The post Diversify the tube. appeared first on Algebrawesome.

]]>I studied math because I found it interesting and a challenge. The subject is based in problem solving and I am gravitated toward a system defined by this concept. My favorite teachers focused on the dialogue of math as a means to examine problems and present situations in different ways. I view much of math is a way to state the same thing in different terms so that a pattern is more visible. I think that’s cool stuff but not everyone does.

You know what else, I am a goofy white male. What does that have to do with anything? Nothing and a great deal. It should mean nothing but I find a ponderous number of math teachers to be goofy white males. While it is in no way true that all white males share the same cultural experiences it means that we likely do not share the experiences of non-white male students. That issue would not be a huge challenge for me if I taught at a suburban boys school but not in most any other school. The reason it is important is that a black female student may have a much easier time identifying a black lady teacher. The girl sees that her teacher is interested in math and decides to follow suit because of the model set by her teacher and not for whatever esoteric reasons we like to have.

Different population groups treat math differently. I have worked in schools where all of the advanced students were female and I have been in ones where few of the girls developed any competence in the subject. Women, in particular (funny to say for half of the population) have societal expectations that can drive or stunt their learning. If they are to marry early and tend to the house, then they don’t have the confidence or motivation to pursue their studies beyond a comfort zone. Oddly enough, many of the girls in lower socio-economic areas see that they will need to have strong careers to support themselves and their families and school is the most available avenue for them to achieve. Those who push for more women in STEM should be pursuing these groups for they are driven to work hard and overcome challenges to get a strong career.

I work to inspire all of my students but realize I can’t. The most challenging students lack confidence and I find trouble connecting with them in a way that they are motivated. I tend to feel that what they really need is a person they can identify with to aid them.

We can’t have a specific teacher for each student in the classroom but we have powerful and great resources outside of the classroom. As more teachers are using variations of the flipped class, we have in our hands a tool that can let each student learn from people they can identify with. Unfortunately, the mechanism is currently broken. Most of the math videos are made by goofy white men. There a few others but not nearly enough. Students and teachers need enough videos to find the best ones to deliver the subject to them.

The good news is that we are faced with a fairly easy problem to solve. Anyone who feels should add to the library of learning videos. It’s fun to do and watching others will help you analyze your own teaching. Present lessons based on your strengths. Show to others what math is to you. You don’t have to make videos, just take the time when searching through them to find different ones. Ones with different types of people and different types of presentations.

The post Diversify the tube. appeared first on Algebrawesome.

]]>The post Fixing the broken. appeared first on Algebrawesome.

]]>As I was leaving the city, I realized that I had forgotten a pencil and frantically found a convenience store that carried writing utensils. The corner store never has what you need when you need it and has made my life far less convenient with their promises of ease.

The sky looked and felt a touch ominous and spring has the most violent weather but I really needed to not worry and focus on the mater at hand of getting to the test site and taking the danged test.

Some time down the road I found the place, signed in, heard the never-ending instructions, and filled in bubbles. Filling bubbles, I can’t imagine how many kids fill in now days. I was only taking one test so I got to leave then; as I was heading to my truck, I could tell the weather was making a severe turn. Tornadoes were definitely in season. I checked my radio on the drive back and realized that I was just in front of a massive storm. It was to be a race and I didn’t feel like getting stuck somewhere outside of West Memphis is such a mess. I also wondered what was happening to all the folks taking the next test. A co-worker of mine who was there told me later that they had to spend some time in the shelter and wait till the tornado warnings lifted.

I did well on the test. I knew I did well when I left and was just waiting for the score so I could send it along. I had cleared one of the hurdles, though others would get in my way.

Everyone has tales of standarized tests and they will get more because they have permeated to all aspects of professional society since they are quick and easy to grade and a good test is a measure of skills/knowledge. Someone can do HVAC installation or sell fireplace inserts for years, he or she can know his trade but still not be promoted because of a test. These tests have real ramifications for those who take them.

