QIS Key Concepts for Early Learners: K-12 Framework

High School Math

Incorporating QIS into High School Math

    For each key concept, the group identified the mathematics required to understand the concept presented. While there are a total of nine QIS Key Concepts, we only included the subset that had clear mathematical content covered in middle school and beyond in the framework. Some key concepts include multiple concepts, so if a single key concept has multiple individual applications of mathematics, it is included multiple times.

    Once the mathematical concepts for each key concept were identified, the group identified the Common Core State Standard associated with the mathematical concept as well as the course in which that content is typically taught. (The Common Core State Standards for Mathematics are available here: https://www.nctm.org/ccssm/)

    Individual courses were then identified that commonly teach that common core state standard. However, there were two circumstances in which multiple courses were identified for the same learning goal. First, not all states and school districts cover the same standards in the same courses, so the same standard might be taught in different courses (e.g. Algebra 1 or Geometry). Second, some concepts are introduced in one course and might be covered in more depth in a follow-on course, so instructors could choose to cover the Quantum concept in either course (e.g. Algebra 1 or 2).

    To create relationships between different concepts, we considered whether the mathematics or QIS material being covered in one key concept was then used in a subsequent one. In the learning trajectory, there are two kinds of learning goals, both of which we had to consider.

    1. Mathematical concepts that will be used in quantum later (e.g. the probability of two independent events is their product).
    2. Applications of mathematical concepts to quantum (e.g. entangled qubits’ outcomes are not independent).

    Document organization:

    This document has several pieces of information associated with each learning goal of the learning trajectory.

    1. QIS Key Concept
    2. Relationship of Key Concept to mathematical concept
    3. Common Core State Standard associated with the mathematical concept
    4. Course that in which the concept is typically taught
    5. Relationship between this learning goal and any pre-requisite learning goals

    The purpose of the QIS K-12 Key Concepts Math Focus Group was to create a document that would be useful to curriculum developers and teachers, providing guidance about places where high school mathematics learning goals can be satisfied at the same time as content in the QIS K-12 Key Concepts. 

    The focus group brought together experts, educators familiar with teaching and research of mathematics concepts at high school and/or university levels. The members were:

    • Eugenie Alvares, Simpson Academy for Young Women, Chicago, IL
    • John Brown, Lake View High School, Chicago, IL
    • *Diana Franklin, University of Chicago, Chicago, IL
    • Kit Golan, Lesley University, Cambridge, MA
    • Maajida Murdock, Baltimore County Public Schools, Baltimore, MD
    • *Brent Yen, University of Chicago, Chicago, IL


    *Designates working group leads, conveners, and/or framework editors.

    The result is a set of activities that both teach mathematics skills typically taught in high school as well as very early QIS concepts. These are not meant to be full activities or lesson plans – different instructors may use different languages, choose to go into different amounts of depth, etc.  We hope, however, that by providing examples of synergistic activities, curriculum developers will be able to use these (and their own ideas) to create either individual activities or sequences of activities that build math skills and knowledge while, at the same time, introducing students to some basic QIS concepts.

    The output is downloadable via the following link. We are releasing this first version for feedback from the community. Please reach out to us with your comments/questions at edwardse@illinois.edu.


    Resources and Tools

    The resources in this repository are created and submitted by members of the quantum education community. We review them prior to posting and provide information on suitability for different audiences. We also note when teachers have either co-developed or reviewed the resource. Did we miss anything? Contact our team to let us know!



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