"Why do we need this anyways?

     The way math is taught has changed plenty throughout the years, with new discoveries, new technologies, and new educational requirements. Even with those differences, there is one experience that all math teachers have, and that is answering the age old question, “Why do we have to learn this anyways?” Telling kids that they “simply must” never works, so what are we to say? Most of my teachers told us we will need it for college, for work, and just for everyday life. But the most memorable answer I received was, “You may not ever need this. If a stranger runs up to you and asks you to solve an algebraic expression, you should run. But at least you are learning valuable problem solving skills.” All these answers, however, seemed vague to me. As the impressionable teenager I was, their vague answers did not exactly pique my interest in my studies of mathematics. In fact, it made me think they mattered even less. The issue here is that what all those teachers said is true. Math learned, especially in secondary school, is used for college, work, and simply growing those necessary skills. Those things, however, really do matter, so how do we make students understand that? I think math lessons need to include more realistic, everyday examples. I mean, who’s buying eighty-six bottles of dish soap? Another idea that could be useful would be dedicating a day to explaining the usefulness of math. This could look like an activity day, or maybe even guest speakers. Once a student knows why it is so important, I’d wager that they’ll be more inclined to take their mathematic studies more seriously.

Is Math Really a Useless Subject?

In school, I’ve always heard students say, "When I am older, I am going to have a job that does not require math, so why do I need to be in this math class." If I am being honest, before deciding I would be a math teacher, I thought the same thing. Since deciding that I want to be a math teacher, I have been thinking about what I would say if students asked "when am I ever going to use this?". Why should my students care about a subject they "will not use” in the future? After a lot of thought, you still need basic math skills and critical thinking that this class teaches you, to be successful in the real world. 

I would first tell my students that the more practice with basic math, the easier day-to-day life math is. The math done daily is primarily subconscious, like when shopping, counting money, time management, etc. For counting money, let's say we want 76 cents. To figure out how to get there subconsciously, we are using the formula 1x+5y+10z+25c=76. When going out to dinner with friends and splitting the bill, you are doing math to determine how much you owe plus your share of the tip. This basic math does not seem to be too complicated, but without these math classes, it would be harder for you to do with ease. 

Another reason why math is important is for the critical thinking practice students get. Math is not just about numbers; it also has to do with how you come up with equations and solutions. When solving a problem we figure out the tools we have and then solve the problem with the tools we have been given. This can be applied in many situations, one being a crisis at work. When dealing with this crisis, you're going to figure out the crisis and assess what tools you have to help you figure out how to solve the issue at hand. So it is not so much about numbers in math, it can also apply to how we are thinking. This is important because it allows students to create a subconscious way of solving issues. 

Lastly, many kids use the argument that "I have a calculator, so if math comes up, I'll just use my calculator." That is great and all, but without a math class, you will not know how to set up the equation you need to solve on the calculator. 

Math is hard, so it makes sense why students think of math as a "waste" of time. I think helping students understand why it is important is essential because no one likes doing something just because it is required. So, explaining why can help students see the importance of the subject they are learning, which can also help them want to put more effort into a class.   

Leni Lottman

references: 

https://www.niu.edu/mathmatters/everyday-life/index.shtml

https://www.prodigygame.com/main-en/blog/why-is-math-important/

How Math-Solving Tools Can Help Students Learn

With today’s technology, students have access to a variety of math-solving tools that can assist them in understanding and mastering mathematical concepts. Some teachers may worry that these tools encourage shortcuts, but when used correctly, they can be powerful learning aids.

Many math tools, like GeoGebra and Desmos, provide interactive visual representations of equations, graphs, and geometric shapes. Instead of solving equations on paper, students can see how changes in variables affect graphs in real time. This helps them better understand mathematical relationships and patterns.

Apps like Photomath break down problems into detailed steps. Instead of just providing an answer, they guide students through the entire process. This can help students understand the reasoning behind each step. Although Photomath and apps like it aren’t skilled in word problems, other tools such as ChatGPT and Google Gemini can take a word problem and guide students through the solution.