We need to take standardized tests seriously as a skill that students need to learn. As far as evaluations and all the other drama created by NCLB, testing is part of the game and not a measure of our proficiency. We need to prepare kids for future tests so they can always have the skills to get past them. They need to separate their individual worth from test results and see them as part of the game to play. If they really want to change the rules then they will have to play the game before they can reach the point that they can do so. Teachers have been forced to focusing more effort than they should on tests because they are tied with individual and school evaluation.

I don’t know if you will find a more stressed out group than Algebra 1 teachers (at least in Tennessee). The Algebra 1 End of Course always creates the biggest problems and most of the schools at or near failing are doing so depending on that one test score. These are generally freshman and the fate of the school depends almost entirely on what the kids know coming in. I have seen all manner of creative efforts to get kids past the test. So much money, stress, work, time, and resources for one focus that is not the students. This test has been put in place as a major component of teacher evaluation and bad scores should lead to removal of bad teachers.

Somewhere, somehow, someone pushed across a narrative that schools are failing because they are filled with bad teachers. Where are they all? I haven’t found them. There are some teacher better than others but all the ones that I met work hard for their students. They teach and guide the kids in a meaningful way. Their students don’t score drastically higher or lower on the tests. If the scores are too low they are put on surplus and find another school. How can that be! Schools can’t get rid of all of the “bad” teachers because there aren’t enough to fill positions. That problem was somewhat addressed by the influx of Teach For America folks. You know which teachers are the worst? First year ones. They can turn into world class educators but they are most likely going to be chewed up and spit out by the system first. The evaluation system does more to get rid of good teachers than bad ones.

Teachers need to promote the professionalism of the trade. We do not have the money to change minds but we have the numbers and the good will of people. I know I am always proud to tell strangers that I am a teacher and they are always thankful. In a few minutes, I can help this person more deeply appreciate the field and instill more support for educators as a whole. That step is one we can all take pretty easily and one that can have a widespread impact. We have changed the discourse of what learning should look like in the schools, now we need to spread that discourse into the public. When the public dialogue shifts into favor of real reform, then we can face the challenge of doing so head on.

For now, do the best you can and work always on being a better teacher. Focus on what the students need to learn and how you best facilitate them. Tests are part of the game and help learners understand them as such and find ways to succeed on them.

The post Fixing the broken. appeared first on Algebrawesome.

]]>The post Testing for what. appeared first on Algebrawesome.

]]>At this time, we have models in other countries of better education systems that don’t use testing. The education communities are constantly proving that we need to foster real growth and learning for the best success but it falls on deaf ears. Your tax dollars pay for people with PhD’s to find the best solutions but those results are not use because someone else paid legislators for a different solution. I want the smartest people solving the hardest problems, not the richest.

I got lost somewhere in this train of thought but it is a question I am still working with. I believe all students can learn math and can find value in the subject but algebra is not the only math out there. Even as a math, it is a toolbox and not an end.

- to be continued.

The post Testing for what. appeared first on Algebrawesome.

]]>The post Problem solving, thinking, and some effort.. appeared first on Algebrawesome.

]]>Some posts are written down on paper first, this ain’t one of them. It’s really just disguised laziness. I like the challenge of problem-solving. I like teaching math and I liked the part about math where you work real hard to figure something out and then figure it out. It is a special accomplishment and why people always view math as hard and a measure of intelligence. It is often a challenge but it is not any more of a measure than any other study, we just measure it on a different part of the scale than we do other things.

I work to try and help people build their schema of math understanding and develop that part of reasoning and symbolic logic. Unfortunately, I am not the most organized individual so I haven’t refined how to best reach my goal. My goal also involves changing others’ viewpoints and that just don’t always work so well. People are a stubborn species and teenagers are a stubborn subset of people. Getting them to buy into a different view of the world, particularly one based in the unexciting system of algebra, feels like a pointless fight at times. My only advantage is that the students do believe that something about the subject is good for them, even though they have to ask “When will I use this?” every class.

