A British Math(s) Teacher now living in Indianapolis, USA, aiming to show my students how questions are often more important than answers. Presenter of the 360 Podcast, the MathEd Out Podcast and contributor for the Guardian Teacher Network.

# “Hey, ChatGPT: Write me a blog post about how to effectively use ChatGPT when teaching Mathematics”

Disclaimer: The following is written by ChatGPT

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Mathematics is one of the fundamental subjects that many students struggle with. As a language model trained by OpenAI, ChatGPT can be a useful tool for educators to help their students learn math concepts effectively. In this blog post, we will discuss how to use ChatGPT to teach mathematics.

1. Use ChatGPT as a math tutor ChatGPT can be an excellent math tutor for students who need extra help. By using natural language processing, ChatGPT can understand student’s questions and provide answers in an easy-to-understand way. Students can ask questions on various topics such as algebra, geometry, calculus, and ChatGPT will provide accurate answers.
2. Use ChatGPT to explain difficult concepts Math can be a difficult subject, especially when it comes to understanding complex concepts. ChatGPT can help teachers explain difficult math concepts by breaking them down into simpler terms. Teachers can input complex math problems or equations into ChatGPT, and it will generate step-by-step explanations. This will help students understand how to solve complex problems.
3. Use ChatGPT to provide practice problems Practice is essential in learning math. Teachers can use ChatGPT to provide practice problems for students. Teachers can input a specific type of problem, and ChatGPT can generate multiple variations of that problem. Students can then practice solving these problems and get instant feedback from ChatGPT.
4. Use ChatGPT to provide real-world examples Students often find it challenging to connect math concepts to the real world. Teachers can use ChatGPT to provide real-world examples that students can relate to. For example, ChatGPT can provide examples of how algebra is used in finance, or how geometry is used in architecture. These examples will help students understand how math concepts are used in the real world.
5. Use ChatGPT to keep students engaged Students often find math boring and uninteresting. Teachers can use ChatGPT to make math more engaging for students. ChatGPT can generate fun and interactive math games that students can play. Teachers can also use ChatGPT to create math challenges for students to solve. These challenges can be used as part of a classroom activity or homework assignment.

In conclusion, ChatGPT can be an effective tool for teaching mathematics. By using ChatGPT as a math tutor, explaining difficult concepts, providing practice problems, providing real-world examples, and keeping students engaged, teachers can help students learn math concepts effectively. As a language model, ChatGPT can provide accurate answers and generate engaging math activities that will make learning math more enjoyable for students.

# Thoughts after Two Months of Using Illustrative Mathematics Alongside the Desmos Curriculum

It was time for a change. Our middle school needed a new curriculum that would meet the needs of our students and provide a rich and engaging environment to learn 6-8 Math. After spending months sifting through various curricula, with a little help from edReports, we were able to identify Illustrative Mathematics (IM) as the lead contender. It was not long before we discovered that the Desmos online platform followed the IM scope and sequence very closely and that they had the potential to be an amazing complement to each other. We are now two months into using both platforms and I can honestly say we are not looking back. So, I wanted to write a brief summary of what we are seeing after the first two months of using these curricula.

## 1) They are amazing together

The two platforms complement each other well, not only in sequence, but in the way that Desmos is designed with IM and OpenUp in mind. You can find complementary lessons for each topic and you can decide which lesson makes the most sense for your students and your own sequence. The material is engaging and the learning is rich.

## 2) There is a lot of material

Sometimes too much. In the case of IM, there is a lot to cover in a 50-minute lesson, and I often have to cut some of the material to ensure I spend enough time on the main ideas. I know they have to cover enough to meet state standards, but I regularly find that I need to skip certain lessons just to get through a unit in time to move on. Desmos is often closer to being able to get through all the activities in a useful and timely way.

