Pure and Applied Math

In one of my blogs I had mention these things called pure and applied math. Just to refresh your memory, pure math is doing math with just numbers. It’s what we do in the math lab now. Applied math is taking pure math and putting it in a context that is important to you. You would be learning math, but it would be based around something like the economy or robots. It’s something that interest you and that’s what makes it applied math.

In my meetings with Mr.Payeur we’ve discussed how next year instead of just having the math lab, applied math classes will also be offered. This will be another opportunity to help earn math credits. Although you’ll still be enrolled in the math lab, you have the opportunity to take an applied math class along with it.

A few classes that will be offered next year are:

• Beep Bot

In this class, you will learn how to control robots. You will use real-world math skills to control robots and to analyze their data. By the end of the semester, you will have completed a Critical Thinking complex assessment focused on an inquiry about robots or your choice.

• Destination: Unknown

In this class, you’ll take on the role of a scientist who is sent to an interesting location. You’ll decide what you want to study, what your house/laboratory will look like, how to secure potable water, and what to do with waste – all while maintaining a strict budget. By the end of the semester, you will have a completed Critical Thinking complex assessment that showcases a 3D scale model of your living space and your budget proposal.

• Wealth and Poverty Economics

In this class you’ll explore the true cost of the wealth gap through stories, data, and the mathematics of our economic system. By the end of the semester, you will have a completed Critical Thinking complex assessment focused on an inquiry of your choice.

• Cipher This! (Steganography and Cryptology)

In this class you will create your own enciphered message, with the deciphering process, and the application of the cipher to a real world situation. By the end of the semester, you will have a completed Critical Thinking complex assessment where you have explored other methods of encrypting.

Pure and Applied math are both important things and the math lab was designed so that you could do both. In the math lab you would continue to do pure math, but on the side you would be able to take another class which would be an applied math class. You’d have the opportunity to do both. This way you would be doing math that relate to real world problems.
All the time students rant and rave about how the math in the math lab doesn’t apply to the real world. Now, with applied math classes ,they will have the opportunity to do so. Changing the math program made it possible to do this. It may not be everyone’s favorite, but it made both students and teachers schedules flexible so they could do both. Keep leaving suggestions and visit my blog again for the latest information on the math lab.

How Our Brains Learn Math

 

I figured since I was doing research on the math lab, I might as well dive into how the brain operates and how it learns math.

According to Kevin Hartnett, researchers identified three regions of the brain that predict improvement in math learning: The posterior parietal cortex, ventral temporal occipital cortex, and the prefrontal cortex.

Cortical territory: Most researchers agree that memory, language, attention, temporal-sequential ordering, higher-order cognition, and spatial ordering are among the neurodevelopment functions that play a role when children think with numbers.

Posterior parietal cortex: The Posterior parietal cortex plays an important role in planned movements, spatial reasoning, and attention. (Blue Part)

Ventral temporal occipital cortex: The occipital lobe is one of the four major lobes of the cerebral cortex in the brain of mammals. The occipital lobe is the visual processing center of the mammalian brain containing most of the anatomical region of the visual cortex. (Green part w/ arrow)  

Prefrontal cortex: This region of the brain has been implicated in planning complex cognitive behavior, personality expression, decision making, and moderating social behavior. The activity of this brain region is considered to be orchestration of thoughts and actions in accordance with internal goals. (Pink Part)

According to the Basics of Mathematics, for children to succeed in mathematics, a number of brain functions need to work together. Children must be able to use memory to recall rules and formulas and recognize patterns; use language to understand vocabulary, instructions, and explain their thinking; and use sequential ordering to solve multi-step problems and use procedures. In addition, children must use spatial ordering to recognize symbols and deal with geometric forms. Higher-order cognition helps children to review alternative strategies while solving problems, to monitor their thinking, to assess the reasonableness of their answers, and to transfer and apply learned skills to new problems. Often, several of these brain functions need to operate simultaneously.

(The section that is highlighted is the most important part)

Reviewing alternative strategies while solving problems: Means that when solving new problems, you reach out to others to see how they are solving them, and respecting different ways of solving problems.

Monitoring their own thinking, assessing the reasonableness of their answers: Means thinking about how you think about the problem, changing the way you literally see it (for example graphs, tables, equations), and then making sure that your answer is possible for the situation.

Transferring and applying learned skills to new problems: Means using old techniques in new problems, finding similarities and testing those out.

So, basically when it comes to learning math many things in your brain need to work together and aside from that, people need to focus on these key things; These are the things that help people succeed in math. And in the math lab for the most part these things go on which is good. This means that the math lab is supporting student’s math learning. Keep leaving suggestion and comments and please visit my blog again for the newest information about the math lab.

Link to website used

Link to website used

How Do Students Feel About The Updates

After the updates to the Math Lab were applied, I decided to have a round two of interviews so I could ask students about their thoughts on the updates and compare it to how the felt about the Math Lab before.

