“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.

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.

 

Ten Webites I Check Before Starting Every Unit

There are many excellent resource sites out there with inspirational teachers making great resources. However, when it comes down to it, there are only a handful of websites I check on a very regular basis. To make it to this list, I am generally looking for tasks that:

• Are ‘low floor/high ceiling‘ giving access and challenging everyone at their own level
• Have multiple approaches, giving students room for creativity
• Are challenging and hence interesting
• Will give me permission to teach skills
• Make skill practice, more interesting
• Have a story for students to follow

There are many activities out there that fit these descriptions, but there is only so much time in the week. During breaks I have more time to explore but these are the sites that I can check quickly with high yield for your classroom (in no particular order):

1. Mathematics Assessment Project – A website produced from a partnership with the Shell Centre (University of Nottingham, UK) and the University of California at Berkley. Here you will find tasks that will help the common core standards come alive in your classroom. Full of rich activities that encourage discussion and investigation.

2. Standards Unit – This has been around for a while but is still one of the first publications I look at and is close to my picture of what mathematics education should like. A rich, dense set of activities that will give you great ways to work on various skills and topics.

3. YouCubed – A relatively new site that has come out of Prof. Jo Boaler’s (Stanford) efforts to encourage the ‘growth mindset’ in the classroom. I am interested in anything that comes from the idea that anyone can be good at math.

4. Open Middle – I came across this site relatively recently and am sad that I didn’t find out about it sooner. it’s tag-line is: ‘Challenging Math Problems Worth Solving’ and tips the proverbial hat to the school of thought that says that you don’t need to have tenuous links to real world problems in order to get buy-in from students. It appeals to the problem solver in all of us.

5. Emergent Math – With its routes in Problem Based Learning (PBL), emergent math is useful not only for those who want to tear up the textbook and start again with an integrated curriculum, but also for people who just want great projects that they can slot into their established curriculum. Lots of links to sites not mentioned here so worth a look.

6. Mr. Barton Maths – Lots of great resources and activities that will make your classroom a more interesting place. Enough said.

7. Tarsia – Sometimes students just need to practice. There I just said it. But using Tarsia you can avoid ‘death by worksheet’ and get students to practice without really realizing it. It also great for discussion and you can tell very quickly if students have answered everything correctly or not. For more, see Why I Love Tarsia.

8. NRich – Great site for ‘low floor/high ceiling’ problems that will challenge anyone in your classroom. Students may like to explore this outside the classroom, too. Sortable by topic and I believe they are coming out with a common core curriculum map, quite soon.

9. Dan Meyer 3 Acts Spreadsheet – Act 1 –  You show a video or picture prompting discussion, prediction and estimation as well as the all important step of coming up with the variables that are to be investigated. Act 2 – Students get the information they need to solve the problem. Act 3 – Once students have solved the problem in various ways and presented you show them the solution. There is a lot more to it than this and to pull these lessons off well is a true art form. But the only way to get better at these is to try them. So try them! More info here.

10. Mathalicious – Math lessons based on the real world problems. $185 for 12 months subscription (I think currently they are also doing pay-what you can) but well worth it. Excellent for creating the need for the math you teach.

It takes me around 90 minutes to trawl through these websites at the beginning of a unit but is well worth it when it comes to lesson planning and I know half of the activities I am going to do already. As with any of these activities they will need to be (and should be) adapted for your classes and situation but they provide an excellent starting point from which to plan.

What websites are a must-check when you are planning a unit? Leave a comment, below.

The Great Wall of Questions

Any strategy that raises the level and status of questioning in my room is useful. I found that there were times when a student asked a great question but that it was just no the time to go into that topic too deeply. I have also found that there are times when I have a 5-10 minutes gap in my lesson where these topics would fit into nicely.

The Great Wall of Questions is my attempt to solve these two problems at once. If a student asks a great question, then I proclaim ‘get it on the board!’ to the delight of the person that asked. They know that if it goes on there I think it is an important question, one that is worth thinking about for a longer period of time. When there is a good moment I will take a question and try to get students thinking about some answers or at least ways to find the answers (I am going to avoid just answering the questions as much as I can). Here are the rules:

• A question only goes on the board if it has come out of genuine curiosity (rather than an attempt to get their name on the board)
• Their name goes with the question and the color of the stickie determines which class it came from
• When the question has been addressed (different from answered), a small dot goes on there so we can see what needs to be looked at in the future.

I only have four questions on there so far this semester (after 8 school days). I am hoping that by the end of the semester the board will be full. Here goes….

Summer Reading 2014

Summer is rapidly approaching. A great time to reflect and decide what I want the next 12 months to look like. Time is precious and I want to read books that will not just improve my philosophy but that will help on a day to day basis. I am currently looking forward to devouring these two books:

I’ve been thinking a lot this year about how to teach my students how to learn, how to think for themselves and direct their own learning. I’ve skim read ‘Making Thinking Visible’ before but I’ve been looking forward to going through this with a fine toothed comb and extracting every word of worth from its pages. The philosophy statements in the first couple of chapters is worth a read all on its own. It seems clear that students who can name and show their thinking processes do a lot better than those that just go with the flow. I would like my classroom to foster the former. Thoughts to be blogged/tweeted as I go along.

