#### Teaching Math Concepts Without Your Standard Worksheet

As a teacher, it may feel impossible to design a classroom of students that do not experience math anxiety. While some of these students might benefit from additional instruction, the reality is that being taught through repetition and encouraging rote memorization simply cannot compete with learning through engaging activities. By embedding concepts into opportunities for problem-solving and exploration, learners can develop logical ways of thinking which contribute to mathematical understanding overall in more meaningful ways. This is particularly true in early childhood when learning is significantly connected to tangible experiences.

Because of this, I have decided to explore mathematical concepts using coding and music to engage students in multimodal and cross-curricular learning. Although perhaps unconventional, upon deeper analysis of these three topics it becomes clear that many of the skills required for success require transferable skills for mathematical competency! Keep scrolling to find two lists of resources (first coding, then music) that I have compiled with increasing complexity to get you started!

# Coding for Math

## Resource #1:

## Left Brain Craft Brain — Blog Post

Anne is a chemical engineer turned stay-at-home mom who uses her expertise to create creative STE(A)M (science, technology, engineering, art and math) projects for her children. I know what you’re thinking, “Isn’t this post supposed to be about math?”, it is! But coding is part of software engineering and she has a great post that introduces young children to coding language through kinaesthetic play!

Conditional statements in coding are “if…, then…” queries that prompt an action. With this concept, she plays a game similar to Simon Says where one student is a programmer and the rest are computers following commands with varying levels of difficulty that you can use to support developmentally appropriate practice.

What makes this activity so great is that it’s a perfect introductory lesson that supports kinaesthetic and social learning and introduces mathematical concepts like:

- Cause and effect (correlation between
*programmer*statements and*computer*reactions); - Sequencing/Patterning (ie. for multiple movements).

## Resource #2:

## Grid Patterns on the Floor — Blog Post

Marc Faulder is an Apple Distinguished Educator and in this post, he postures that in order to make coding meaningful to students, their experience with concepts should **begin “unplugged”**. I happen to agree with him.

In this lesson, he uses tape on the ground to create paths for trucks and challenges students to match the visual code on the white boards with the correct paths. He goes on to use an electronic programming toy called a Bee-Bot but I will go into this in more detail in the next section.

This is an amazing way to challenge young learners in a way that supports learning:

- Sequencing/Patterning (including the idea that patterns can be a repetition of one)
- Representation (using visuals to communicate ideas);
- Mathematical vocabulary related to spatial sense and direction (ie. forward, left);
- Problem-solving and reasoning (ie. this path goes all the way up, but this code turns so they don’t match);
- Size/Position;
- 1:1 Correspondence/Counting.

This activity could be easily extended by making:

- Growing patterns on the floor;
- A large grid using tape for students on a floor (many classrooms even have tiled flooring and can investigate how to get from one location to another) or on a table;
- Mazes;
- Adding barriers;
- And creating their own questions.

## Resource #3:

## Programmable Toys

There are many resources out there that allow for children to program toys to perform different functions. Unfortunately, for the time being many of these resources are incredibly expensive and may not work for many teachers and caregivers on a tight budget but this list would be incomplete without at least a cursory nod to these resources. If you do choose to purchase one, I encourage you to do some research and look at consumer comment sections before you make this sizeable investment. Because I have not tried any of these out myself, I do not feel comfortable recommending one to you so I will include a few links to products at different price points and videos that help you see the toys in action.

Without further ado, here is a short list:

- Cubetto
**$$**

- Bee-Bot
**$$$**(as afore mentioned) and it actually offers a class bundle set

I love the opportunities for social learning and if you can afford the expense, the opportunities for learning mathematics are clear:

- Sequencing/Patterning (including the idea that patterns can be a repetition of one)
- Mathematical vocabulary related to spatial sense and direction (ie. forward, left);
- Problem-solving and reasoning (ie. I only pressed up once and I needed to press it twice);
- Measuring distance;
- Size/Position;
- Time;
- 1:1 Correspondence/Counting.

Students can even learn to build their own coding areas by measuring how far the toy goes or racing two toys that have different paths!

## Resource #4:

## ScratchJr — App

First and foremost, I have done quite a bit of research on different coding apps for children and this is at the top of my list as it is **free**, requires** no registration** and yet does not** **sacrifice** quality**! That is great news for educators (or caregivers) on a budget. In the app, children begin with a simple template where they can add cartoon characters, text, landscapes, sound and movement to create animations. Because it is so visual, it can be easily used by learners who are still learning how to read.

See the video below to see an introduction and tutorial.

The video above outlines how the app can be used to create projects that are student-led or provided by educators. This opens up opportunities for students to engage in creative play that builds upon mathematical processes including:

- Estimation (ie. how many times does the car need to go right until it drives off of the screen?);
- Problem-solving and reasoning (ie. when I added the
*repeat*button, it didn’t stop so I used a*loop*instead); - Representation (using visuals to communicate ideas);
- Mathematical vocabulary related to spatial sense (ie. up, down, grow, shrink, etc.);
- Patterning/Sequencing;
- Size/Position;
- Time.

Coding also encourages self-correcting behaviours rather than requiring students to receive assessment from an adult–building child agency.

## Resource #5

## Code.org — Website

This **free **website is all about providing a sequential, pre-planned format for learning code in a highly visual way. For its youngest users, it actually begins with puzzles designed to teach sequencing and mouse control (dragging and dropping) with steadily increasing levels of complexity.

Eventually puzzles turn into mazes and that increase in complexity (ie. by adding *loops*) with key objectives like getting the Angry Bird to reach the pig. All the while, students are introduced to key coding principles like *debugging* and becoming exposed to the idea that making mistakes is natural and an opportunity for learning.

