Guest Post: The Math Stigma

This week’s post comes from Andrew Petersen, who graduated with a BS in theoretical physics from Weber State University. He recently accepted a post at a company doing data analysis, making this his last guest post as an AcerPlacer instructor.

Struggling with the attention needed to do well in math in my elementary school, my friend nudges me, “Uuugh – I suck at math, want to go ride bikes?” I agree, knowing that I will never get anywhere with math, and riding bikes sounds immensely more entertaining. As children we develop into a social construct already in place, slowly built upon by thousands of generations of humans in our cultures. This social boundary subconsciously forces us to think and do certain things to fall within the norm. One of those things is that math, as a subject learned by a lot of people, is hard.

From birth and within our social boundaries, we are told that math is hard by our peers, mentors, and often times our parents. Those we look up to have labelled mathematics as the F-chord of our academics, and we probably aren’t good at it. After being told this, when attempting to learn math, we expect it to be difficult – we know it’s challenging – it seems like an impassible hurdle. This thought process and structure, I think, is entirely ironic. The only reason some people are inherently good at math, or anything for that matter, is due to their development and environment when growing up. This tells me that how we think of and structure things (math, baseball, reading…) is completely moldable. Then I also think – “Isn’t that how we learn…everything?”

Often I thought being good at math was due to a higher intelligence and a crafty creativity that I simply didn’t have. After years of studying and graduating university, I finally have the realization that an inherent intelligence was not the key – persistence and good habits were. A lack of this realization manifests into students often misdirecting their blame and anger. Every once in awhile I will have a student who struggles through the whole class even while working hard, retakes the class, then repeats. That student then begins to blame the institution – “My instructor was at fault, the math at my school sucks.” Yet this is misdirected anger, because those students don’t lack the intelligence, they lack the habits when writing and learning mathematics. They don’t work problems top to bottom, they skip steps, and they just get lazy. It’s understandable, all of us are lazy at some point, but this is the skill that needs to change.

We all learn differently, and many times while sitting in class I have struggled to keep up with my notes. For a long while I would finish writing out my thoughts, then move on with what the instructor was at next – but I am behind at that point, and continue that progression for the rest of the class. In most classes, no matter the subject, the instructor must get through a set amount of material. Due to time constraints, that often means they must teach faster than the students are comfortable with. As a student, I would blame the professor, until I realized this was misguided. It took years to discover that I need to listen, regardless of what I get written down. It is far more important to absorb what the instructor is saying through my senses, then fill in the rest later.

To break this stigma, we need to instill a social construct around our children that math is like any other subject, we just must learn how to learn. First though, we must do this to ourselves, and redefine how we think of mathematics in the first place – it does not take a especially smart person to learn math, it takes persistence and good habits.

Editor’s Note: An F-chord is a particularly difficult chord to play on a guitar.

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Guest Post: Ownership in Education

Kramer McCausland is an instructor at AcerPlacer. He is working on a double bachelors in mathematics and philosophy at Weber State University.

Student success is often on my mind. My hope is to find some simple equation that I can then offer up as the easy solution to the question of, “How can I learn this? How can I succeed in this class?” I often push myself to learn better techniques, to find better strategies, to practice being more clear. In short, I think that if I can be the perfect teacher, then every student I teach will succeed. Now, it is useful for us teachers to improve, but that’s only half of the puzzle, the other half is the student. I’m currently a student as well as a teacher and what I want to write about today is how to be a better student. What follows are the things I tell myself on the first day when I start a new class. And the tips and tricks I use to be more successful at learning.

The class I’m about to take is my class.

The knowledge I’m about to learn is my knowledge.

The responsibility to succeed is mine.

