emergent math

Lessons, Commentary, Coaching, and all things mathematics.

About

Geoff Krall, PhD

I am a Fort Collins, CO resident and long-time math teacher and coach. I am the author of Necessary Conditions: Teaching Secondary Math With Academic Safety, Quality Tasks, and Effective Facilitation and helped pioneer the University of Wyoming Rural Teacher Corps. I have a PhD in Math Education from UW and love traveling all over the Front Range and the Western Slope. I have a passion for coaching math teachers, particularly in small, friendly systems.

Necessary Conditions: Teaching Secondary Math with Academic Safety, Quality Tasks, and Effective Facilitation was published in 2018 and is available from Stenhouse Publishers. 

About the website
Feel free to poke around the website. You can check out the blog, featured posts, problem based curriculum maps, or check out my Professional Development Services page. Below you’ll find a list of my publications and presentations.

You can email me or follow me on bluesky. Or use the contact page to get in touch.

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Abridged CV

Courses taught in the past few years

  • NASC 5600: Math and Statistics for Science Teachers
  • MATH 1400: College Algebra
  • MATH 0975: Developmental Mathematics
  • MATH 2120: Measurement and Geometry for Elementary Teachers
  • NASC 5225: Assessment MMA
  • EDEL 1410: Math for Elementary Teachers
  • NASC 5410: Numbers, Operations, and Patterns

Memberships and Professional Responsibilities

  • Associate Editor, Colorado Mathematics Teacher. (2017-Present)
  • Mathematics Support Coach, Meridian High School and Junior High
  • National Council of Teachers of Mathematics, Member
  • TODOS Mathematics for ALL, Member

Publications

Books

Krall, G. (2018). Necessary Conditions: Teaching Secondary Math with Academic Safety, Quality Tasks, and Effective Facilitation. Stenhouse Publishers.

Bicer, A. (Ed.), Krall, G., et al. (2022). Creativity-Directed Mathematics Tasks For 5th Grade Common Core. ISTES Organization.

Journal Articles

Bicer, A., & Krall, G., et al. (2023). The relationship between pre-service teachers’ spatial thinking ability and their mathematical creativity in the context of problem-posing. Research in Mathematics Education.

Krall, G. (2023). Teacher-designed mathematical portfolio assessments: Motivations, potential benefits, and lessons learned. Canadian Journal of Science, Mathematics, and Technology Education.

Krall, G. (2023, May 4-5). Profiles in Mathematics Portfolios: Potential Benefits and Lessons Learned [Paper Presentation]. American Educational Research Association 2023 Annual Meeting, Chicago, IL, United States.

Krall, G. (2022). Crafting an online, digital portfolio to better understand the SMPs. CCTM, November. https://www.cctmath.org/november-2022-practical-practices

Krall, G. (2020a). Review of Mathematical Imagining: A Routine for Secondary Classrooms by Christof Weber. Colorado Mathematics Teacher, 53(1). https://digscholarship.unco.edu/cmt/vol53/iss1/4

Krall, G. (2020b). Student Math Portfolios—A How to. Mathematics Teacher: Learning and Teaching PK-12, 113(7), e8–e9. https://doi.org/10.5951/MTLT.2019.0382

Cotton, W. R., Krall, G. M., & Carrió, G. G. (2012). Potential Indirect Effects of Aerosol on Tropical Cyclone Intensity: Convective Fluxes and Cold-Pool Activity. Tropical Cyclone Research and Review, 1(3), 293–306. https://doi.org/10.6057/2012TCRR03.05

ORCID-ID: https://orcid.org/0000-0003-0636-2873

Presentations

Wyoming Innovations in Education Conference 2024 – Saratoga, WY: Using Student Portfolios to Build Academic Identity 

SMTS Saskatchewan Understands Math (SUM) Conference 2023 – Saskatoon, SK (Featured Keynote and Workshop)

Teton Science School 2023 Symposium – Jackson, WY: The University of Wyoming Rural Teacher Corps: Experiencing PBE Through the Eyes of Pre-Service Teachers

NCCTM Annual Conference – North Carolina 2022 (Featured Keynote): “I Keep My Math Everywhere: Necessary Conditions for Learning Mathematics”

NCTM Regional Conference – New Orleans 2022 (Featured Speaker): Identity-Building Assessment: From a Number to a Showcase of Knowledge

Ankeny Summer Academy – Ankeny, IA (Keynote): Academic Safety: Creating a learning environment that welcomes and challenges all learners

CMC-South 2021, Palm Springs, CA: Identity-Building Assessment: From a Number to a Showcase of Knowledge

CCTM 2021 Annual Conference (Virtual): What does it even mean to ‘express regularity?’: Interpreting, assessing and scaffolding the SMPs

NCTM 2021 Atlanta: What does it even mean to ‘express regularity?’: Interpreting, assessing and scaffolding the SMPs

NCSM 2021 Atlanta: Identity-Building Assessment: From a Number to a Showcase of Knowledge

MCTM 2021 Featured Speaker: “A brief history (and imagining) of assessment”

Clark County Schools Secondary Math Conference 2021: The Care Gap: How Math Creates It and How We Can Use Math to Close It (Keynote Speaker)

NCTM Virtual Conference 2020: The Care Gap: How Math Creates It and How We Can Use Math to Close It

Mt. Holyoke Effective Practices Session (Webinar) 2019: Inquiry: Plain and Tall

NCTM Regional Conference – Boston 2019: Fantastic Tasks and Where to Find Them

CCTM Annual Conference 2019: Fantastic Tasks and Where to Find Them

NCTM Regional Conference 2018 – Seattle: Necessary Conditions: Essential Elements for Secondary Math Learning

NCTM Shadowcon 2017: The Art of Mathematical Anthropology

NCTM Annual Conference 2017: The Struggle Is Real: Tasks, Academic Status, and Productive Problem-Solving

NCTM Annual Conference 2016: Fumbling Towards Inquiry: Starting Strong in Problem-Based Learning

Global Math Department 2015: Designing Systems of Teacher Learning around Student Work

NCTM Regional Conference 2015 – Nashville, TN: Fumbling Towards Inquiry: Starting Strong in Problem-Based Learning

Northwest Math Conference 2015, Whistler, BC (featured): Problem-Based Learning Institute

Northwest Math Conference 2015, Whistler, BC: Toward Problem-Based Learning: A Quick Look

New Tech Annual Conference 2015, Chicago, IL: Fumbling Towards Inquiry: Starting Strong in Problem-Based Learning

NCTM Annual Conference 2015, Boston, MA: Adaptation: Developing Open Problems from Closed Curricula

NCTM Annual Conference 2014, New Orleans: Setting the Scene: Designing Your Problem-Based Classroom

Equip Conference 2013, Plymouth, IN: Designing Mathematical Tasks

North Carolina New Schools Scaling STEM Conference 2012: Toward Developing Mathematical Thinkers: Problem-Based Learning

North Carolina New Schools Scaling STEM Conference 2012: Getting Students to Struggle (and Engage) With Math