Hi David! Thank you for your questions. In the Summer of 2017, we held a 4-week summer workshop for a group of middle-school math teachers and STEM and CS education faculty and graduate students to design six initial modules. These modules were then piloted in the 2017-2018 academic year, and various assessment data were collected including student (pre-assessment and post-assessment for math and CS concepts, interviews, and MISO surveys) and teacher (interview) data. To make sure we were meeting students where they are, we held another 4-week workshop in the summer of 2018 to revise these modules based on the analysis of the assessment data. During this workshop, we also developed another six modules. The twelve modules were piloted in the 2018-2019 academic year and the same data were collected. These modules were refined in Summer 2019 based on data collected. This iterative process continued through the 2020-2021 academic year. 

As for your last question, we purposely developed our units to have real-world problem connections that are accessible to both genders and multiple races. Also, we purposely tested our modules in schools with high minority populations (gender is pretty much equal in public schools). Here is a link to a table of the demographics of the schools where these modules were implemented (pseudonyms are used for the schools).

Hi Myriam! Thank you for your questions. These instructional modules integrate CS concepts into middle-school general mathematics courses. The modules can be used to cover the following topics:

• Grade 6
  • Working with factor pairs
  • Unit rates
  • Combining like terms
  • Understanding mean
• Grade 7
  • Integer addition
  • Integer subtraction
  • Ratios & proportions
  • Drawing polygons & exploring angles
• Grade 8
  • Translations
  • Reflections
  • Rotations
  • A transformations art project

We have designed the teacher notes so that teachers may support students with Scratch. In these instructions, we guide teachers on how to program in Scratch and how to set up studios for each problem. Having these studios provides teachers the ability to easily share students work with the class and for students to view each other’s work. This is especially useful for classroom debugging sessions, which is beneficial for students who are learning how to code. Because these modules were temporarily implemented remotely due to covid, we also have videos students can reference for additional help with programming and math concepts.

Hi Ashley, at CPR2 we also have a lesson exploring angle measure of polygons. We use Turtle in Python to push students to discover the relationship between the measure of interior and exterior angles of a regular polygon as the number of sides increases to infinity.  We have not tried it with 7th graders but would be aligned with our grade 7 math standards, maybe as an enrichment activity. I see your lesson is for 7th, would you mind sharing the ideas your lesson addresses?

Hi Cynthia!  In this module, students explore the mathematical concepts of supplementary, adjacent, interior and exterior angles, proportional relationships, and area of polygons. The CS topics introduced in this module are variables, expressions, input/output, sequencing, selection, and iterating. The module is composed of four sections and takes about a week to implement. 

Section 1: Drawing Squares
In this section the students will use Scratch to:

• Construct squares with different side lengths
• Calculate the area and perimeter of the squares 
• Determine the relationship between the perimeter and area of the square

Section 2: Changing Angles 
In this section the students will use Scratch to:

• Visualize and calculate supplementary angles
• Explore making closed figures
• Determine the relationship between the number of sides and the interior angle measure of a regular polygon

Section 3: Determining angle of turn based on number of sides
In this section the students will use Scratch to draw: 

• An equilateral triangle
• A regular hexagon
• A regular dodecagon

Section 4: Programming Sprites to draw any regular polygon
In this section the students will use Scratch to:

• Create any regular polygon
•     Determine which angles of turn will create a regular polygon
•     Relate the exterior angle of a regular polygon to its number of sides
• Write a Scratch program to create any regular polygon by obtaining the number of sides and side length from User input. (Program computes the required angle measure.) 

Hi Noelani! Thank you for your questions. For your first question - A little of both! We developed a module specifically for introducing Scratch to students. This module covers getting started with Scratch and the basics of programming in Scratch. New concepts are also introduced in modules containing mathematical content (content tested via standardized testing) – the introduction of these new topics is driven by math instructional needs. In our current implementation, teachers implement the introductory module once before the modules containing mathematical content.  

As for your last question, helping them to think algorithmically and exposure/experience with Scratch might be helpful. I do not know and specific projects off the top of my head that would be useful to you but check out the projects on the Scratch website! I’m sure there is something there.

Hi Cynthia!  Here are the mathematics topics we cover in each module and the programming topics covered in each module. The modules we developed in this project are predominately math modules, the CS content is incorporated to support math education. I’ll dive in to the Ratios and Proportions module as an example. This module has 6 sections and takes about a week to implement.

• Section 1: Introduction to steepness
  We start the module by having students look at sections of roller coasters and talking about which parts are the scariest. We then relate this to steepness.
• Section 2: Programming your robot
  As an introduction to algorithmic thinking and debugging, students emulate the relationship between a robot that executes code and the sequence of commands in a computer program by giving their teacher instructions on drawing a roller coaster segment (right triangle).
• Section 3: Drawing in Scratch
  Students draw different roller coaster segments in Scratch. This allows them to visualize triangle with different steepness and prepares them to explore a way of thinking about the mathematics behind steepness. This activity allows students to reflect on their instructions from the robot activity and gives them practice with algorithmic thinking and debugging their programs.
• Section 4: Describing steepness
  This section does not contain any programming components, but formally introduces steepness, ratio, and the constant of proportionality. It consists of two parts: a discussion of segments with the same steepness and practice problems that involve using the constant of proportionality to describe steepness.
• Section 5: Drawing the roller coaster segments with the constant of proportionality
  This section allows students to use Scratch to implement what they learned in the last section. In this section, students have their sprite draw different roller coaster segments with the same constant of proportionality and then draw segments with different constants of proportionality. This task requires students to use the constant of proportionality while introducing the programming concepts of variables and expressions.
• Section 6: Proportionality & Chicken Wings
  This section gives students another context for using the constant of proportionality – by comparing the costs of chicken wings at different restaurants. There are no programming tasks in this section.