That supremely frustrating question is why I am shifting to a class more focused on problem-solving rather than mechanical-computational skills. I am also moving in that direction because modern students have astoundingly little space or need to recall facts and skills. They are absorbing information at peak levels. They know fifty times more bands that I did at the same age. So much of the working memory I need access to for traditional learning is used up on things far more interesting to teenagers. So….how do I teach a subject that requires a significant amount of this cognitive process? I have faith, perhaps too much, in my ability to present the information to people in way that makes sense but the same people often don’t store it. I am trying to circumvent this issue by using a problem-solving approach or a method in which I guide students to construct their understanding of mathematical systems. Both methods require thinking and both require effort from the students. Effort is a challenge in the subject. Student often ask for help as soon as they read a problem. He or she may work on it for a minute or two but rarely long enough to reason through it.

I have worked on a problem-solving approach for a few weeks in one of my classes and I am seeing signs of change, though. I hear fewer more questions and students seem to be following my guidelines to find some manner of solution. Next up, setting up the problems so that individuals develop an understanding of the rules of higher math. Until now, we were working mostly with old computational skills. I am adopting my system from Exeter’s Harkness math but I am confined to less time and with a broader range of students. I do know they are more engaged and that students who could care less for a lecture on solving quadratics enjoy they can find different ways to solve a problem. Watching people use different methods has taught me a great deal about math over the past few years. Ehh, I just got tired and stuff so I will continue this later…

I work to try and help people build their schema of math understanding and develop that part of reasoning and symbolic logic. Unfortunately, I am not the most organized individual so I haven’t refined how to best reach my goal. My goal also involves changing others’ viewpoints and that just don’t always work so well. People are a stubborn species and teenagers are a stubborn subset of people. Getting them to buy into a different view of the world, particularly one based in the unexciting system of algebra, feels like a pointless fight at times. My only advantage is that the students do believe that something about the subject is good for them, even though they have to ask “When will I use this?” every class.

That supremely frustrating question is why I am shifting to a class more focused on problem-solving rather than mechanical-computational skills. I am also moving in that direction because modern students have astoundingly little space or need to recall facts and skills. They are absorbing information at peak levels. They know fifty times more bands that I did at the same age. So much of the working memory I need access to for traditional learning is used up on things far more interesting to teenagers. So….how do I teach a subject that requires a significant amount of this cognitive process? I have faith, perhaps too much, in my ability to present the information to people in way that makes sense but the same people often don’t store it. I am trying to circumvent this issue by using a problem-solving approach or a method in which I guide students to construct their understanding of mathematical systems. Both methods require thinking and both require effort from the students. Effort is a challenge in the subject. Student often ask for help as soon as they read a problem. He or she may work on it for a minute or two but rarely long enough to reason through it.

I have worked on a problem-solving approach for a few weeks in one of my classes and I am seeing signs of change, though. I hear fewer more questions and students seem to be following my guidelines to find some manner of solution. Next up, setting up the problems so that individuals develop an understanding of the rules of higher math. Until now, we were working mostly with old computational skills. I am adopting my system from Exeter’s Harkness math but I am confined to less time and with a broader range of students. I do know they are more engaged and that students who could care less for a lecture on solving quadratics enjoy they can find different ways to solve a problem. Watching people use different methods has taught me a great deal about math over the past few years. Ehh, I just got tired and stuff so I will continue this later…

The post Problem solving, thinking, and some effort.. appeared first on Algebrawesome.

]]>The post Art above all. appeared first on Algebrawesome.

]]>Art has never been a more important commodity. We live in a world focused on design and have reached a point where we are so immersed in information that creativity separates the wheat from the chafe.The application of art has spread into every facet of our lives and is integral in all fields, yet art has been marginalized in formal education. I remember feeling overwhelmed with a student load over 200 until I spoke with an elementary art teacher who had over 500 kids. As they limit art teachers and courses in many schools, we should take it on ourselves to fulfill this need and as an opportunity to expand our own classes. Not everyone needs to apply the arts but anyone who can should. I have enough confidence in visual arts to use them as a part of my classes and find those lessons are some of my very best. I wish I was a musician but it ain’t happening.

