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.

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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: F.A.T. City

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.

It’s a bit of a weird title, isn’t it? Let me explain. F.A.T. City is a workshop done by Richard Lavoie in order for adults to understand what having a learning disability feels like. F.A.T stands for Frustration, Anxiety, and Tension, three things that are extremely common among students with learning disabilities. Though we may think that in today’s world we are well aware of disabilities and that the fight has already been fought to gain rights for students with disabilities, we still sorely lack education for teachers in how to best help these students. This is especially important for the not-so-apparent learning disabilities. There are many students with dyslexia or processing deficits who either never get diagnosed or struggle getting the help they need. As teachers, this will be what we unknowingly need the most help on. In the words of Richard Lavoie himself, “I came to recognize — for the first time — the great irony of the teaching profession: Those of us who teach school usually did well in school ourselves and enjoyed the experience — why else would we return to the classroom to make our living? Therefore, the kid whom we can best understand — to whom we can relate most — is the one who does well in school and enjoys being there… Conversely, the kids whom we understand the least are the kids who need us the most. The struggler, the special-education student, the failure.”

Now as teachers in education, we need to look at what aspects of our behavior can be causing students with learning disabilities to experience frustration, anxiety, and tension and then avoid these as much as we can. It has been showed in many studies that if the negative affect is high in among learners then their ability to learn diminishes. So we as teachers need to make sure we are not instigating situations in our classroom that could cause unneeded anxiety or tension. Here are some common situations we create in our classrooms that we may not be aware of.

For the sake of time teachers will often demand answers quickly, and since they may not be giving sufficient time to students, this can cause them to freeze or become anxious. In essence, the student becomes a deer in the headlights and we as teachers may assume a number of things from them being stupid to thinking that they just haven’t been listening. Now teachers may not always be conscious that they’re doing this. Oftentimes teachers get caught up in the need to cover all the material, they feel rushed, and then they consequently rush the students which really just makes things worse overall. Another tactic that teachers use both consciously and subconsciously is using sarcasm to demean the student when they don’t answer correctly or quick enough. Imagine this, say student Jimmy has dyslexia and it takes him twice as long as the other students to figure out an answer. You’ve asked the class what 2+2 is, they’ve answered and then you ask Jimmy what 2+3 is and he says 4. You tartly reply, “why yes Jimmy, 2+3 is 4”, the class laughs and you move on not thinking much of it. But what does it feel like to be Jimmy? He had just barely figured out your first question and bravely put forward his answer and in return he got laughed at. Now rarely do teachers intend to tear students down, but they can do it unintentionally if they aren’t careful. Haven’t we all let out a quick retort without thinking? As such, sarcasm should never be used to negate wrong answers given by a student who took a risk by answering.
Other things to avoid are telling students to “try harder”. How does one just try harder? And teachers often state this as if students with learning disabilities are not already trying their hardest. We as teachers often see things as being easy because we’re coming from a higher vantage point of already knowing the answer. Take the picture below; do you see the image in the picture?

FAT City 1

Why don’t you see it? Well look harder! Now, it doesn’t make much sense to tell you to look harder, does it? Rather you might need me to give some structure to help you see where the eyes, ears, and nose of the animal are in the photo and then you’ll be able to see that it’s a cow.

FAT City 2

Similarly, it doesn’t help to tell students to try harder. Instead, if they have a learning disability and are not understanding we need to give more structure and guidelines to help them to see the overall picture we’re trying to show.
All in all, we must be careful to try and make our classrooms low in frustration, anxiety, and tension especially for students with learning disabilities. While some nerves can help heighten ability, too much can inhibit learning in many students. This responsibility lies mostly on us as teachers and we need to be educating ourselves in how we can best help students with learning disabilities in order to give them just as many opportunities to learn as everyone else.

Guest Post: Reformers in Math Education

Today’s guest post comes from Madison Hodson, an instructor at AcerPlacer who studies mathematics/statistics education at Utah State University.

In this article I would like to highlight a few educational reformers. I would also like to discuss a brief history of education and the impact that it had on mathematics and mathematics education.

Johann Pestalozzi was an educational reformer of his time. He believed that all children deserved a fair chance to attend school and be educated. He tailored the curriculum to meet the needs of each of his students, especially the underprivileged and poor children. Johann’s influence was not limited to the 1700’s alone; today we have education and teaching criteria similar to Johann’s approach to education. Examples of Johann’s influence in today’s education include: an emphasis in children taking an active role in their learning, having a well-rounded education system, and a student-centered teaching approach. Johann also emphasized that school and home are both places for learning to take place and that parents and teachers must work together to make that happen. He also introduced the focus on not only what subject is being taught, but how that subject is being taught. These are just of few of the valuable contributions made by Johann that influence our educational system today.

Another reformer that I would like to mention is Franz Gall. Prior to Franz Gall’s work, the world believed that the intellect and all learning came through the heart and the soul. Franz Gall changed that belief to the knowledge that is still held today- that learning and intellect stems from the brain. With this newfound discovery, Gall divided and categorized the brain into separate sections that each serve a specific purpose. Gall’s findings are helpful in teaching mathematics because we can target specific concepts or learning ideas that engage various parts of the brain. We can also recognize that everyone’s brain works a little differently, meaning that individuals learn differently. As math teachers, there are many methods and examples that we can use to convey the same concept to our students. We have the resources and knowledge available to us to target specific teaching methods that will yield the best long term results.

As educators, we have the responsibility to not only help our students understand how to solve complex math problems, but also to teach them how these concepts can be useful and applied to real-life problems. Critical thinking and problem solving skills are indispensable assets that all individuals must learn in order to succeed. Math teachers are fortunate because we can combine our curriculum with applicable examples that will give students useful skills for life.