## 3) They are truly discussion based, in the best way

In the last two months, I have had some of the best conversations I have ever had in my classroom. Students have been engaged and interested as IM and Desmos use prompts such as “which one doesn’t belong”, “what went wrong”, or “which student is correct?”. These are rich conversations that spark curiosity and help my students consider the mathematics from various angles. It is a more creative and interesting way to think about mathematical ideas and it has been amazing to see students engaging with ideas they have never considered. IM pledges that “selected activities are structured using Five Practices for Orchestrating Productive Mathematical Discussions (Smith & Stein, 2011)” and I believe it. Their prompts are excellent and I am already seeing deeper understanding as a result. As a side note, my students are huge fans of Desmos’s polygraph activity (the mathematical version of ‘Guess Who’) and this has seen some amazing results. They also enjoy the opportunity to create a challenge for a classmate (as long as they can solve their own problem first) and this has them engaged for significant periods of time.

## 4) The formative assessment you get through Desmos is unbeatable

I generally aim to know what every student is thinking at least 2-3 times during a lesson and Desmos makes this very easy to do. With its custom dashboard, it gives you the power to view all student activity and provide individual feedback to students. You can display student work on the screen and anonymize the screens to avoid embarrassment. You can compare answers with their screenshot function and instantly glance over the whole class’s level of understanding.

## 5) IM is free and Desmos is very affordable!

At this point, I don’t understand why every school in the country is not jumping at the chance to use IM. It’s free and completely customizable. I have known some curricula to be prohibitively expensive and the idea that IM is completely free and a rich mathematics curriculum makes it a no-brainer to me (although you do have to pay the publishers if you want the extra workbooks etc). Desmos is also affordable compared to many textbooks and I would highly recommend this if your district has the resources.

In conclusion, barring an altogether different experience in future units, I would wholeheartedly recommend the IM/Desmos combination. With the richness of IM, coupled with the complementary manipulatives and discussions coming from Desmos, I have every hope that our students are going to fly. But, granted this is only two months in, and I could be completely wrong. I somehow doubt it.

# 360 Podcast – Brian Simmons on Mindful Teaching and Learning Through the COVID Pandemic

Welcome to the first episode of season 3 of the 360 podcast! In this time of returning to in-person instruction during the global COVID pandemic, we chat with Brian Simmons, a mindfulness teacher and educational leader from Manhatten, NY. We discuss ways that we can use mindfulness and meditation to help us teach and learn well through this uncertain time.

“I was an award-winning writer/producer for Comedy Central, and was suddenly struck down with a 10-year debilitating illness that changed my life trajectory. It sucked, but it was totally worth it.

Along the way, I learned very deep lessons about how Mindfulness and ancient wisdom can help a person exactly when they need it most – when life doesn’t cooperate. Today, I am an educational leader and mindfulness teacher in NYC, and I use this experience to relate directly to real people with no time for nonsense.

Regardless if you are a skeptic, seeker, educator or student of any age. When I was first introduced to meditation culture in the 90’s it made me cringe. It still does sometimes, but the practice of Mindfulness changed my life. And, it blew my mind. I believe it will do the same for you.

I’ve spent decades practicing fiercely with some of the best meditation teachers on earth. I’ve completed teacher training at the Center for Mindfulness at UMASS Medical College and am a graduate of the Community Dharma Leaders program at Spirit Rock Meditation Center in Woodacre, CA. I also serve on the teacher’s council at NY Insight Meditation Center in Manhattan and am a meditation teacher on the 10% Happier App. I’ve learned powerful techniques and perspectives that work, and I love sharing them with people.”

Mindfulness in Education

Navigating Life Changes

#### Help Us Spread the Word!

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# Connection and Reflection: 5-ish Tools for Teaching Mathematics During the COVID-19 Pandemic

#### This is hard.

I’m planning out my start of year classes and it’s just beginning to hit me that I can’t do group work in the same way, and I can’t walk around the class in the same way, and I won’t be able to help a student in quite the same way. Students will be wearing masks, and will be sitting 6ft apart. With a strong belief in learning being a social activity, this semester is going to be like no other.