The core of visible thinking is using language to express thinking. Words are great but many people think more clearly through other sensory communication. They hear music, create visual solutions, organize a dance, create through food or otherwise find a way to communicate in a manner that is natural to them. Embrace these differences for we all enjoy the products of great music and fine food. Pay attention and you can recognize deep levels of problem solving while providing students an avenue they want to express themselves in.

Why art when you have so much else to worry about? Engagement, learning, fun, differentiation… perhaps I should expand.

Engagement is the most clear reason, and the linchpin of successful art projects in content area subjects. I have many students that will do everything in their power to not solve another equation but really want to make the cool drawing. Students who love art have a reason to focus on the math. Other students feel like they can’t draw can use the tools of math to create something they can be proud of. Everyone wants to make work they can show off (it’s also useful for your student displays and portfolios). I have the attention of the full cross section of students with a good art project and so the math element that I am most focused on becomes a lot easier.

One of the challenges in formal education systems is putting all of the pieces together. Students view algebra and geometry as different little problems focused on different things and not elements of a way of understanding issues. History is a study of interactions and reactions rather than a seemingly infinite list of dates and names. A good art project can pull the various elements and combine them so the student create something that demonstrates a cohesive comprehension of the subject.

Art provides another very special purpose in management. Students are people who faces struggles at home and in school. We try to provide the best space for their learning but sometimes they are too upset to focus. I like to keep some easy and engaging activities for students who need a way to relax. My handiest toy is an old spirograph. The child explores how it works and focuses intently on making awesome designs and I can focus on teaching the rest of the class. I know the student is learning and the simple allowance on my part shows that I care. He or she no longer views me as another disciplinarian and is willing to trust my guidance as an educator.

Art is outside of the box. It is freedom constrained by medium and nothing else. It is visible and design thinking in action. Anything so powerful has its challenges. Good projects are not easy to create nor are they always easy to implement. Students are often hesitant to embrace creativity in traditional classes. They get better with practice.

Projects take time so pay attention how to make them move more efficient but don’t be overly worried for a good project can cover a lot of content. Once you start one in the class, you are indebted to finishing so students have the final product. It could easily be the best part of the class all year and one that the students take the most from. When designing or finding projects, aim for a balance. The project should not be a paint-by-numbers but it needs enough guidelines or directions for the students to know where to go. Students most likely won’t be able to learn and apply a new concept in a profoundly creative way all at one but they can learn through the applications you have guided them through.

Art projects are fun. I love coming up with new ones and long for the day when I can teach all of algebra through art. Always go through the process yourself beforehand so you can identify potential pitfalls. Do they need to use a ruler? Is it digital music? A music video? You will face a thousand questions about the medium so figure out how to answer them beforehand. If you start of with these things early in the year then future projects move along nicely.

All this nice, how about an example? I am starting a new page on the site for projects and will include the one that led to the image up top. I invite anyone who has developed really good projects to send them along. Let’s keep working together and make schools far cooler.

The post Art above all. appeared first on Algebrawesome.

]]>The post The art of the question. appeared first on Algebrawesome.

]]>I teach math. The beauty and challenge of math is that it is a study of carefully ordered thinking. We have all kinds of rules, terms, properties, and muck but it is at its heart a system of logical reasoning and problem solving. Math is not “the” system but it is the most universally accepted one. As a math teacher, I answer lots of questions. So many questions. Too many questions.

Only teachers can understand the litany of questions students ask during a class. That blaze of interrogatives accosted in my first days in the classroom. As I look back, my steady need to respond was probably the most exhausting part of that first year. What harm is there in questions?

