward, R. B., & Spindel, J. (1983). *Choices: A Unit on Conflict and Nuclear War*. Washington, D.C.: National Education Association, Union of Concerned Scientists, and Massachusetts Teachers Association.

## Research Activity

- Johnson,Mina Catherine*, Johnson,Mina Catherine*, Johnson,Mina Catherine*, Campana,Ellen, Campana,Ellen, Coleman,Grisha, Glenberg,Arthur Mitchell, Kelliher,Aisling G, Kelliher,Aisling G, Kinach,Barbara, Megowan,Colleen, Megowan,Colleen, Savenye,Wilhelmina C, Tinapple,David A. Embodied STEM Learning Across Technolog-Based Learning Environments. NSF-EHR(8/15/2010 - 7/31/2016).

## Courses

Spring 2021 | |
---|---|

Course Number | Course Title |

MTE 412 | Mathematics in Elem Schools |

MTE 482 | Mthds Teaching Math Sec School |

Fall 2020 | |
---|---|

Course Number | Course Title |

EED 537 | Math Methods & Assessment |

SED 560 | Teaching Math with Technology |

Spring 2020 | |
---|---|

Course Number | Course Title |

MTE 412 | Mathematics in Elem Schools |

MTE 482 | Mthds Teaching Math Sec School |

Fall 2019 | |
---|---|

Course Number | Course Title |

EED 537 | Math Methods & Assessment |

Spring 2019 | |
---|---|

Course Number | Course Title |

MTE 482 | Mthds Teaching Math Sec School |

EED 537 | Math Methods & Assessment |

Fall 2018 | |
---|---|

Course Number | Course Title |

EED 537 | Math Methods & Assessment |

SED 560 | Teaching Math with Technology |

Spring 2018 | |
---|---|

Course Number | Course Title |

MTE 412 | Mathematics in Elem Schools |

EED 537 | Math Methods & Assessment |

Fall 2017 | |
---|---|

Course Number | Course Title |

EED 537 | Math Methods & Assessment |

SED 560 | Teaching Math with Technology |

Summer 2017 | |
---|---|

Course Number | Course Title |

SED 547 | Teaching Math-Middle Grades |

Spring 2017 | |
---|---|

Course Number | Course Title |

MTE 482 | Mthds Teaching Math Sec School |

EED 537 | Math Methods & Assessment |

Fall 2016 | |
---|---|

Course Number | Course Title |

MTE 412 | Mathematics in Elem Schools |

SED 560 | Teaching Math with Technology |

Summer 2016 | |
---|---|

Course Number | Course Title |

SED 547 | Teaching Math-Middle Grades |