Selected Published Papers

"Pattern Building and Modeling in Beginning Algebra" New York State Mathematics Teachers' Journal, November, 2014, 64(3), 124-129.

“Attention! Attention! This is NOT a (Multiple Choice) Test” American Mathematical Association of Two-Year Colleges MathAMATYC Educator, September, 2014, 6 (1), 17 - 22.

“Not Your Father's Equation Solving - Corrected” Florida Council of Teachers of Mathematics, Dimensions in Mathematics, FALL 2013, 33 (2), 14 - 23.

“When Will I Ever Use This Stuff?” California Math Council ComMuniCator, pp. 25-28. December, 2013.

“An Analysis of Connections Based on Neuroscience,” Texas Mathematics Teacher. (2013)

“Learning - Changing the Connections in the Brain,” The New Jersey Mathematics Teacher. (2012)

“Federal Tax Schedule Y-1: Piece-wise Defined Function. No, Wait; It's an Absolute Value,” New York State Mathematics Teachers' Journal. (2012)

“Capitalizing on Basic Brain Processes in Developmental Algebra – Part One,” MathAMATYC Educator 2 (2), 4-7. (2011)

“Capitalizingon Basic Brain Processes in Developmental Algebra – Part Two,” MathAMATYC Educator 2 (3), 28-31. (2011)

“Capitalizingon Basic Brain Processes in Developmental Algebra – Part Three,” MathAMATYC Educator 3 (1), 10-13, (2011)

The Neuroscience of Connections Visualizations & Generalizations in Knights, C. & Oldknow, A., eds. Enhancing Mathematics with Digital Technologies. Continuum Press. London, UK. (2011)

"Generalizing Patterns in Algebra for Long-Term Memory Understanding" ( California Math Council, ComMuniCator, (34, 2), December, 2009 )

PREPRINT "Dynamic Visualizations in Teaching Algebra" Ohio Journal of School Mathematics Spring 2009

"Implications of neuroscientific research on teaching algebra" International Journal on Continuing Engineering Education and Life-Long Learning (2008)Vol 18 Nos. 5/6 2008 p 585

PREPRINT "Neural Associations through Mathematical and Contextual Connections," 2008. Ohio Journal of School Mathematics

Why Use a Function Approach when Teaching Algebra? Texas Mathematics Teacher, 53(1), 10-16. (2006)

Hand-Held Graphing Technology in the Developmental Algebra Curriculum (Preprint) MATHEMATICS AND COMPUTER EDUCATION, 37(3), 301-314. (2003).

Developmental Algebra with Function as the Underlying Theme 2003. Mathematics and Computer Education, 37 (1), 63-71

Graphing Technology - Tool of Choice for Teaching Developmental Mathematics 2001. The AMATYC Review, 24 (1), 41-55

On Teaching Intermediate Algebra from a Function Approach 1999. Virginia Mathematics Teacher, Vol. 25, No. 2

Sharp Corners, Rates of Change, Systems of Equations, CAS, and Geometric Transformations All in One Problem 1998. Proceedings of the 2^nd T³ Japan National Conference

Just for Algebra Students

Neuroscience Excerpts from

Laughbaum, E. D. (2013), Foundations for College Mathematics, 3e, Red Bank Publishing

Basic Brain Function – A Beginning

Basic Brain Function – Can Algebra be Simple?

Basic Brain Function - Connections

Basic Brain Function –What’s with the Prefrontal Lobes Stuff?

Basic Brain Function –Visualizations I & II

Basic Brain Function – Unconscious Processing

Basic Brain Function – Distributed Learning

Basic Brain Function – Connections Revisited

Basic Brain Function –Enriched Environment

Basic Brain Function - Learning

Basic Brain Function - Graphing Technology

Basic Brain Function –Attention

Basic Brain Function – Practice Practice Practice

Basic Brain Function – The Role of Dopamine

Basic Brain Function – Meaning and Understanding

Selected Presentations

“Neuroscience and the Role of Pattern Generalizing in Algebra,” CMC-South 54^th Annual Mathematics Conference. (2013)

“Unlockthe Algebraic Mind through Patterns & Visuals,” Conference for the Advancement of Mathematics Teaching. (2013)

“Order Is Significant-Teaching Pencil and Paper Developmental Algebra belong AFTER Teaching with Technology,” (PowerPoint of Talk) International Conference on Technology in Collegiate Mathematics. (2013)

"Core Brain Function as Applied to Pedagogy and Curriculum," Bowling Green SU Mathematics Education Faculty Seminar (2013) See samples in AMS talk from 2012.

