April Is Math Poetry Month

 

I just discovered that April is Math Poetry Month in addition to being National Poetry Month and Math and Statistics Awareness Week.  The poetry used in class could be either sharing mathematically based poems or having students write their own poetry.

Although it is about half way through April, you still have time to engage in exposing your math students to poetry.  Let's start with some sites that have poetry you can share with your classes. 

One is through the Mathematics Association of America with a lovely page of poetry. Part of the page has poems with a mathematical theme such as Geometry by Rita Dove or types of mathematical poems based on structure with examples.  They discuss the visual poem, the concrete triangular poem, square poems, haiku, and other variations of syllable poems.

The acorn naturalists have a lovely page that discusses the idea that by knowing the mathematical structure of a poem, it should make writing poetry so much easier. They talk about how many of the poems with the rhythmic sing song sound is due to the math of the number of lines and number of syllables in each line.  Then there are the constraints or rules for certain types of poems such as Haiku where you are limited by the 17 syllable frame.

This National Geographic blog has a lovely discussion on how math and poetry intersect written especially for teachers. They provide discussion ideas such as comparing poetic structure with mathematical formulas, types of mathematical poems with examples, and even links.  Everything you need for a lesson on the subject.

If you do a quick search for math poetry, you'll find lots of sites and suggested youtube videos to help you do this in class.  This can show how similar math and poetry are.  Let me know what you think, I'd love to hear.  Have a great day.

Encouraging Persistence In Math Class

 

This year, I ended up working with students who ended up on an online class because their original instructor left early and although certified in math, wasn't comfortable teaching it.  I arrived in time for the second semester and I've had to work with most of them to develop persistence.  They've been learning to complete their work without shutting down and giving up.

In addition, many students are hesitant to try possible solutions if they are not sure they are correct. For some reason, many students believe they should find the correct answer immediately without making any mistakes.  Sometimes, that is a hard attitude to overcome. 

One way is to use low floor and high ceiling problems so that weaker students are still able to do the problem as well as those who are much stronger in math. This type of problem has few skills needed to attack but contains multiple levels of complexity to provide challenge for those who need it.  

Another possibility is to use open ended problems that have more than one correct answer. This tends to confuse students who have always been taught that there is only one right answer and it takes a while to figure out how to answer it.  In addition, this type of problem allows them the opportunity to work through the frustration of finding the right path.  This helps build the persistence needed to work this and other types of problems.

Furthermore, if the problem allows for multiple solutions, it shows students that there is not necessarily a single way to solve the problem.  Students need to know that there maybe more than one way to solve a problem because it encourages students to use their creativity while allowing every student to exercise their problem solving abilities.

In addition, try to set things up so that students feel as if they are not being judged.  It sometimes pays to remove any and all factors that might inhibit students from thinking outside the box.  It makes them more willing to try things they might not otherwise try.  One way to make it easier is to assume students will not solve it and rather than grading the final product, grade the process they used to try to arrive at an answer. 

If you grade it using participation, it means weaker students are more likely to do well because they tried and it levels the playing field for them.  Furthermore, the instructor needs to learn to answer requests of helps from students so they don't give the answer but encourage all students to keep trying.  

One piece of advice is to throw in the occasional easy problem so students don't burn out and being able to solve a problem here and there helps student persistence.  Don't worry if the problem doesn't have anything to do with the topic being studied in class.  The problem doesn't have to.  

Don't be afraid to integrate problems regularly into class time so students get used to doing them.  Once a week is enough but be prepared to have students complain the first few times.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 If the worlds smallest bat, the bumblebee bat, weighs about 1.76 grams, how many bats would you need to weigh 500 grams?

Warm-up

 

If the smallest monkey is the same height as a toothbrush, and a toothbrush is about 7 inches long, would the monkey fit in the palm of your hand?  Explain your answer.

New Math Game At The New York Times

 

Apparently, there is a new daily math puzzle being printed by the New York Times.  It's called "Digits" a daily numbers puzzle. It is available for free right now in the beta version here.

It takes a few minutes to figure out how it works but it is fun once you work it out.  Basically, it gives you a target goal with several numbers that you apply operations to so you get as close to your target goal.

One of my puzzles had a target goal of 195 with the numbers 2, 3,5, 10, 15, 25.  The idea is that I take two numbers and perform an operation.  I might start with 3 x 10 = 30 and the window will show the equation.  Then I might do 2 x 15 = 30 and again the equation will appear in the side window.  I can then take the sums and add them together to make 60. Then I might multiply 25 x 5 to get 125 and add the 60 to 125 to get 185.  I am aiming for 195 so I am 10 off and I can try again.

I decided to try 25 x 5 = 125 and then multiplied the 125 by 2 to get 250.  I multiplied 15 by 3 to get 45 and then did 250 - 45 = 205.  The last equation was 205 - 10 = 195.  Just after I finished the wrong attempt, I realized that I needed to go higher and work down rather than trying to work up. 

For the daily puzzles, there are 5 puzzles you work your way through.  I had 94, 251, 382, and 456, so it starts with the smallest number and works through the numbers up to the highest.  You can earn up to 3 stars for each solution that you make and you do get stars for getting as close as possible.  