One challenge in learning math is recognizing mistakes and correcting them. AI-powered math tools can highlight errors and offer explanations, allowing students to learn from their mistakes immediately instead of waiting for teacher feedback. This promotes learning and reinforces problem-solving skills.

Not all students learn at the same pace. Math-solving tools can act as personalized tutors, providing extra support for students who need it. Instead of feeling frustrated and stuck on a problem, students can get hints as to what the next step is in their problem. This builds students' confidence in math.

When used correctly, math-solving tools are not just shortcuts to answers. They are learning aids that help students visualize, practice, and understand math better. The key is to use them as a supplement to learning, rather than using it as a replacement for critical thinking and problem-solving skills. By using these tools, students can develop a deeper appreciation for math and improve their ability to tackle complex problems with confidence.

By Ericka Ackmann

The Importance of Connecting Math to Other Subjects: Approaches in Teaching

Making connections between math and other topics is a potent strategy for engaging students in math as future teachers. Math is frequently viewed as a stand-alone subject, but connecting it to science, art, history, and music makes it more interesting and meaningful. This method develops creativity and critical thinking, in addition to helping students understand how mathematics is used in everyday situations.

Math is crucial to science. It is used to analyze data, predict outcomes, and resolve issues. Algebra, for example, aids in population growth predictions and chemical equation balancing. Students can observe how math is used in the real world when math is incorporated into scientific classes. Art also relies heavily on math in everyday life. To produce balanced designs, artists must employ symmetry, geometry and proportions. Students might investigate how artists such as Leonardo da Vinci enhanced their works by utilizing mathematical forms or the golden ratio. This enhances their comprehension of mathematics and enables them to recognize its beauty. Math is used in history to evaluate patterns and trends, such as population increase or economic shifts. Students have a greater comprehension of historical events and see how math can be used to explain historical changes when they are taught to apply math in history. Additionally, music also gives a means of connecting creativity and mathematics. In music composition, ideas like time signatures, fractions, and patterns are crucial. Students can understand how math is used in artistic expression by integrating music into math instruction.

By relating math to other disciplines, teachers can create a dynamic learning environment where students view math as more than just a way to solve equations. It promotes deeper thinking, creativity, and problem-solving. Adopting this strategy as aspiring math teachers can help students see the practical applications of math and make it more engaging and meaningful.

In conclusion, students' learning experiences are enhanced, and their real-world applications are illustrated when math is connected to science, art, history, and music. We can make math more interesting and motivating for the upcoming generation of students by demonstrating how it relates to the real world.

By Jalyn Kampshoff

Why does everyone hate word problems?

Whether it be elementary school, high school, or college level math, one sentiment reigns true for the vast majority of students – everyone hates word problems. Even for many people that consider themselves “math people” and enjoy solving math problems, the wordy questions tend to garner the most disdain. Why is that?

I think that applying math to real life situations in the early years (kindergarten, first, second grade) is actually much more intuitive for kids than just working with numbers; because they aren’t yet familiar with words like addition and subtraction, using realistic scenarios that they would encounter such as giving or taking away every day items typically makes much more sense to them. However, as math gets more complex, that dynamic flips, and the abstract problems without a real-life connection become simpler and easier for students to grasp. At some point, story problems stop being a tool that helps students understand math and become an obstacle students must overcome before they even get to the math; according to an EdWeek Research Center survey, when elementary students struggle with word problems, 50% of them “can read the word problem, but they can’t understand the mathematical question being asked.”