What do you think of the new updates?

Two out of the eight students I interviewed had said that the they didn’t really like the updates and they weren’t very useful. However, the two who said the updates were somewhat helpful said that it gets people talking more and understanding more about things they didn’t get before with the direct instruction and workshops.

Is what we’re doing in the Math Lab more helpful than before?

All of the students said the workshops are somewhat helpful, but everything else seems the same. It’s not much more different than before except we have workshops that are kind of helpful, and community activities in the beginning of class that students don’t necessarily like.

Are the workshops in the beginning of class helpful?

To some, the workshops are slightly helpful. Often, the workshops include activities that they haven’t reached or have already passed, so they’re not helpful at the same time. Students who are in calculus, they just do their regular work, since the workshops don’t really apply to them. They’ve just have been doing the same thing they’ve been doing since the beginning of the year.

What do you think of the community activities at the beginning of class?

It’s a good change, but since students have gotten into a flow where they prefer to get right to their math work, the activities in the beginning of class disrupt them. One student suggested that instead of having like little greetings and talking about our weekends and how we feel, we should have a critical thinking activity in the beginning of class to get our brains working.

Have you seen a change in the math lab community since the updates, if so what?

All except one of the students I interviewed had said that they didn’t really see a change in the math lab since the updates, but the one student had say that some student have progressed a lot faster now that they’re getting help with what they’re struggling with. Others, there hasn’t been much change. She said she had thought it all had to do with mentality, and whether or not the students willing/able to grow with the help that teachers are giving them, and I agree with her.
From the interviews, I took that the updates didn’t really change the math lab. When having the second set of activities I took into mind that I should interview the same students I previously interviewed. I did this to see if their feelings had changed about the math lab since the updates. Sadly everyone felt the same and the updates didn’t really change much. I mean workshops are somewhat helpful, but they could probably be better. Please leave suggestions and visit my blog again to help make the math lab better.

Talking To Strangers

My math teacher, Mr. Payeur and I decided that interviewing students and teachers just wasn’t enough. So to take my project to the next level, I went down to the Scout and Co. Coffee shop with Mr.Payeur and talked to strangers our math program. We figured since we had gotten opinions from people in the school why not see what people outside of school have to say.

Scout and Co Coffee Shop

During the coffee shop visits, I interviewed two college graduates with very different opinions on our math program.I asked them to compare our math program to the way they did math in high school and I asked which they would prefer.

The first person I interviewed was a woman named Lindsay, who majored in philosophy in college. When talking about her math experience in high school, I noticed that it was very similar to the way we did math last year. Things like algebra, trigonometry, and precalculus were separate math classes, kind of like the way IMP’s were divided last year. IMP 1, IMP 2, and IMP 3 were all separate math classes. After talking about her math experience I explained the way our math program worked. I told her about how it was all on computers, and how it was all problem-based learning. I told her that the teachers didn’t really give you direct instruction and you would explore the math on your own. because it was a way to work at your own pace. After discussing both our math experiences I asked her if she could go back to high school which math program would she prefer and she said ours. She had said that integrated classrooms seemed pretty cool, and that some students may prefer the classroom taught classes because they really didn’t have to learn. With the math program students are learning even more because they’re doing it on their own, hence problem based learning. She suggested that instead of having all students work the same way, they should divide the students into learning types. Put those who like to work independently with others who like to work independently. Put those who like to interact and do hands on learning with others who like to interact and do hands on learning. Rather than making each student work in a way that isn’t benefiting them.

The second person I interview was a woman named Jamie, who majored in environmental studies in college. Like Lindsay, I asked Jamie about her math experience in high school and she had said similar things to what Lindsay said. The classes were pretty basic classes like, algebra, trigonometry, and precalculus. Again, like the IMP’s last year, they were divided into different classes. After explaining our math program I asked her which math she would prefer and unlike Lindsay she said she would have still prefered to do the math she use to do. She had said that the way she use to do math is better because seemed to be easier than the way we do math.

As you can see both these people had different opinions on our math program, and I thought it was good to get out and see what other people who haven’t experienced math the way we have to understand what it was like. I thought that maybe if the public thought that the old math was better than the way we do math now, it might help my argument for changing the math lab. From my two discussions I discovered that your opinion on the math lab will vary depending on who you are and how you learn. Which means the math lab should stay open to any suggestions that could make it better for students. Keep commenting and leaving suggestions, visit my blog again for the latest insight on the math lab.

What Do Students Really Think About Math Lab?

Example of community activity at the beginning of class.

So, before all of the updates were applied to the math lab I went around and conducted several student interviews. Ten to be exact, I received a variety of different answers to the questions I asked. Everyone is entitled to their own opinion of course, so I expected to see many different answers. Depending on who they are and how they learn it will affects their point of view on the math lab, so I interviewed both students who liked the math lab and students who didn’t just to be fair. Interview questions and answers:

Generally how is math lab going for you?