However, my priorities remain fairly consistent, although how it looks will be different this year, especially as I may need to be able to pivot between in-person and virtual learning for the foreseeable future. They are:

• To give the students a positive and engaging experience of learning mathematics
• To help students learn collaboratively
• To help students to become learners, reflecting on their own progress and being able to adapt accordingly

In summary, my priorities for the year, whether in person or through the computer, are Connection and Reflection.

Connection: This will be especially true if we end up going fully online, but the more ways the students can connect with each other the better the learning will be.

Reflection: This has always been important, but in a time where we can not really meet with students one-on-one, we have to get creative in terms of helping students to reflect on their own learning.

Here are some tools that I will be using for student connection and reflection in the coming weeks:

## Flipgrid (Free)

Flipgrid is a k12 social platform where students can share videos with each other and with their teacher in a safe and transparent way. This is a great tool for general introductions, class social interactions, or creating reflection videos for assignments.

Marco Polo (Free) is a good alternative, too.

## Desmos Activity Builder (Free)

With some phenomenal options for sharing thinking between students and giving teachers full access, Desmos Activity Builder is a must-have in the connected math classroom. You can use one of the pre-designed activities from Desmos or other teachers (use this google search for better results from other teachers), or you can design your own from scratch, or using their hugely helpful templates.

They have taken follow-up discussions to the next level with tools to show aggregated and individual responses, as needed. You can anonymize names, or show named responses.

Desmos has put together some great webinars for you to get quickly up to speed on how it all works. And, it’s all completely free!

## Diagnostic Questions (Free)

Designed by Mr. Craig Barton himself, Diagnostic Questions is a free tool that will give you some great data from multiple choice questions that you can set for students. I like that this software has the option to ask students to submit a summary of their thinking and not just to click on the ‘correct’ answer. This tool is easy to use, set up, and is completely free, giving you a lot of information on student mastery.

ASSISTments is a similar program that is more US based questions.

## Classkick (\$7.99/mnth for Pro Account)

I reviewed Classkick a while ago, and although I haven’t used this for a while, it could be a great way to seamlessly transition between in-class and virtual learning. You can see all students working live on an assignment, giving them live feedback. There is the option for students to help other students, and with a pro account, you can export grade data, as needed.

When it is difficult to walk around the class room in the same way, Classkick is a great way to see everyone’s thinking without having to rely on multiple choice questions.

## Padlet (from \$12/mnth for education account)

Padlet is a great way to organize student responses in a variety of formats including pictures, video, and typing. Useful for both in-person and at-home learning, it is a great tool for students to share ideas with each other, to work on a project, or to post questions. You can also see which student has viewed what if you need to ensure that everyone is engaged.

I hope this list helps you to start the semester/term well and for your students to feel connected and enjoyment in their learning. Feel free to write a comment below if you know of any tools that are a must-check-out for students to connect and reflect in the coming weeks.

# What makes a growth mindset math game? Hint: Avoid worksheets in disguise!

If you were to search for the term ‘math games’ on google, you would get instant access to many sites where you get the chance to practice skills in the guise of a ‘fun game’. For example, in the game Candy Stacker, you get to practice pretty much any skill in any grade and it stacks cake on top of an animal until it reaches a candy. As with many of these games, it is timed, and you ‘fail’ if you get on wrong. These types of games reinforce the fixed mindset that is so often observed in mathematics classrooms.

There are better ways of building fluency and understanding of number. Number talks and Formulator Tarsia are just two great examples. But, are there activities out there that both have that gaming element, and help build a deep understanding of number while promoting a growth mindset, that depth is more important than speed? Thankfully, yes, and here is a list of growth mindset games that I love my students to play, either in a dedicated lesson or in those moments where you have 10 minutes spare. None of these will have timers or ‘fail’ notices. (Note: There are many great card, board, and paper games out there, but I am going to focus on online interactive activities for this post). Click on the images to go to the game itself.

