Does An App Like Photomath Have A Place In The Classroom?

I know that many students use certain apps like Photomath to help them complete assignments but most of the students I know who have done this?  Well they didn't learn the material.  I can tell who has used it because their homework is 100% but on the assessment, they bomb all the problems.  Fortunately, there are things we can do as teachers to use such apps and help students learn the material at the same time.

In this column, I'll use the Photomath but it is only one of several apps that operate in the same way.  You  use the app to "read" the problem and it provides all the steps to show how it was solved and at the end, you have the correct answer.  It is too easy to just copy the material down without thinking.

I've done some reading up on this topic because I want to allow students this choice but I want to make more of a learning experience, especially as I know certain students will be doing it. It's the old, choose your battles so why not acknowledge some students will resort to apps so they do well and because they struggle. 

When you are ready to introduce a new topic, consider using Photomath instead of the example in the textbook. To prepare for this, select the problems you want to use ahead of time so you can determine where possible misconceptions will happen, where students will have trouble, and places students will need clarification.  The nice thing about having all the students using the same app is that you do not have to write all the steps down on the board, instead you can project the results.  Once you have students all on the same problem, you can walk them through the steps needed to solve the problem, pointing out everything they need to know or think about.  

Another way to use Photomath is to have students work in small groups.  They look at the problem and rather than going straight to the answer, they learn to look at the structure and focus on different ways to solve the problem.  For instance, students might start with a problem like 3(x + 2) = 24. Photomath may start by distributing the 3 across the (x + 2) to get 3x + 6 = 24 and go from there but in this problem, you can also divide both sides by 3 to get x + 2 = 8.  Both methods work for this problem.

Furthermore, some apps allow a person the option of looking at more than one way of solving a specific problem.  For problems that fall into this category, have the students look at each of the methods and then discuss which method they believe is the best choice for this problem.  They can also do a compare and contrast of the different methods to see how they differ.

Furthermore, have the students work on a few practice problems and when everyone has completed the assignments, let them use Photomath to make corrections but they aren't just looking at the answer.  They are looking at the process they used to solve the problem.  They are looking for to identify the missteps the made in solving the problem.  This is a great place for a three column sheet.  The first column is where they do the problem, the second column is for the corrected version and the third column is where students explain what they did incorrectly and what they should have done.

It is fine to let students use Photomath at home to correct their homework but they should always take the time to figure out where they made a mistake and what they should have done to be correct.  These are several ways students can use Photomath or similar app in class to help with their learning. It is important to reassure students that making mistakes is just part of the learning process. If students are willing to do an error analysis for problems they miss, they will learn more.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 

If a pound of small cucumbers contain 6 cucumbers and each cucumber can be sliced into 23 pieces, how many slices will be in half a pound?

Warm-up

 If takes half a pound of cucumbers to make one pint of pickles, how many pounds of cucumbers will you need to make a gallon of pickles?

Setting Students Up To Do Well.

For many people, school has started and for others, it will be starting soon.  With students already in and out due to COVID, it is important to establish a framework to help students do well in Math.  It is important to set things up at the start of the year.  

Look at doing something a bit different on the first day of school.  Instead of going over the syllabus, assessments, etc, look at laying down a strong support system, listing expectations, and try to get them excited and inspired about math for the year.

Admittedly, many students arrive in class with the attitude that they just can't do math because they aren't good at it, they inherited their parents ability to struggle, or other similar belief and it is important to change their minds.  They need to believe that they and anyone else can do math. In addition, they need to know that it is ok to both struggle and make mistakes.  They should accept that making mistakes is an important part of learning. So start the year with an activity that can help them change that belief.

One should also create a classroom where children feel included. This means that trust should be built between the teacher and students and that you care for them.  They should understand that you are there because you want to be rather than you are there because you have to be and that you want them there in the classroom.  Without trust and the feeling that you want them there, the classroom may not feel as welcoming and inclusive.

On the first day of class, use an activity rather than standing there and talking all period long.  This shows them what will happen instead of just droning on and on. Choose an activity that graph their attention and gets them involved such as the 10 items one. Begin by asking students how good they are at remembering things. Then give them a list of 10 unrelated items to remember and see how well they do.  Once they've done the list, go back over and help them associate items in a way to help them use these visualizations to remember the list of unrelated items.

Look at selecting another activity to help students explore their mindset using either a 3 act play or even something from Jo Boaler but it needs to be one that will spark curiosity. The activity should leave students feeling as if this year might be fun or interesting.  Then take time to let your students know how you've set the class up to support your expectations and their success.  

In fact, the first day of class is great for a collaborative activity because you are showing them that collaboration is an important part of the learning process.  For the first collaborative activity, consider using random grouping as a way of breaking the ice and having students work with people they would not normally choose to work with.

