Barbara Kinach

7271 E. Sonoran Arroyo Mall
Santa Catalina Hall 350A
Associate Professor
Faculty
POLY Campus
Mailcode
2680

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

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 childrens 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. 

Courses

Spring 2018
Course NumberCourse Title
MTE 412Mathematics in Elem Schools
EED 537Math Methods & Assessment
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