## Factors and Multiples (nrich)

This is probably my favorite of all, building sense of multiplication tables, but students also quickly come to realize that prime numbers are key in this game.

1 Player version: What is the longest chain you can make, clicking factors and multiples of the previous number (see the example in the picture). What is the longest chain that anyone can make? Are there numbers to be avoided at the beginning? Are there good numbers to start with at the beginning?

2 Player version: The winner is the person that can force the other player not to be able to build on the chain, cutting off all possible factors and multiples. Again, are there good numbers to start with? What are the key numbers to minimize the chances of losing the game?

## Connect 4 Factors (Transum)

Another fantastic game to build a sense of numbers, factors and multiples. No timer necessary!

One Player Game: Fill the game board with the counters from both boxes. Avoid lining up four numbers with a common factor (other than one).

Two Player Game: Each player has a box of counters to choose from. Take it in turns to drop a counter into the game board. The winner is the first to line up four numbers with a common factor (other than one).

## Broken Calculator (author unknown)

There are probably other versions out there but this one is the best I have found, even if is relatively basic. The idea is simple: Can you get the target amount using the keys on the calculator that are working. The levels get increasingly difficult, and it is a great way of building a sense of operations.

## Double Take (Transum)

Similar to the popular game on mobile devices, this game builds a sense of base-2 numbers and exponential growth. This one is a favorite with the students. Try to encourage your students to think of and discuss strategies to get further than you would by just trying different ways.

## Got it! (nrich)

A simple game with less than simple strategies. Once again, try to steer students to thinking strategically. Is there a better addition to start with? Is it better to go first or second? If you want a more challenging version of this game where you can’t choose the option that your opponent last chose, you could try transum’s 23 or bust.

## Square it (nrich)

Not a number game, but a great strategy game nonetheless. Students can play either another person or the computer. They must claim all 4 corners of one square to win. Can blue always win? Is there a way to force this every time? What is happening in the middle of the game? What does the end of the game look like?

I hope you enjoyed reading about these growth mindset math games. What are your favorites? Comment in the section below.

# How to Create Your Very Own Math Ed Search Engine

Inspired by Robert Kaplinsky’s Problem-Based Learning Search Engine, I decided I wanted to create my own based on my favorite websites to check before starting every unit.

The process is very simple but at the end of it, you come out with a search engine that will only search websites that you decide are worth including.

Here is a step by step guide to creating your own.

### 4) Give your search engine a name and hit ‘create’

And that’s it. From that point, you can bookmark the search engine, or embed the code into your website. Enjoy! Do share your URL in the comments.

# MathEd Out Event: Going Deeper

The MathEd Out Podcast

### Covenant Christian High School, Indianapolis, IN

The first and second MathEd Out Events were so successful, we are doing it all again! Don’t miss out on your chance to meet with others who are passionate about being the best high/middle school math teachers they can be.

##### The morning will feature:
• Time for delegates to share ideas and top resources with table discussions including:
• Using rich tasks to deepen understanding
• How to go deeper with simple ‘skill practice’
• Discussions with course specific groups (Algebra 1/Geometry etc)
• The popular ‘resource symposium’, sharing all the resources we love best

There are just 60 places for this event. Register soon to avoid disappointment!

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# Ep. 13 feat. Robert Kaplinski on Rich Lessons and Going Deeper in Mathematics

The MathEd Out Podcast

Robert Kaplinsky has worked in education since 2003 as a classroom teacher, district math teacher specialist, and University of California Los Angeles (UCLA) instructor.  He graduated from UCLA with a Bachelors of Science in Mathematics / Applied Science (Computer Science) in 2000 and earned his Masters of Education in 2005.