In a way, this is the teachers way of hooking students so they want to keep trying through the year.  Next time, I'll be looking at the why the first 30 days of class is important.  Let me know what you think, I'd love to hear.  Have a great day. 

How To Turn A Word Problem Into A Rich Math Task.

 

As we all know, most textbooks have a section of word problems at the end of each lesson but these word problems are designed specifically to be done in the same way as the other problems.  They lead to only one answer and rely on students identifying specific key terms to set up the equation.  Rich tasks are much better because are more open ended with multiple possible answers and multiple paths that can be used to solve the problems.

It is quite easy to transform a word problem into a rich math task by following six steps.  Begin with selecting a visual problem.  In other words, choose a word problem that can easily be pictured both in the mind and in the answer.  The answer needs to be expressed visually through a drawing, or by using manipulatives.  In addition, a student should be able to visualize several different ways to solve the question.

Next get rid of all those key words such as "in all", "total", "less than", and all the other words we teach students to look for. Now you have a word problem that has had all the key words removed but whose meaning is still the same. When the key words are removed, students are forced to think about the operation that must be used rather than relying on underlying certain words.

Now rewrite the problem again except this time you are adding in extra details and information that do not contribute to the solution of the problem.  If a student has. been trained to look only for key words, the additional information will confuse students but the reason or doing this is to help students learn to sort through information to decide which is important and which isn't.

Then personalize the problem by adding names to it.  You might choose the name of a student to make it more relatable by everyone.  At this point you've added enough details and names to turn the word problem into a story.  Remember, students relate to stories better than word problems.  You might start with a generalized problem on the specific number of apples needed for a pie and change it into a problem dealing with apple pies for thanksgiving. 

Turn any single step problem into a multiple steps tome it more challenging.  A one step problem might ask how long will it take to peel 30 apples if it takes 2 minutes to peel an apple.  To change this, you might tell someone that it took Sam 5 minutes to peel 2 apples and how long might it take the same person to peel 14 apples.

The final step is to change the numbers to make it more challenging and do not be afraid to end up with fractional answers.  The real world is more likely to end up with fractional answers so it is important for students to get used to working with them.  

So if you want to turn a word problem into a rich math task, just follow these steps to do it rather than searching the internet looking for the perfect topic.  Let me know what you think, I'd love to hear. Have a great day.

4 Steps You Can Do To Help Students Learn Math

 

The new school year is starting and I know of some school districts in the state who have already had to switch to distance due to an outbreak of Covid cases.  Once all the students have been tested, they'll move to a structure where half the students attend school each day but the four steps I'll be sharing with you today.

First off, ask students why at least once a day.  Ask they why the strategy worked?,  Why does it work in all these other cases?,  Why do you have to do this step?.  We know that students who memorize material do not perform as well as those who understand the concept.

When we ask students why, we are letting students know that what they are learning is contributing to their overall understanding of mathematics and overall ability to do it.  It also helps students see the overall bigger picture better. In a sense, it is showing students the tools and helping them understand how to use those tools while seeing that not all tools are used all the time or might be used in a slightly different way. It helps them understand the math rather than just learning to solve problems by rote.  It opens the door for deeper understanding.

Second, rather than focusing on the answer being correct or incorrect, take time to identify what the student did correctly.  This helps the teacher understand what they've gotten and what they didn't so the teacher is able to identify what the student needs scaffolding in.  It also helps the teacher build on what the student understands to take them to the next level.

When teachers analyze where the student got off when trying to solve a problem, it helps pinpoint where student understanding stops.  Furthermore, if enough students stray at the same place in a problem, it tells the teacher that they should either reteach the material or provide scaffolding so the students can move on while learning the material.  

Thirdly, consider using the textbook as a tool rather than as a major part of the instruction.  Find meaningful tasks in the textbook or change a problem into a meaningful task with a small change in numbers or contexts.  Unfortunately, most problems, even word problems in the textbook, are set up so they can be solved in exactly the same way as the numerical problems.  

We as teachers need to learn to change word problems into meaningful task problems.  A word problem generally has a specific set of numbers, one or more operations that the student uses to arrive at a single answer while a meaningful task often has less information with the possibility of multiple correct answers. Furthermore, they don't have key words to tell you the operation so you can't underline them. 

Finally, allow students to have the opportunity to solve a problem mentally before explaining how they solved it at least once a day. This means they don't use any pencils, paper, or digital device so as to improve their sense making, creativity while helping them feel as if they are mathematicians.

In addition, mental math helps students become more accurate with their calculations, it helps students develop a deeper conceptual understanding, it helps improve student memory, and helps increase SAT and ACT scores.

Making just these four changes will help students understand concepts better so they can improve their ability to do math and raise their grades.  Let me know what you think, I'd love to hear.  I'm going to be traveling to Sweden and Iceland over the next couple of weeks but I'll still be posting.  Have a great day.

Warm-up

 

What if each leaf weighs .32 ounces?  How many leaves are in a pound?