“Pattern Building in Algebra,” T³ International Conference. (2013)

University of Akron AMS Sectional Meeting -- Issues in the Preparation of Secondary Teachers of Mathematics, "Connections from Brain Science to Teaching Connections" (2012)

“Thirty-five% (35%) of Ohio's Matriculating Seniors must be remediated!,” (PowerPoint) OCTM 62^nd Annual Conference. (2012)

“Technology without neuroscience is like food without nutrition,” T³ International Conference. (2012)

“Teach Senior Remedial Algebra II through a Function Approach with the TI-84,” T³ International Conference. (2010)

“The Graphing Calculator is a Teaching Tool, Not a Confirming Pencil & Paper Math Tool,” International Conference on Technology in Collegiate Mathematics. (2008)

“Three Compelling Reasons for Using a Graphing Calculator,” California Math Council-South 49^th Annual Fall Conference. (2008)

“Teaching Developmental Algebra Isn’t Brain Science. Wait… Yes It Is.,” 33^rd AMATYC Annual Conference. (2007)

Keynote Address "Teaching and Learning Algebra based on Neuroscience/Cognitive Science Research" 8th International Conference on Technology in Mathematics Teaching, Hradec Kralove, Czech Republic. (2007)

“The Meaning of A Function Approach to Teaching Algebra" National Council of Teachers of Mathematics 82^ndAnnual Meeting (2004)

More to Data than Modeling (School Science and Mathematics Association 2003 Annual Conference)

The Exponential Function - More Important Than Ever Ohio Council of Teachers of Mathematics 53rd Annual Conference (2003)

High School Mathematics Remediation through a Function Approach, National Council of Teachers of Mathematics 81^stAnnual Meeting (2003)

Remedial Algebra with Function as the Underlying Theme, (National Council of Supervisors of Mathematics 2003 Annual Conference)

A Teaching Lesson on Factoring Polynomials with Technology 15^th Annual International T³ Conference (2003)

Modernizing the Developmental Mathematics Curriculum through Algebra from a Function Approach National Association for Developmental Education 27^th Annual Conference (2003)

Ideas on Teaching the Linear Function National Council of Teachers of Mathematics Central Regional Conference (2002)

The Teaching of the Quadratic Function: An Introduction Ohio Council of Teachers of Mathematics 52^nd Annual Conference (2002)Open-ended Questions and Guided Discovery in Beginning/Intermediate Algebra ICTCM 11^th Annual Conference (1998)

Issues with the Developmental Algebra Curriculum and Resulting Pedagogy

Published version.

This paper addresses 4 issues in the remedial algebra curriculum from a neuroscience perspective.

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Beliefs for the Algebra Curriculum & Pedagogy

Revised 1-17-2019

“Beliefs for the Algebra Curriculum & Pedagogy” provides evidence for changing four beliefs we have for algebra education. The beliefs are explain/example, practice, supplements, and the algebra curricular approach.

Using Core Brain Function to Teach Algebra

• An Overview

• Visualizations in Algebra

• Generalizing Patterns in Algebra

• Connections as Neural Associations At the Core of Learning

• Enriched Environment

• The Role of Dopamine

• Practice Practice and More Practice

• Memory of the Abstract

Science-Based Remedial Algebra Still interesting

• Graphing Calculator: Teaching Tool or Math Manipulator

• Why Is Algebra a Gatekeeper? Formerly NEW

• Theory or Science? Somewhat New

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Algebra through Function Academy-Duck, North Carolina, Field Research Facility

· 2008 registration and information Pictures

Previous AMATYC Summer Institutes-Duck, North Carolina, Field Research Facility

"Developmental Algebra Using a Function Approach"

· 2002 Institute Report Pictures

· 2003 Institute Report Pictures

· 2004 Institute Report Pictures

· 2005 Institute Report Pictures

· 2006 Institute Report Pictures

· 2007 Institute Report Pictures

Previous AMATYC Summer Institutes - Duck, North Carolina, Field Research Facility

"Teaching in Context"

· 1999 Institute Report Pictures

· 2000 Institute Report Pictures

· 2001 Institute Report Pictures