Most students had said that it wasn’t going to well, it seemed kind of slow pace and they felt like they were falling behind because they weren’t getting enough assignments done, but others said it was going pretty good.

Do you think math lab is a good opportunity to work at your own pace? If so, is working at your own pace something you want to do?

All of the students said that it was a very good opportunity to work at your own pace, but isn’t helpful for those who procrastinate because they fall behind easier.

Do you feel pressured when doing math at your own pace because of credits?

The results were mixed, some students said yes because they don’t feel motivated to do the activities for homework and some students said no because it makes them feel more motivated to get their work done.

How many assignments do you finish a week? Do you think you’re meeting expectations for getting a math credit this year?

Almost all of the students said they tend to finish 1-3, it also varied depending on each student and what assignment they had been working on, some even said they only finished ⅓ of an assignment.

Personally do you like the way math used to be or do you like the math now? Why?

The results were mixed. Most students preferred it the old way because they were learning a lot more with a teacher in the front of a room showing examples and explaining in detail what things were, but others said they like it better this way because they enjoy the independence they have.

Do you feel like you’re making progress in math the way you did the old way? Why?

The results were mixed. Some students said they felt like they were making the same progress and some students felt like they weren’t making any at all, because they were doing the assignments just to get them done and they weren’t taking in the learning, they weren’t really remembering what they’ve been doing.

Do you mind going back to help others with past problems that you’ve already completed? Why?

The results were mixed. Some students don’t really mind because it’s good learning experiences, but some students do because they want to focus on their own work. One student had mentioned that it wasn’t really happening anyway because the students don’t seem close enough to enforce it.

When you enter the math lab do you feel like it’s like a community?

Students said that everyone is kind of just in their own little world when you enter the math lab and students don’t usually approach each other. One student had said that when she ask for help from other students, she feels like she’s disturbing their learning with hers, and it slows down their learning when they have to go back into previous assignments that they have finished a while ago.  

Do you feel like the way you’re learning in math lab is benefiting you in your math skills? How?

Student feels like their doing assignments just to get them done, no memorization happening, just doing it to do it, not really learning it. Students said it prepares them with skills on becoming independent but as for math skills, there is not really improvement.

Do you have any suggestion that might make the math lab better?

Student suggestions included:

• More instruction and workshops that benefit every students.
• More teachers.
• More lessons, like more direct instructions.
• Give participation grade based on students going into math lab everyday and their working.
• Once a week have a normal class with instructions.
• One unit work as a class then one unit work alone.
• Bring the old math system back, but only on one side of the room. For those who need help in figuring out the equations or the systems to do the work, they could get help in the form of small class. For those who know what they’re doing, let them continue working at their own pace.

From the interviews, I took that there is a majority of students that don’t like the math lab and there is a portion of students that think the math lab is okay, and think that there are a few things that could make the math lab better. What I am most interested in is the suggestions that you guys have that could make it better, so keep leaving comments and visit my next blog to see what student think about the changes that have been made to the math lab.

Why Did They Change The Math Program?

Wait, wait, wait. Let’s rewind. Why did we change the math program in the first place? This is a question many students are probably asking themselves and others.

As you may know from reading my previous blogs, I have weekly meetings with Mr. Payeur and of course the “why change” question has come up several times. Here’s some of the reasoning behind changing the math program:

• To benefit students online skills
• To make it so we can have both pure and applied math
• To make math flexible  
• To build a community of math learners
• To create a place where students can work at an appropriate pace for their own needs.

To benefit students online skills:  Math lab is a place where students do a lot of online learning. The online aspect is important because colleges are becoming more and more advanced in using technology and it’s important for students to learn those skills. In a way, math lab teaches those skills.

To make it so we can have both pure and applied math: Pure math is doing math for the sake of math. It’s basically just equations.  Applied Math is taking pure math and putting it in a context that is important to you. The IMP’s are a kind of applied math. Math lab would open up student schedules so they could take applied math classes.

To make math flexible: The administration wanted math lab to be flexible and to not control schedules. Math lab opens up an opportunity to teach pure math, but to also open up student and teacher schedules to create applied math classes. In applied math classes you would learn about things that are important to you, but math is included in it. In the previous years, students had just one math class, and now with math lab students have the opportunity to work on regular math, which is pure math, and have the opportunity to choose an applied math class to take on the side. Students would be benefiting in math in two different ways.

To build a community of math learners: Teachers want all the math students to cooperate and work together because in a way all of our math relates. It’s a way to begin to allow students to take control of classrooms, because they’ll be able to go in and have student lead conversations and everyone would be asking each other questions instead of waiting around for teachers to help them.

