Barbara Kinach

- Barbara.Kinach@asu.edu
- (480) 727-1283
- 7271 E. Sonoran Arroyo Mall Santa Catalina Hall 350A Mesa

Biography

Barbara Kinach is a mathematics teacher educator-researcher interested in issues of teacher subject-matter knowledge and how the tasks of mathematics teacher preparation influence pre-service teachers’ (or, PTs’) mathematical understanding and teaching practice. One line of her studies focuses on the role of manipulatives and instructional explanations in transforming PTs’ procedural views of mathematics and mathematics teaching. Another research stream explores the different teacher moves or logics of instruction that teaching different knowledge types (e.g., information, skills, concepts, problem solving practices, argumentation) requires. Kinach’s cognitive strategy (IACTS) for developing pedagogical content knowledge modifies Perkins and Simmons’ “levels of understanding” framework to characterize depth of teacher content understanding in mathematics. Semiotics as the study of (mathematical) signs, developing early algebraic thinking, and the problem of the logically disconnected U.S. algebra curriculum are other areas of interest. Through design research she is developing tasks related to generalizing figural sequences to assist PTs in facilitating the transition to symbolization that all early algebra students undergo. Kinach aims to transform the procedural understanding of mathematics and the preferences for direct-instruction teaching methods that PTs typically bring to their studies in the mathematics methods course. Her aim is to progress PTs’ thinking toward teaching practices that foster meaning and purpose and the rich type of mathematical understanding called for by the National Council of Teachers of Mathematics (2000) and the Common Core State Standards for Mathematics (National Governor’s Association 2010).

Research Interests

Guiding Research Questions:

- What prior experience do pre-service teachers have with using visual representations to learn concepts and solve problems in mathematics?
- In the absence of such experience, what types of tasks generate an appreciation for the role visualization plays in mathematics learning and an ability to use visual tools effectively to develop math concepts, processes, and relationships?
- What do pre-service teachers need to know about learning mathematics through visualization in order to effectively support student learning using visual tools?

Current Research Projects:

In an APS-funded grant with the MIND Research Institute, Kinach and colleagues are investigating “the impact of ways that ST Math game technology is used” on children’s mathematics achievement. ST Math is a neuroscience-based K-8 mathematics curriculum that teaches mathematics concepts visually without words. The team hypothesize that providing students with visual experiences of mathematics concepts prior to the introduction of concept vocabulary will result in increased mathematics achievement and problem-solving ability for all students, but especially for second-language learners.

Publications

Kinach, B. M. (2016). Digital visualization tasks for mathematics teacher development: A semiotic chaining analysis. Paper presented at the 13th International Congress on Mathematics Education, Hamburg, Germany, 24-31 July, 2016.

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

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.

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).

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 |

Spring 2016 | |
---|---|

Course Number | Course Title |

MTE 482 | Mthds Teaching Math Sec School |

EED 537 | Mathematics Elementary School |

Fall 2015 | |
---|---|

Course Number | Course Title |

EED 537 | Mathematics Elementary School |

SED 560 | Teaching Math with Technology |

Summer 2015 | |
---|---|

Course Number | Course Title |

SED 547 | Teaching Math-Middle Grades |

DCI 599 | Thesis |

Spring 2015 | |
---|---|

Course Number | Course Title |

EED 412 | Mathematics in Elem Schools |

MTE 412 | Mathematics in Elem Schools |

EED 537 | Mathematics Elementary School |

Fall 2014 | |
---|---|

Course Number | Course Title |

EED 412 | Mathematics in Elem Schools |

EED 537 | Mathematics Elementary School |

Summer 2014 | |
---|---|

Course Number | Course Title |

SED 547 | Teaching Math-Middle Grades |

DCI 599 | Thesis |

Spring 2014 | |
---|---|

Course Number | Course Title |

EED 412 | Mathematics in Elem Schools |

Fall 2013 | |
---|---|

Course Number | Course Title |

EED 412 | Mathematics in Elem Schools |

EED 537 | Mathematics Elementary School |

SED 560 | Teaching Math with Technology |

Summer 2013 | |
---|---|

Course Number | Course Title |

SED 547 | Teaching Math-Middle Grades |

MTE 598 | Special Topics |

DCI 599 | Thesis |