“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.

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Thoughts? Write your response in the comments section below.

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.

The Desmos dashboard makes it very easy to glance at students’ progress

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.

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:

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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.

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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!

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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.

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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.

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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.

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Visual Patterns and Coding – Part 1 – Linear Relationships

I have been running a ‘visual pattern’ every week with my 6th grade (pre-Algebra) classes. You can read more about this here.

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.

 

Gapminder is Awesome

I wanted something that would open up the world of scatterplots to my statistics students; something where they could really get a sense of correlation and causality. I decided to do a project based around the fantastic GapMinder World and it payed off.

First I showed this video of the master Hans Rosling at work with the graphs his foundation came up with.

I then gave these instructions to my students:

You (and max one other person) are to prepare a 3 minute presentation on a GapMinder graph of your choice.

Instructions:

• On a computer go to the gapminder website by clicking here
• Play around with the explanatory and response variables until you find two that you think show some sort of relationship
  • If you are struggling to find variables with a link, click ‘Open Graph Menu’ and play around with graphs that have already been created.
• Your presentation must include answers to the following questions
  • What are your explanatory and response variables?
  • What is the link between variables at the start (before you click play)?
  • What do you notice happens over time?
  • Are all the countries close together or more spread out? What does this mean?
  • Are there changes to any particular country that are of interest to you?
  • What if you isolate by continent? Are there any changes that are of interest to you?
  • Is there anything else that stands out with your graph?
  • Are there any outliers to the trend?
  • Does this graph bring up any other questions that you would want to investigate further? What information would you need to answer these questions? Is this information available?

Your presentation must include the time series animation (when you press play) as well as PowerPoint slides using screen shots of points of interest.

You will be graded on:

• Content (out of 6)
• Presentation (out of 4)

What went well

• This was a great way to get across a sense of scatter graphs and will be awesome to segway into taking about correlation and causality.
• This was enjoyed by the students and really got them thinking about statistics and global affairs
• It was good to give specific questions for the students to answer. In my experience just saying ‘present for 3 minutes on a graph of your choice does not give great results’

Even Better If

Next time I do this, I think it would be good to model what an excellent presentation looks like. I missed a good opportunity to teach this skill.

Desmos is Awesome

I love Desmos. I love how user-friendly and clean the whole thing is. I want my students to love it too, so I used the first lesson back after midterms to let them play.

The Aim

For my students to get a feel for the shape of various functions and relations through using Desmos to create a piece of art. (CC Standard F.BF.3)

The activity

• Students take a look at http://www.desmos.com/art to see what is possible just by typing in equations (Great hook)
• I explain to students that they have this lesson and a homework to come up with a piece of art of their own using desmos.com/calculator.
• I have a sheet ready with some example functions (linear, quadratic, circular relations, radical and rational) for them to use if they are struggling. I also introduce the idea of sliders for them to use.
• They have around 50 minutes plus a homework to come up with a piece of art of their own.

 

Some of the resultant artwork

What went well

• Any lesson where students are crying out for the Math is a good thing. It was amazing to be asked how to draw a smiley face using a parabola and domain and range and how to draw circles and ellipses. I had one student ask how to do a ‘diagonal porabola!’ I had to look that one up.
• Students were constantly engaged. Sometimes frustrations got the better of them and they needed some encouragement to keep going but generally, the lesson went really fast.
• It was great for all abilities. Students that normally struggle got the chance to play around with linear and quadratic functions, helping them to understand what changing the numbers did to the graph.

Even better if

• This was too early in the year to do this lesson. I would like to do this next time at the end of the year when students had more functions and tools at their finger tips. I did like how it cemented the need for domain and range, though.
• This lesson is leading into our quadratics unit. Going back I would have really liked to focus far more on parabolas so that our next lesson on Vertex Form would make sense from the start. I still think it will help, I just think I may have missed an opportunity to go deep rather than broad.
• This lesson relies heavily on technology. Being a Bring-Your-Own-Device school, some students had tablets that were very tricky to use (this also happened with Khan Academy). I may have to rethink how I do this and use it possibly for homework.

Student Reaction

Here are results from a mini survey I did at the end of each class

Students also said:

This activity allowed me to visualize what adding variables does to the shape of an equation.

I loved the creativity involved with it, but also the brain work involved when trying to make different shapes and move them around.

Technical difficulties were frustrating, but I realize this is something that is hard to fix.