In terms of math, children are learning:

- Problem-solving and reasoning (ie. when I added the
*repeat*button, it didn’t stop so I used a*loop*instead); - Representation (using visuals to communicate ideas);
- Mathematical vocabulary related to spatial sense (ie. up, down, left, right, etc.);
- Patterning/Sequencing;
- Measuring distance;
- Spacial Reasoning;
- 1:1 Correspondence/Counting.

# Mathematics In Music

## Resource #6:

## Wooden Dowels — “Musical Instrument”

Here is where I let you know that despite the fact that I have been a music teacher for several years, instead of spending money on rhythm sticks or drum sticks for simple rhythm activities, I often use craft wooden dowels like this. I actually buy them in different sizes so students can **compare** the size with the sound it makes and because the are so inexpensive, they can even take them home to practice and personalize them. That said, there are really great grooved rhythm sticks that expand the horizons for exploration especially if you make a pairs with one grooved stick and one regular one. Also, word of caution: these are NOT drum sticks and should no be used to hit any kind of drum instrument because they could be damaged! They should only be used to tap against each other or on something that you have tested beforehand.

Here’s a beat and rhythm introduction for those of you who do not have a music background and may need some support with the rest of this post.

In terms of mathematic development, sticks (or clapping) can be explored in a number of ways depending on how you choose to incorporate them into your classroom. They can be used to help students express skills in:

- Subitizing (ie. when in an activity paired with dice);
- Patterning (repeating, extending, or creating patterns
- adding and subtracting;
- Part-whole (ie. if reading music, beats per measure);
- Skip Counting;
- Stable Counting Order
- Mathematical language (ex. comparison);
- and so much more!

For students who have sound sensitivities, I recommend using scarves as a tool to explore mathematics in music.

On the other side of the spectrum, for students who need more physicality and sensory input (grip and vibration) from their instruments, I recommend the following resource…

## Resource #7:

## Boomwackers — Musical Instrument

These hard plastic tubes have been designed to play notes when tapped by an object (like another Boomwacker or “wacked” against the floor. This is a great excuse to take music and mathematics lessons outside to give students some space! There are also numerous visual play-along videos on YouTube like this one. It is amazing how a rhythmic instrument can get more complex when notes are added–especially if you incorporate note changes and co-operative movement.

Here are some of the ways Boomwackers can be used to support mathematic learning:

- Mathematical vocabulary (ie. comparison of tempo, rhythm, beat);
- Sound Sequences/Patterns (ex. call and response, building their own, or extending a pattern);
- 1:1 Correspondence/Counting/Subitizing (ex. recording their songs with objects, dots, or notes as their increase their musical competency);
- Addition/Subtraction;
- Part-whole (reading music);
- Skip Counting (timing);
- Measurement/Introduction of Fractions (ex. exploring length of Boomwackers and how they compare to each other? How does that relate to the distance between notes on the scale? Size of instrument compared to which note is highest/lowest?).

## Resource #8:

## Tap Tap Boom Boom by Elizabeth Bluemle — Picture Book

This book is all about the sights–and particularly–the sounds of a city during a heavy rainstorm. The people in the story run for cover as the weather rages and hide out on a subway platform and the words “tap tap boom boom” repeat throughout the story. Some of you may have used rhythmic books with a lot of repetition like this one to support literacy development. This one could be read with students holding musical instruments to support the storytelling and is yet another way to use sound to foster:

- Mathematical vocabulary (ex. comparison between duration and volume of sounds);
- Sequence/Patterning (ex. some students can do “tap tap” and others “boom boom”;
- 1:1 Correspondence/Counting (ie. Educator can ask: How many times do we use our instruments if the book says “tap tap”?;
- Problem-Solving.

## Resource #9:

## Music Visualizers — Website

I included the gallery for the projects in the link above, but for the purpose of being clear, I am going to talk about this post specifically (screenshot pictured below). This is a great tool to incorporate music and technology in your classroom. Just as the instructions on the right side of image suggests, clicking specific keys isolates parts that instruments play. What is interesting about this song in particular is that the instruments all follow a specific pattern altered very slightly–that’s what makes a song a pattern (as opposed to a round).

Students can either analyze this independently, in small groups or as a classroom minds on and by doing so can explore:

- Patterning in music;
- Adding and Subtracting;
- Sequence and Counting;
- Data management via active listening (ie. how many times does each instrument repeat its pattern in 30 seconds?);
- Measurement (ex. exploring length of Boomwackers and how they compare to each other? How does that relate to the distance between notes on the scale? Size of instrument compared to which note is highest/lowest?).

## Resource #10:

## Garageband — App

Finally, once your students feel comfortable with patterns in music, they can explore overlapping sounds for themselves. Of course, you may do this by allowing your students to create complimentary overlapping patterns of music and perform live, but you may want to allow them to experiment with preset loops in an app like Garageband which is free on Apple devices. It allows learners to compare looped sounds on tracks that they can add or change as they see fit.

This app supports mathematical learning in:

- Mathematical Vocabulary (ie. how many drum tracks compared to guitar tracks);
- Measurement (ie. time/duration of sound/volume);
- Patterning in music;
- Subitizing and Counting (ie number of tracks);
- Adding and Subtracting;
- Data management.

Resources:

Baroody, A.J. & J. L. M. Wilkins. (1999). Mathematics in the early years. Reston, VA: *National Council of Teachers of Mathematics*, (pp. 48-65)

McGarvey, L. M. (2013). Is it a pattern? *Teaching Children Mathematics, 19* (9), 564-571.

*Teaching Children Mathematics, 14*(4), 226-231.

*Teaching Children Mathematics, 20*(5), 310-317.