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Barbara Kinach

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Associate Professor
Faculty, POLY Campus, Mailcode 2680
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. 

Fall 2017
Course NumberCourse Title
EED 537Math Methods & Assessment
SED 560Teaching Math with Technology
Summer 2017
Course NumberCourse Title
SED 547Teaching Math-Middle Grades
Spring 2017
Course NumberCourse Title
MTE 482Mthds Teaching Math Sec School
EED 537Math Methods & Assessment
Fall 2016
Course NumberCourse Title
MTE 412Mathematics in Elem Schools
SED 560Teaching Math with Technology
Summer 2016
Course NumberCourse Title
SED 547Teaching Math-Middle Grades
Spring 2016
Course NumberCourse Title
MTE 482Mthds Teaching Math Sec School
EED 537Mathematics Elementary School
Fall 2015
Course NumberCourse Title
EED 537Mathematics Elementary School
SED 560Teaching Math with Technology
Summer 2015
Course NumberCourse Title
SED 547Teaching Math-Middle Grades
DCI 599Thesis
Spring 2015
Course NumberCourse Title
EED 412Mathematics in Elem Schools
MTE 412Mathematics in Elem Schools
EED 537Mathematics Elementary School
Fall 2014
Course NumberCourse Title
EED 412Mathematics in Elem Schools
EED 537Mathematics Elementary School
Summer 2014
Course NumberCourse Title
SED 547Teaching Math-Middle Grades
DCI 599Thesis
Spring 2014
Course NumberCourse Title
EED 412Mathematics in Elem Schools
Fall 2013
Course NumberCourse Title
EED 412Mathematics in Elem Schools
EED 537Mathematics Elementary School
SED 560Teaching Math with Technology
Summer 2013
Course NumberCourse Title
SED 547Teaching Math-Middle Grades
MTE 598Special Topics
DCI 599Thesis
Spring 2013
Course NumberCourse Title
EED 537Mathematics Elementary School
MTE 598Special Topics