I think that there are two main causes of this problem: students don’t understand the point of the problems they’re solving, and they don’t know how to solve them. Firstly, it’s difficult for students to be engaged and enthusiastic about word problems when so many of them seem to be completely detached from their everyday lives. The early word problems that use giving/taking things like toys or apples resonate with students because it’s something that they can see themselves doing or using in their everyday lives, but that relatability basically vanishes as soon as more complex concepts like algebra are involved. The other problem is that students are rarely taught how to think through word problems and reason their way to the underlying math – instead, they are often taught shortcuts like keywords or phrases to look out for. While it’s possible for students to learn how to do a type of word problem like this, it makes it all too easy for them to learn the steps for solving a certain problem without actually understanding why those steps work and how they interact with the mathematical concepts they are supposed to be using.

So what can we do? For one, we have to do a better job of showing why students should care about what they’re learning. I think this is a prevalent issue in much of education, and math is no exception. This isn’t exactly a change that can happen overnight, but making little changes like showing students practical applications for a concept (not in a format like a word problem, but just for demonstration) or explaining how it’s related to some careers they’re interested in would be an excellent start. Additionally, we have to do a better job of not only explaining the word problems; we have to make sure we convey the reasoning behind the work, as well as how students could think through a new type of word problem if they were given one. Sarah Schwartz from EdWeek calls this “schema-based instruction,” and the main idea is to teach students how to make a mental map of some math-related event, which then allows them to find their way to the solution. Though I’m sure there will always be some sighing and groaning when students hear it's time for a word problem, I think that working toward these changes can change these problems from being considered public enemy #1 to a fun challenge. 

Reference:

https://www.edweek.org/teaching-learning/why-word-problems-are-such-a-struggle-for-students-and-what-teachers-can-do/2023/05

Is struggling vital for a student's success?

    Merriam-Webster's dictionary defines struggle as making strenuous or violent efforts in the face of difficulties or opposition. This doesn’t sound like something that would happen much in a classroom. I mean, violence is definitely not something I’d wish to see in a classroom. However, the reality is that struggle is an integral part of being a student.

    For the sake of clarity, I should tell you, that the type of struggle that I’m referring to is productive struggle. The difference here is that productive struggle is where a student is actively engaging with a problem to push their understanding. Rather than facing a difficult situation and turning towards frustration and stagnation, which is how I’d describe unproductive struggle. Productive struggle is what can allow a student to take steps toward growth and understanding. This is because it builds resiliency, deepens understanding, and encourages a growth mindset. 

    Undoubtedly, not every student who enters your classroom is going to come ready and excited to struggle. It can be so discouraging to feel not smart enough, drowning in assignments, or even inferior to peers. But these are all very real and common feelings to be felt as a student. As a teacher, it is your job to help your students through these moments. Not by lessening their workload or giving them an easy way out, but rather by encouraging them to lean into a productive struggle mindset. 

    One impactful way to help students foster a productive struggle mindset is by setting an example for them. After all, you are their teacher, their authority, someone they should be looking up to and learning from. Let your students in on the workload and struggles that may be on your plate, but model resiliency. Show them that even when your responsibilities pile up, you can still push through it. When you have a lot of grading to do, lessons to plan, or research to publish. Share this with your students, but also share that you’ll push through it despite the struggle it may produce. 

    One other really important part of helping students foster a productive struggle mindset is creating a failure-friendly classroom that focuses on process over product. According to research done by Georgia State University, the fear of failure ranks among the worst fears that the country endures. I think one of the reasons this can be exemplified in education is because it is merely the beginning. Education is the beginning step that is meant to set you up for success in the future. I know as a student myself, struggling in the classroom has placed an exorbitant amount of doubts about my personal capabilities and chances of success in my future. Which can be so heavy and discouraging in an environment that isn’t failure-friendly. 

    Having teachers who support failure with grace and provide guidance in times of need is imperative to growing a productive struggle mindset. Acknowledging that homework assignments and lessons are a time of learning and ultimately failing. When these failures happen to your students, let them. Don’t jump in to rescue your students. Let students find the motivation to figure it out, ask for help, and try again. This is when both academic and intellectual growth will transpire in students. Remember, learning cannot be done without starting at a base level with little to no understanding. Failing is bound to happen, and that’s okay. It is important that students are told and shown that failure is part of growth and should be applauded when handled the correct way. That being, handled with resiliency and embrace instead of frustration and stagnation. 

