Bridging Math and Computer Science Through Binary Code

Educator connects math and computer science concepts through binary code.
Made by Embark Labs
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About this Micro-credential

Key Method

Educator uses discussion and manipulatives to illustrate the link between math and binary code.

Method Components

Components of an effective lesson that teaches binary:

Discussion should include the following key points:

  • Data input into the CPU is converted to binary code where each individual input is processed one at a time.
  • Deconstruct the concept that every piece of data input into the computer CPU is converted into ones (1s) and zeros (0s)
    • Use a light switch example on or off (see Resources section for guidance)
    • Use true/false examples
    • Use the empty (0) or full (1) example to demonstrate the binary concept
    • Other connected/relevant vocab, such as bits and bytes

Manipulatives

  • Including an emphasis/elaboration on pattern recognition

Example discussion

  • Educator guides students to an understanding of how binary code is the foundation of all computer processing through a discussion on how binary represents data using 0s and 1s, relating those positions to that of a light switch.
    • The binary system is used internally by almost all modern computers and computer-based devices. Each digit is referred to as a bit.
  • Educator encourages students to identify other examples like the "light switch" example that demonstrates the application of binary code (such as true/false, on/off).
    • Explain how original computers were actual switches. Binary can be explained as the position of the switch, the position of origin.
    • If in binary you encounter a zero, you do nothing. If you encounter a 1, you flip the switch. Explain in clear terms using a variety of examples (on/off, true/false, yes/no). There is no gray area.

Guiding questions

  • Do you notice any similarities between counting in math and counting in binary?
  • Do you see a pattern emerging?
  • Where else in the technology world do you see a pattern of doubling? (hint for “Moore’s Law”)
  • Can you predict when you’ll need to add another place value?
    • Discuss the pattern that begins to appear; have students predict the next occurrence where they will need another space (see Resources section for more context).

Examples of manipulatives

  • Teacher uses math manipulatives, such as two-sided counting chips or flash cards, to illustrate patterns in a binary number system
  • Use the two-color counting chips to have students build a model of counting in binary from 0 to 16 (see Resources section for guidance)
    • Building the pattern using the counting chips. Instructor hint: If this is 100, which is 4 in binary, what do I need to put down to represent 5?
    • Instructor hint: Remember, these are positions; they are not numeric values

Demo Videos

https://www.youtube.com/watch?v=zQ0YF9h45JA

https://youtu.be/pbR0cENzQ2k

Research & Resources

Supporting Research

  • Boggan, Matthew, Sallie Harper, and Anna Whitmire. Using Manipulatives to Teach Elementary Mathematics. Greensboro, NC: Carson-Dellosa Pub., 1994. Web.
  • http://www.aabri.comwww.aabri.com/manuscripts/10451.pdf
  • Fuson, Karen. Children’s Counting and Concepts of Number. N.p.: Springer Science & Business Media, 2012. Google Books. Web.
    http://bit.ly/1JzeEse
  • Fuson, Karen. "The Effects on Pre-service Elementary Teachers of Learning Mathematics and Means of Teaching Mathematics through the Active Manipulation of Materials." National Council of Teachers of Mathematics. Journal for Research in Mathematics Education (Jan. 1975): 51-63. Web.
    http://bit.ly/1XypRLU
  • Fennema, Elizabeth, Piet Human, and Alwyn Olivier. "Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics." Educational Researcher (1996): 12+. Research Gate. Web.
    http://bit.ly/1OTAt2v

Resources

Embark Labs Explore CS Courses and PD opportunities

Embark Labs is an education program that introduces elementary and middle school students to design and computational thinking in a hands-on, collaborative way.

Unit 1, Lesson 1.2: Introducing Binary: http://embarklabs.com/explorecsunit1free

Additional Embark Labs resources

Unit 1, Lesson 2: Sending Binary Messages. Code.org CS Principles

In this lesson, students work in groups using classroom supplies and everyday objects to develop their own systems for encoding and sending simple binary messages, messages that only have two possible value.
http://bit.ly/1QJPOTF

Google Computational Thinking course

A free online course helping educators integrate computational thinking into their curriculum
https://computationalthinkingcourse.withgoogle.com/preview

Brain Rules

In Brain Rules, Dr. John Medina, a molecular biologist, shares his lifelong interest in how the brain sciences might influence how we teach our children and how we work. In each chapter, he describes a brain rule—what scientists know for sure about how our brains work—and then offers transformative ideas for our daily lives. http://www.brainrules.net/about-brain-rules

CS Unplugged

CS Unplugged is a collection of free learning activities that teach computer science through engaging games and puzzles that use cards, string, crayons, and lots of running around.
http://csunplugged.org/

Sample Lesson

Algorithmic Thinking
http://bit.ly/1Py24FN

Submission Requirements

Submission Guidelines & Evaluation Criteria

To earn the micro-credential, you must receive a passing evaluation for Parts 1 and 3 as well as a “Yes” for each component in Part 2.

Part 1. Overview questions

(150-word limit for each response)

  • Activity description: Please provide a short, contextual description of the activity in which the discussion and use of manipulatives was demonstrated.
  • Activity evaluation: How do you know your students increased their proficiency as a result of your using manipulatives to teach math/binary?
  • Have you incorporated computer science/computational thinking into your classroom instruction before?
  • (Optional) Have you attended an Embark Labs PD session before? If yes, please clarify where and when. Additionally, if you engaged with Embark’s instructional materials, please identify which resource was used.

Part 2. Evidence/artifacts

Educator must submit a video that highlights their discussion points and includes evidence of students’ ability to recognize patterns related to binary.

Part 3. Educator reflection

Provide a reflection, using the following questions as guidance (200-word limit):

  • What was the impact of integrating math manipulatives with your students? Were there any relevant challenges or observations with this practice?
  • How did using these methods to bridge math and computer science (binary code) affect your comfort level in teaching computer science/CT in your classroom?
  • How might you improve/differentiate this lesson in the future?

Except where otherwise noted, this work is licensed under:
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
http://creativecommons.org/licenses/by-nc-nd/4.0/

Requirements

Download to access the requirements and scoring guide for this micro-credential.
How to prepare for and earn this micro-credential - in a downloadable PDF document

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