He has presented and conducted professional development at across the United States and Canada.  His work has been published by Education Week (20122015) and the American Educational Research Association (AERA).  He has consulted for major publishers including Houghton Mifflin Harcourt and Pearson.  Robert is a member of the National Council of Teachers of Mathematics (NCTM), National Council of Supervisors of Mathematics (NCSM), California Mathematics Council (CMC), Orange County Math Council (OCMC), and Greater Los Angeles Mathematics Council (GLAMC).  He also co-founded the Southern California Math Teacher Specialist Network, a group that includes over 170 math teacher specialists from…

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# Visual Patterns and Coding – Part 2 – Exponential and Inverse Relationships

Once we have got to grips with the basics of using python to create ‘visual pattern calculators’, it is time to take our thinking to the next level. Up to now we have only been looking at linear relationships with a straight line graph.

The visual pattern above is a quadratic relationship as the pattern grows in a linear fashion in two directions (It’s useful to talk separately about the width vs. length and then bring them together). The nth term is either (n+1)^2 or n^2+2n+1. Can you see both in the picture?

Let’s pause for a second. In 6th grade, I can use visual patterns to introduce the idea that a quadratic has two linear factors! I had HS seniors that struggled with this idea. I love this!

Next comes the coding. Again, we use CodeSkulptor to ‘skulpt’ our function in three lines: Input, Function/Output, and the display output command. The difference in this is that for exponents we have to use **.

OR:

Also, I get the students to Desmos to see if their prediction of the graph are correct. This brings up great discussions about why the graph is the shape it is in quadrants two and three.

OR:

I have also introduced the idea of an inverse function; using python to create a function that would enable us to answer the question: What step would contain 400 blocks? This forces the student to consider inverse operations and the fact that order matters. Here is the code (python reads from top to bottom so you can include this all in the one program):

The benifit of this has been less about coding or nth term and more about introducing the composition of functions. It also enabled me to run some rich lessons on the topic of ‘Straight Line vs. Curvey Lines – Who Cares’ exploring linear vs. exponential relationships with finance and population growth.

The effects of this series will not be truly measured until these students take Algebra, next year. However, my hope is that this will have given them a solid foundation for many of the concepts that they will study in the coming years. We’ll see…

# Visual Patterns and Coding – Part 1 – Linear Relationships

To bridge the gap between pattern and function and following an online course I took with Rice University, I have started to introduce some basic coding. Python in particular. Even after one lesson of using coding and graphing, I have been able to have rich conversations about the differences between functions, input/outputs, the shape of a graph and the y-intercept. Here is the process I have taken them through:

Part 1: Have the students run through a basic (linear) visual pattern (from visualpatterns.org) using this sheet and reviewing using this slide:

The nth term for this pattern is 4n+1.

Part 2: I now challenge them that we can create a calculator for this pattern using the Python coding language. I use the free python interface CodeSkulptor (from Rice University) to do this. I take them through step-by-step with some great conversations about functions and inputs/outputs.

The nice thing about CodeSkulptor is that when you hit the save button, it creates a brand new URL meaning that each student will have their own URL to post and share.

They can then change the input and see clearly what happens to the output.

(Note: Lines with # are ignored by the interface)

Part 3: They then go to the Desmos Online Graphing Calculator and input the function y = 4x+1 to confirm or deny their prediction for the graph shape, from the start of the exercise. This is a great opportunity to talk about ‘step zero’ (as well as step -10 etc.) and why they graph is the shape that it is. I feel it is also important to stress the difference between 4n+1 as an nth term and y=4x+1 (which includes everything in between).

Their homework is simply to follow the steps with a different (linear) visual pattern and to share their CodeSkulptor URL’s and Desmos screenshots on the class’ wiki page.

For student assistance I created this video:

Where Next?

There are two main places that I would like to take this:

• Exponential functions
• Inverse functions

I’m really excited about where this journey will take us. My hope is, that as these students start Algebra proper, next year, they will have a strong sense of functions graphs and their connections with patterns and geometry. Here goes…..

Have you done anything similar? I would love to hear your ideas/thoughts in the comments section, below.