    Struggle will happen. It should happen. As an educator, it is your job to model a productive struggle mindset to your students and foster a failure-friendly classroom so that your students are set up for success despite the struggle that you might induce in their lives. 

By Ava Werning

References 

https://scholarworks.gsu.edu/cgi/viewcontent.cgi?article=1051&context=ays_cslf_workingpapers#:~:text=1%20Interestingly%2C%20fear%20of%20failure,population%20endure%20in%20this%20country. 

https://www.goyen.io/blog/productivestruggle#:~:text=This%20kind%20of%20deep%20engagement,connections%20between%20texts%20and%20ideas.&text=When%20students%20learn%20to%20embrace,abilities%20can%20grow%20with%20effort. 

https://www.merriam-webster.com/dictionary/struggle

Homework: Helpful or Harmful?

There is always question and conversation among math teachers on the subject of homework. Do you assign homework daily? Practice makes perfect, right? How many homework questions should I assign? Again, practice makes perfect, right? Do you grade homework by completion or correct answers? As an educator, you desire your students to get the correct answer, right? But what about the learning process? How do I handle the issue of students cheating on homework?  

Recently in my Math 371 Technology for STEM Educators course, we discussed platforms on which students often cheat on homework, such as Photomath, Symbolab, Mathway, and several other AI math solvers. We noticed after doing some research that there are tons of math solver apps or websites that are available to use, and that those platforms are being used by students in the classroom. Math solver software is especially used on assigned homework. This poses the question, if students are cheating on their homework, then how helpful is the homework? Knowing that there are math solver applications available for use, is there still a purpose for assigning homework?  

As a class, we discussed that some educators and researchers suggest that math solver applications aren’t harmful to students and are almost helpful because students are shown the steps on how to solve a problem when they are stuck on their homework. Sounds legit right? Because all of us who have used math solver programs felt like we understood the concept of the homework better after allowing the software to do the problem for us, right? I’m guessing most would disagree. Although some math solver programs can be helpful in showing steps or processes on how to solve a particular problem, sometimes the software isn’t as accurate as it appears, but more importantly, you learn best by doing, and using AI or math solver software hinders the learning process.  

Even if we are aware that it is more beneficial for our students to work problems out on their own and assess their mistakes to learn from them, how do we avoid students cheating or using AI or other math solver applications to complete homework? Do we forget about homework altogether? I’d like to suggest what is, in my eyes, a better solution to the situation many teachers (not just in math classes) find themselves in when pondering assigning homework in class.  

As Madyson Stricherz mentioned in her blog about “The Flipped Classroom” on January 30, a flipped classroom model is one where students complete projects, activities, or homework in the classroom instead of at home or outside of the classroom. This could be one solution to avoiding AI or math solver applications being used to complete homework; this way, the teacher is allowed to monitor how the students complete the homework and can be there to answer students' questions while they work through the problems. Secondly, as we did in Math 361 Geometry for Teachers, assigning “discussion” and “turn-in” problems could be a good way to keep students from using AI or other applications to do their homework for them. This strategy of assigning homework could look like assigning some key problems for students to try on their own, knowing that they can bring any questions to class the following day and the class would discuss the problems as a group. Additionally, turn-in problems may be only a few problems that demonstrate the particular skill or concept that is being learned at the time and could be due to “turn-in” at the next class period. Also, you could allow the class to discuss how to start the turn-in problems but still complete them on their own, but having the material and the knowledge from working on and discussing the “discussion” problems could help the students be able to better apply what is talked about in class to completing problems on their own.  

Ignoring the technology that is out there is not going to solve the problems of cheating on homework or less understanding of classroom content. Finding creative ways for students to still learn by doing, but taking the temptation or even the option of using technology in an unhelpful way to do their homework for them can help solve the question of homework: is it helpful or harmful?  

By Katelyn Wittnebel