These are what I remind myself every time I take on the challenge to learn something new. The truth is that education is not passive. Too often, the student is portrayed as this empty bucket that the professor is there to pour knowledge in to. The sage on the stage. But, I’m afraid, that’s not how we learn. Education through osmosis is a nice fantasy, but the reality is different. It takes work, it takes patience, but most importantly, it takes ownership. It takes a firm conviction that this education is yours. The truth is that there are going to be bad teachers, there are going to be good teachers that have bad days, and there are going to be days where good students aren’t feeling like themselves. So how can we as students insulate ourselves against these misses in our education? By being truly responsible for what we’re learning. What I’ve compiled are a few tips for the proactive student.

  1. Take good notes, review those notes, revise those notes: Make sure you’re jotting down the key points when learning something new. Then, check those points against a secondary source. In the day we live in, every part of education can have a corollary online (for instance, I just double-checked on google how to spell “corollary”). Very few people in this world can “learn” something after just hearing it once. Learn it in class, learn it again later, revise your notes on the subject as your learn more.
  2. Communicate with your instructor: It may be surprising, but teachers are people too. They may gloss over, overlook, or entirely forget to mention something in class. If you’re unsure of what something means find an opportunity to meet with your instructor and talk about it. In the perfect world your teacher would clearly and concisely explain exactly what’s troubling you, but in this world it may take some leg-work on your part to get the best education.
  3. Be patient with yourself: As cliched as it sounds, we all learn at our own pace. If I have one major qualm with the education system most of us find ourselves in, it’s the ideas of deadlines. I’ve met students who can understand everything they need to know about percentages in one hour of instruction, and others where the same material might take them 5 hours. Now, I’m not a total idealist here, and it is probably important that we learn how to learn quickly. But do your best not to become discouraged. Know yourself. Know how much you can retain in one sitting. And find steady study habits that work to your strengths (but that’s a topic for another day).

This education is yours. Take it seriously. Take ownership.

Guest Post: Literacy in Mathematics

Our guest author today is Stacie Leavitt, an instructor at AcerPlacer who recently got a degree in math education from Weber State University. She will begin teaching for the Weber County School District this Fall.

A few years back there was a standard set in education that literacy should not be taught in our English classes alone, but that it should be taught in every single subject matter. Now for the History or Spanish teachers in a school, that may not feel like too high of a demand, but for math teachers it came as an abrupt surprise and a rather daunting task. “Now we’re not only teaching them math, but we have to teach them how to read too?! Those are almost entirely unrelated subjects!” As such, literacy is still highly overlooked when it comes to most math classrooms. However, if we take a deeper look at what literacy really is, maybe we can find more connection there than we thought.

Literacy in its most basic definition is the ability to read and write, but The National Literacy Trust includes [that], ‘A literate person is able to communicate effectively with others and to understand written information.’ So let’s dive a little bit deeper into these definitions. What exactly do we read and write? Our language is a mixture of symbols that when put in a certain order then mean a certain thing. We then need to be able to decode these symbols, use them to communicate, and be able to write about them. Similarly, much of math is being able to read the symbols to grasp their meaning, communicate about them, and then use those same symbols to write down your response. In fact the techniques used to decode and comprehend a paragraph are very similar to those used to decode and comprehend an equation. So how are literacy and math any different? They’re not really, it’s just teaching a new language within our own language. This is the idea that if we were to emphasize in our classrooms, we would not only be able to teach literacy but we would actually be able to teach math better and connect it more to skills that many of our students already have.

Now as a teacher myself, some of the main things that I have observed in different classrooms that separate literacy and mathematics are the absence of real world texts, few to no story problems, and the emphasis on the procedures instead of actual comprehension. In many of these classrooms, I can understand why a teacher would feel to build their curriculum this way due to the demographics of the school where maybe the majority don’t have high levels of literacy or math skills, are ESL learners, or their family situation can make it almost impossible to assign homework to take home. However this is exactly the classroom situation where there needs to be more focus on decoding and comprehension of text, especially the symbols and their meaning. Authentic math texts would be great for students to be exposed to in order to help them realize that math is more than just a process. It’s something people have wondered about, written about, built, discovered, and created. It’s both true and fallible and it’s ok to make mistakes in. Similarly real world story problems (not ones about buying 60 watermelons) can help them see how they can use these decoding and comprehension tools in a work or real world setting. But the biggest problem of them all is the the focus on the procedure. When this is overemphasized in a classroom it cuts off the need for students to become literate in math. There’s no need to decode the equations, comprehend what they’re meaning and what they do end up writing isn’t actually being understood. Their ability to tell you what they wrote and what it means is completely gone. Teachers wonder why, and honestly it’s because we don’t teach enough literacy in math.