This is the other book I’m really looking forward to going through. It has come highly recommended and anything that is going to help me become better at asking questions and promoting debate and discussion is worth a look. I haven’t even opened this yet so watch this space for highlights online and in my classroom.

Because LeCarre is amazing.

What will you be reading this summer? Any recommendations?

 

Virtual Filing Cabinet 1.0

I trawled, I tweeted, I tried to find the best of what was out there. I have posted the first draft of my virtual filing cabinet here and in the process, learned the following:

• There are so so many great lessons and activities out there!
• There are far too many to include them all
• It is hard to choose which ones to include
• There are some incredible teachers who I would like to be more like
• I’m really excited about trying just a handful of things I found
• I want to do a lot more project based lessons
• This is a working document and will evolve with my teaching

If you haven’t already I highly recommend you trawl some websites and create one of these yourself. Chances are, it will be unique to you and your teaching style and philosophy. Here is a list of websites to get you started. 

Let me know if you think there are any glaring emissions.

What my students think of Khan Academy

Recently, I used this and this Khan Academy activity to test my students’ understanding of graphing inequalities as part of our Linear Functions Unit. Having not broadly used KA before, I wanted to gauge my students’ reaction and try and work out if I should use it more regularly to give me and the student, good feedback. After the activity, I gave a quick Google Form Survey to ask my students what they thought. The results are below:

Other student comments included:

I think this really helps envision the problem, and it really helped me. I would thoroughly enjoy doing this again, although it is kind of hard to maneuver around on it.

I liked the system, but I really hated the fact that we had to get three right in a row, because if you accidentally make a mistake, you can’t go back, you’ve just permanently failed.

It was good for practice but too easy to make technical mistakes. Graphing is harder to do on Khan academy.

This feedback, coupled with talking with students during the activity told me these things:

• We are a Bring Your Own Device (BYOD) school with many varieties of device. Laptops were fine but some tablets were pretty difficult to use with KA. It was hard to move things across the screen
• The instant feedback is awesome and students really enjoyed/were frustrated at (in a good way) knowing immediately whether they got things wrong or right.
• I think in the future, I will mainly use KA for homework where students can do things at their own pace and use their home computers rather than tablets.
• The idea is great but I’m going to have to think about the most useful way to implement it as part of the wider experience, for the student.

Have you used Khan Academy in the classroom. Any good tips on how it can be integrated without the frustrations above?

Seven Squares – The Essence of Mathematics

This post is my attempt at being part of the ExploringtheMathTwitterBlogosphere community.

This week (or last weeks) challenge is to post your favorite rich/open ended math task.

Without doubt mine is nrich’s Seven Square’s problem. To my mind, this captures the essence of what mathematics is all about: Patterns. I love starting my Algebra 2 course with this to give them a sense of why we do the Math.

In class I will give each group a set of toothpicks. Some use them, others go straight to the drawing but all seem to get into it at their level/pace straight away. It’s amazing what comes up from students of all abilities.

A great extension to this is Dan Meyer’s toothpick activity. There is no end to shapes that students can investigate. It is one of those ideas that is great for all ability levels and really does help when you are dealing with the content skills throughout the course. I find that I refer back to this lesson, often.

What I learned from Dan Meyer

Yesterday I realized, many of my students are currently motivated by the threat of:

• Getting a bad grade
• Not getting into college
• Getting yelled at by parents.

This is not good. In my mathematics classroom I would like my students to be motivated by a need for math, a hunger for math. I want them in a position where they are begging me to give them the mathematical tools they need to solve problems. Yesterday, I came a little closer to understanding how to get to this point by attending a conference given by the inspirational educator, Dan Meyer.

He has pioneered what are known as the 3acts lessons where students are presented with a photo or a video that inspire questions leading to a multilateral problem solving environment. I’m not going to go into detail here; I just wanted to share one or two thoughts from the day.

There is a common theme throughout his videos and that is the word ‘per’. How does one thing change with another? Miles per hour, Mass per Volume, hot dogs per minute. This is the heart of mathematics and something we all meet every day. Present a problem with changing variables (without just giving them what they are looking for) and you are presenting them with a problem that will need mathematical modeling to solve.

The difference is, whereas in textbooks, all the information is given to you at the start, in Dan’s lessons, hardly anything comes from the teacher. A nugget of information here and there to aid the process and to give something for the students to use, but mainly it is the students that have to identify variables, come up with the process in order to solve the problem (that they came up with) and hence make conclusions, with no mention of standards at all. What an amazing process!

The whole thing is a great validator also. With a lot of space for making predictions and coming up with ideas, the glory is not given to ‘the clever one’ but to those who make the effort of contributing. Every student has intuition.

Finally, I learned that Dan Meyer is human. I’ve been to conferences before where you leave feeling bad if you are not producing every lesson based around super rich tasks with resources that take hours of pain staking work to produce. Dan agreed that sometimes lectures are needed to fill in the gaps, that time needs to be spent preparing students for specific standardized assessments and that teachers often have little time with which to work. This was refreshing.

What was inspirational about yesterday was that this was not a plan to change everything about the way I teach. It was about elegant strategies to introduce the need for and the process of mathematical modeling; to create the hunger for the mathematics so that students then want to know how to e.g. divide rational expressions.

Good math is like a good movie; you know the point throughout the whole thing.

I’m really excited to give these lessons a try.

The three acts lessons mapped with common core standards can be found here.