I noticed that as long as I do not submit my attempt, it doesn't seem to count so I can use the undo button as many times as needed to go back to the beginning and try again.  I find this helps me eliminate possibilities in my brain. 

This is something you could use in your classroom for older students to help them develop a better number sense.  Give it a try and let me know what you think, I'd love to hear.  Have a great weekend..

 

Examples Of Chat GPT Responses.

 

After writing the entry on Chat GPT, I thought I would share some of them with you so you could see what type of responses you are likely to see. Some have explanations, some don't.  I chose a vocabulary type question, an algebra one, and a calculus one just so you have a better idea of what it can do. I will tell you that I sometimes have issues with it due to how lousy my internet is.

Question - "What is domain and range?"

Answer - In mathematics, the domain of a function is the set of all possible values of the independent variable (usually denoted as "x") for which the function is defined. The range of a function is the set of all possible values of the dependent variable (usually denoted as "y") that the function can output for all the possible values of the independent variable in its domain.

To put it simply, the domain is the set of inputs for a function, and the range is the set of corresponding outputs. For example, if we have the function f(x) = x^2, the domain is all real numbers (because we can square any real number), and the range is all non-negative real numbers (because the square of any real number is non-negative).

Question - Evaluate 5x^2 - 2x + 3 if x = -3

To evaluate 5x^2 - 2x + 3 when x = -3, we simply substitute -3 for every instance of x in the expression and then simplify:

5x^2 - 2x + 3, when x = -3

= 5(-3)^2 - 2(-3) + 3 (substitute -3 for x) = 5(9) + 6 + 3 (simplify exponent and multiplication) = 45 + 6 + 3 (simplify multiplication) = 54 (addition)

Therefore, 5x^2 - 2x + 3, when x = -3, equals 54.

Question - "Find the fourth derivative of sec^2 x.

Answer - To find the fourth derivative of sec^2 x, we need to differentiate the function four times.

Let's start by finding the first derivative:

y = sec^2 x

dy/dx = d/dx (sec^2 x) = 2 sec x tan x

Now, let's find the second derivative:

d^2y/dx^2 = d/dx (2 sec x tan x) = 2 (sec x tan^2 x + sec^3 x)

Next, let's find the third derivative:

d^3y/dx^3 = d/dx [2 (sec x tan^2 x + sec^3 x)] = 2 [sec x (2 tan^3 x + 3 tan x)]

Finally, let's find the fourth derivative:

d^4y/dx^4 = d/dx [2 sec x (2 tan^3 x + 3 tan x)] = 2 [2 sec x (6 tan^2 x + 3 sec^2 x tan^2 x + 3 sec^4 x + 2 sec^2 x) + sec x (6 tan^2 x + 6 sec^2 x tan^2 x)] = 2 [12 sec^3 x tan^2 x + 24 sec^5 x + 18 sec^3 x tan^4 x]

Therefore, the fourth derivative of sec^2 x is 2 [12 sec^3 x tan^2 x + 24 sec^5 x + 18 sec^3 x tan^4 x].

You should check it out and play with it. Head over to chat GPT and explore. Let me know what you think, I'd love to hear.

Chat GPT In The Math Classroom?

 I am sure you've heard of Chat GPT.  It is one of the hottest things out on the internet right now. There are so many ways to use it, at least according to all the e-mails I'm getting from people wanting to sell me training on it.  Yes, I've checked it out for writing things but not really for math. About 80 percent of the time I try it, I can't get a real response.  

Chat GPT is a language model created by Open AI that generates a response to any question typed into the "chat" window because it's been trained to answer questions.  According to what I've read, you can type in a math problem and will receive a response explaining how to solve it. 

One article stated that chat GPT is quite good at performing basic operations such as addition, subtraction, multiplication, and division along with solving systems of linear equations and quadratic equations because mathematical expressions and equations are the central components of mathematics.  It can even solve more complex subjects such as differentiation and trig, depending on the problem, it may not solve it correctly.

I brought up a chat window and asked it a few different mathematical questions from a "what is" to get a definition of a mathematical term, to solving a linear equation to taking the derivative of x^2 and it provided answers for all of them.  It even gave written instructions for each step so if you asked for the steps, all students have to do is copy it down.

According to one article I read, chat GPT may not be able to solve every problem, especially if it is a complex problem that requires a specific method or formula to solve. In addition, it does not always provide the most efficient way of solving the problem, much like a GPS that doesn't always provide the most direct route home.  It also stated that the chat GPT has difficulty solving problems that require a certain level of real world knowledge.

Another article indicated that chat GPT is good for teachers who want to generate new problems that include explanations of how to solve them and additional practice problems of the same type. Since chat GPT is a language model, teachers should check any problems and examples formulated by this AI to make sure they are correct. In addition, it has been suggested that students read explanations formulated by chat GPT to check for logic and any fallacies. 

I know there is a fear that students will use this digital product to do homework but if you as a teacher use multiple and frequent assessments, it becomes quite obvious they are copying rather than trying to learn the material based on their answers.  Let me know what you think, I'd love to hear.  Have a great day.