Guest Post: The Validity of Knowledge Measurements and Grading

Today’s guest post comes from Madison Hodson, an instructor at AcerPlacer who studies mathematics/statistics education at Utah State University. Here she exams what makes a “good” math question.

The validity of a knowledge measurement (a question on an assignment or exam) is broken up into two parts— relevance and reliability. For a question to be relevant, it must reflect the unit goal or objective and it must contain the correct mathematical content and learning levels. Reliable questions are those that when answered would give non-contradictory results.

If a measurement is relevant, then, once answered, proper evaluation can take place regarding the students knowledge and application of learned concepts. It is important for educators to clearly define their learning objectives ahead of time. This way, they can make sure their lessons cover all aspects of the objective. Having stated the objectives of each lesson also allows educators to draft relevant questions to homework and tests that cover and reinforce learned principles.

To aid in reliability, one of the most important qualities for each question is for it to be stated clearly. There must be no confusion as to what each question is asking and there are no ambiguous answers. This ensures that there are no discrepancies in the results from each question. Students either grasp the question and answer correctly or they don’t. The author personally thinks this aspect is important because she has felt confused by questions or answers on tests before.

Grading rubrics are imperative to ensure that scores are recorded based on fulfillment of the learning objective. For each question, there should be a rubric assigned that clearly designates the quantity of points that will be awarded for each answer. The rubric must be designed so that no matter who is scoring the question— there should be no controversy as to what answer(s) merit any specific amount of points. Having a rubric of this type will not allow any discrepancies between scores and will aid in the validity of each test score.

The purpose of knowledge measurements is stated in it’s name. Questions are posed to test the students knowledge and measure what they have learned and retained. By having clear objectives, relevant and reliable questions, and a precise grading rubric— educators, specially mathematics and statistics educators, are able to accurately determine their students knowledge, understanding, and application of concepts that have been taught. By taking time to generate relevant questions and watching for discrepancies within the students responses, educators will have valid results to base evaluations off of.

Guest Post: The Fall Factor

Ryan Brown is an instructor at AcerPlacer and is working on a BS in mathematics with a minor in secondary education. He is also an avid rock climber.

Mathematics can be used for an infinite amount of reasons. I specifically am going to discuss how math can be used to find the safety of a fall for a rock climber. There is a simple equation that one can solve to find out the danger in each possible fall. The equation is: (Fall Factor) = (Height of the fall before the climbers rope begins to stretch)/( Length available to absorb the energy of the fall). It can also be written as F= H/L. A fall factor of 2 is the greatest that one could have while lead climbing; this would mean that the climber would fall past the belayer or hit the ground. The smaller the fall factor, the softer the fall for the climber. Knowing this equation can help climbers place gear safely so they can have the safest and most optimal climbing experience.

Guest Post: Math Stigma and a Study

Jodie Larsen has a BS in applied mathematics from BYU-Idaho. In addition to teaching at AcerPlacer, she tutors students on several topics in math

“When will I ever use use this?” A question we, as mathematics instructors and connoisseurs, hear on a near-daily basis. You may have heard your past math teachers say such things as, “You’ll use this every day!” or simply look at you like they just cannot comprehend how anyone would NOT use math every day of their lives.