To create a place where students can work at an appropriate pace for their own needs: This is pretty self explanatory. Math lab makes it available to students to  work at their own pace.

As you can see their intentions for changing the math program were good, but of course there are some flaws, change isn’t alway going to be perfect the first time. Math lab right now isn’t the best, but eventually it will be. I agree with the online concept of math lab because colleges are advancing in technology and it’s important to prepare us for it. Not only that, math lab is helping us to become independent learners and it’s important for students to know how to be independent when it comes to college.

Keep leaving comments and visit my blog again for more information on the math lab.

Updating The Math Lab

When I first started this project, I approached it close-mindedly and had no hope of it being change in any way. It caused me a lot of frustration. As my project progressed, my thoughts changed. Now, changes are actually being made to the math lab.

For the last three Wednesdays, I’ve been meeting with Mr. Payeur. We’ve been discussing the math lab. In the most recent meeting, we discussed the changes they’ve planned to apply to the math lab after February break. These changes included:

• Incomplete grades will go away
• A new buddy system, with a go to person for each student when a teacher is unavailable
• Direct instruction for IMP 1, 2 and 3
• IMP 1 on one side of the room and IMP 2 and IMP 3 on the other side of the room
• Community activity when class first starts
• A daily entrance task
• Last 5 -10 mins closing activity

Mr Payeur had told me that lately he’d been talking to the administration about trying to find a way for us to get credit for what we did last semester. Hopefully, credit will be earned based on the amount of submissions a student has completed.

Math lab was made to be flexible, so it is easy to change. There are several reasons why they changed the math program. One reason is because they wanted to build a community of math learners another reason is that they wanted and create a place where students can work at an appropriate pace for their own needs.

For many, math lab doesn’t seem like a community workspace because students usually stay in their own world at their tables don’t converse with others. The purpose of the community activity when class first begins and the buddy system is to help build that community of math learners that the teachers want to see. The community activity is to help brings us together so we feel more comfortable with each other. As of now, most students I have interviewed said that it’s awkward going up to students they don’t usually talk with. Most of the time they don’t like bugging others and making them  go back to previous activities they’ve already completed. Again ,community activities should help to bring us together and fix these problems.

Student voice is finally somewhat being heard. They are at least trying something different from what they’ve been doing and, hopefully, it works better than how it was working before, because many students, including myself, are struggling and were not making progress in our math work.

Keep leaving your thoughts about the math lab in the comments, I need them to make the full changes to the math lab that I want to see. A change is happening! Students need to keep speaking up! We do have a voice!

 

Unbalanced Equation?

Everyday, I enter the math lab, quietly sit down, open my laptop, and blankly stare at the assignment that I left open. I put my headphones in and loudly play my music, signaling that I don’t want anyone to come over to me.

I look at the problem and it reads, “Measures of all six central angles: 72 Now think about an enclosure that is in the shape of a regular polygon. A regular polygon has sides that are all the same length. Find the area of an enclosure that is built in the shape of a regular pentagon using 300 feet of fencing.” What does this even mean? I don’t know how to find the area of a pentagon.

I look around the classroom and everyone is in their own little world. The room is quiet, except for the few pre calc students discussing their work amongst each other.

Thirty minutes go by and still, I’m staring at my laptop screen. Maybe if I apply the pythagorean theorem to this problem it’ll work… No, no, no. That won’t work. What if I try doing cosine, sine, or tangent it’ll work… Nope, not that either.

Over my music I hear students talking to each other, not about math, but more about their personal lives. Great, how am I supposed to focus now, with everyone talking.  

Another 20 minutes go by and still I’m staring at my laptop screen. Why did they change the math lab? This isn’t working. How do they expect me to graduate if they don’t teach me…

The clock says still another 30 minutes left of class. Some teachers are at their desk and some are sitting with students. I read the assignment over and over again hoping that maybe I’ll understand it this time, but I don’t, so I put my head down and sigh. What’s the point of even trying anymore? I’m not going to finish IMP2 by the end of the year. I’m not even going to get a math credit.

Fifteen minutes later a teacher finally comes over to me and offers me some help. Why are you just now starting to help me? I’ve been sitting here for over an hour and now you decide to come to me. Even after I finish this assignment it’s going to be the same when it comes to the next one.

Here is an example of me in math lab everyday when doing my math work

Five months in and I still haven’t even finished the first unit… It’s never ending. I’m hopeless.

*      *      *      *

This is basically what I go through every time I enter the math lab, and I bet plenty of students feel the same way. Students shouldn’t have to feel like failures every day, and I’m interested in making a change to for everyone who is struggling. In my Community Based Problem Solving class I am working to make the math program work for all students.

What do you think would make the Math Lab better for students? I need as many suggestions as I can get. Please leave them in the comments and visit my blog again to find out what’s happening to change the math lab.