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Design Active Experiences for Deeper Mathematical Thinking (B302)

[Explore and create : BYOD]

Tuesday, June 28, 10:45–11:45 am
CCC Mile High Ballroom 3B

favoritesDr. Mark Hines  
How can you help students develop a mathematician’s mindset? Learn how to model real-world phenomena, create art, and test and apply mathematical ideas through activities designed to give students hands-on practice with mathematical thinking and understanding. You will walk away with a template, design principles and a project draft.

Skill level: Intermediate
Attendee devices: Devices required
Attendee device specification: Laptop: Chromebook, PC, Mac
Tablet: Android, iOS, Windows
Participant accounts, software and other materials: Graphical Analysis
Desmos (for iOS), but we can also use the web version
Focus: Digital age teaching & learning
Topic: Instructional design and delivery
Grade level: PK-12
Subject area: Math
ISTE Standards: Teachers : Model digital age work and learning
Teachers : Design and develop digital age learning experiences and assessments
Teachers : Facilitate and inspire student learning and creativity

Digital tote resources
Description: Presentation URL
Description: Slidedeck and Accompanying Website with resources

Proposal summary

Purpose & objective

The Common Core and the NCTM emphasize that mathematics learning must stand on three legs equally: Procedural Knowledge, Understanding and Application. Many mathematics classrooms struggle with ways to have students apply their knowledge and demonstrate true understanding. The Common Core states that students should be able to:

Construct viable arguments and critique the reasoning of others (CCSS.MATH.PRACTICE.MP3)
Model with mathematics (CCSS.MATH.PRACTICE.MP4)
Use appropriate tools strategically (CCSS.MATH.PRACTICE.MP5)

Participants will examine the language of the standards and share ideas about ways to move from lower level assessment (repeating algorithmic solutions to standard problems) to higher levels of synthesis, application, novel uses and original solutions.
We will walk through 4 class activities and look at student examples from a 10th Grade Algebra 2 class. The free iPad apps Graphical Analysis (from Vernier Software) and Desmos (also available as a web app on any device at were used to have students move from simple rote understanding and repetition to critical thinking about the ways relationships can be expressed and explained through form (graphically) and function (mathematical models and equations).

We will work together to develop a draft of a project for the participants based on their learners specific needs. We will use a backwards design principles accomplish this task. Participants will share and receive constructive feedback on their project ideas.


We will use the good instructional design mantra: Tell, Show, Do.

5’ Intros and Setting the goal

10’ We will first explore the language of mathematical standards from Common Core, NCTM and the International Baccalaureate (IB). This will give participants the chance to look at the standards for their level and students.

20’ We will walk through 4 activities that were designed for 10th grade students. We will look at the design brief, explore the timeline for completion including scaffolded activities, look at examples of student work, and map these projects to the standards.

20’ Participants will be given a framework for designing a math activity, choose a particular standard that they are designing for, and create an outline for a project of their own making. These will be shared via a common digital dropbox.

5’ Questions and feedback

Supporting research

Common Core for Mathematics

International Baccalaureate Mathematics

NCTM principles and standards:


Steve Leinwand, American Institute for Research:

Teaching Channel:

Emergent Math:



favorites Dr. Mark Hines, Mid-Pacific Institute