The truth is, math is all around us and we all use it, to varying degrees, more often than we may even consciously realize. I know people such as welders, electricians, and musicians who upon first consideration may not seem to need math, but it is shocking (especially in the case of the electrician) how often they utilize different types of math in their careers. Even if someone isn’t in any sort of math-related field, they will inevitably end up using such math as taxes, tips, and discounts. That’s not to say the average person will likely use properties of logarithms and population models on a daily basis, but it is quite helpful to know where those types of things are applicable. In my studies of Applied Mathematics and Biology, I was constantly surprised and pleased about just how many correlations could be made. Following, you will find one of my favorite such studies which I was a part of.

For this particular study, we headed out to a region which grew sagebrush and various other scrubby types of bushes and weeds. We started at a certain point and would measure out pre-decided lengths, say 10 feet, in random directions (if it is actually possible to be random which many studies claim isn’t – but that’s an entirely different story). At each 10 foot length, we would measure and take note of different diagnostics of the area such as the height and density (which we estimated visually) of the surrounding plant cover. The idea is that we could then create models for whatever type of animal (be it rabbits, voles, prairie dogs, etc.) and state how much cover said animal would have when needing to hide from predators. We created models which related the height of the animal to how protected that animal would be in that particular region. We also analyzed how visible those animals would be through certain vegetative densities, which of course would also show how visible they would be to predators. Animals which were too tall or too large wouldn’t have as high of a population density in that region due to the inability to hide properly. There are, of course, many variables and things to consider but having a lot of data allowed us to analyze a plethora of correlations and hypotheses.

As stated in the opening paragraph, one misconception about math is that “I’ll never use this.” I, along with my colleagues, aim to break this stigma by finding many practical applications and perhaps, just maybe, finding a niche in which each student can and will apply this beautiful thing we call math (or ‘maths’ in some parts of the world) and think of us whenever they calculate and realize…. we were right…. and that they’re actually enjoying it.

 

Guest Post: An Origin of Numbers

Drew Peterson recently earned a BS in physics from Weber State University. He is currently an instructor at AcerPlacer.

Start counting: 1…2…3…4…5… hopefully you can take it from there. Did you start from one like me? Maybe zero? Why didn’t we start at negative one, or even negative one thousand? It’s estimated that humans have been writing down numbers for at least the past 40,000 years (Ifrah, 2000). It’s really impossible for us to grasp how old this really us, but it really leads me to ask: Why have we been counting and writing numbers down for so long?

Let’s think back to the ancient world – I’m trading in a market place, and I need to know how many bushels of wheat to buy. I know how much I need to make a loaf of bread, it’s… that much. Visually, then, I can determine this from experience. Then the person I’m selling to needs to figure out how to charge me. She can see how many bushels I’ve taken but needs more rigidity — she needs to count how much I’ve taken. So the seller counts, maybe with her fingers, certainly not using the number system we think of now (one, two, three). Of course I don’t have zero bushels, in fact in that time I would ask how you could even see or think of zero of anything – let alone the wheat.

So by necessity we count, and by lack of necessity we didn’t need zero. Think of how bizarre an experience it would be to attempt an explanation of negative numbers to an ancient person, who only counts the things in front of them. I find it hard to put those shoes on, so I’ll produce an analogy: Imagine you’re building a shed, and you need to figure out how wide to make it. Your neighbor, who’s helping you, thinks he knows how long the shed should be. “Negative 10 feet!” he says. Of course, you stare in confusion as this answer makes no sense. How could you possibly have negative length?

Eventually, with the rise of currency, humans gained the need to measure nothing and negative of something, specifically when dealing with loans or any sort of deficits. For example, I’m back in my ancient trading market buying seeds to plant for my farm. I really need some seeds today to plant them in time. Unfortunately, I don’t have enough money, but the seller is kind enough to give them to me anyway. Now I owe her some money; I have a debt that needs to be paid. This is the idea of debt that we are commonly used to today, although our ancient people may not have thought of those as negative numbers.


Resources:

Ifrah, G. (2000). The universal history of numbers: From prehistory to the invention of the computer (D. Bellos, EF Harding, S. Wood & I. Monk, Trans.).