Not much but a great deal can come from the answers. People often ask before thinking. We also answer before doing so. If they do not immediately grasp the concept, they ask for further explanation. These questions are a cue that they need guidance. Embrace these for they are easier to work with then the other people who think they understand and don’t ask. Regardless, you know can now make thinking visible and, if done well, can bring the whole class along. Your motive is to direct the students to ask the right questions. You are the guide in a Socratic dialogue. Avoid responding with an explanation since that didn’t work so well the first time around. Try to ask simple questions that guide the student to respond with answers that build toward understanding. You may also want to ask other students to respond and have the process lead to a discussion. This process takes a profound understanding of the material and some flexibility. There are wrong answers but rarely is there one right one. I have learned a great deal about math by following a student’s line of reasoning. You can make quick assessments of understanding through this process and you can also find the elements that confuse students and lead to faulty reasoning. This second part is extremely useful moving forward because you can present material to address those errors.

However you present the material to your class, this dialogue is a powerful tool and one that inspires strong discussion within the class. It is only as good as the questions are so you may want to start the year discussing how important that all important element is. I am a big fan on this video from Veritasium. You could borrow from him or present the video but the focus is asking the right questions.

More to come one art as visible thinking…

The post The art of the question. appeared first on Algebrawesome.

]]>The post History let’s us tell a story! appeared first on Algebrawesome.

]]>The first lesson demonstrates a unit I plan on doing in my 7th grade Prealgebra class that follows the history of the Pythagorean Theorem and how the Greeks understood the areas as numbers. Students can examine similar shapes as areas of triangles. The Pythagoreans focused on squares on the side of triangles but the theorem works for any similar shapes (semi-circles would be readily done). We can examine the relationships by constructing different triangles and comparing the area of the squares on the three sides. By changing the triangles, we can look at congruence and similarity, as well as the nature of right triangles. This part does not follow the Greek version but will allow us to work with measurements, fractions, and scaling. Once students come to a Pythagorean conclusion, we will move to studying the classic proof of the theorem and finally applications that can develop to the Distance Formula.

The Pythagoreans were an interesting group and they believed that the world should be explainable by rational numbers. They developed harmonies based on ratios of Natural Numbers. My own understanding of music is too slim but we could have a great small project examining harmonies as balances of rational numbers.

Rational numbers were great and wonderful until they studied a square. The ratio of the side to the diagonal of a square is the square root of two. The classic proof of this number’s irrationality is based on the fundamental theorem of arithmetic.As we study this proof, we can study prime factorization which leads to integer exponents, GCF’s, LCM’s and basic number theory. This element also leads to the most interesting part of the history, the story Hippasus. He was rumored to have either discovered the proof or revealed it to an outsider and so the Pythagoreans drowned him at sea.

The proofs are perhaps the most challenging element but it is important for students to see how the process works for proofs are the heart of mathematics. These are not the two column proofs of geometry class but real logical arguments based on reasoning that lead to new understanding. These proofs are challenging and provide wonderful avenues for visible thinking routines. If a student can explain these proofs and then apply them to a variety of problems then he or she will have built a strong foundation for mathematical reasoning.

The unit will take several weeks rather than the single lecture. How is that and why would it be interesting? A 7th grade prealgebra class really needs to cover common core standards for 7th and 8th grade. This unit addresses parts of 3 of the main objectives of 7th grade and 2 of the primary objectives for 8th grade.

Along the way, history provides a narrative arch and allows for many more avenues to explore and keep the material interesting.

For more resources: MacTutor is great. Cut-the-knot is wealth of information.

I will add more to this list and look forward to hearing from y’all.

Next up, history of numbers…

The post History let’s us tell a story! appeared first on Algebrawesome.

]]>The post Technology is just another tool. appeared first on Algebrawesome.

]]>In my time teaching, I have come to depend on computers as a crucial part of my classroom but do not see them as necessary to all. I am currently working on plans that remove the computer from the classroom and have it for outside, where it can best help students. I would love to be able to use the great education tools like geogebra more in the class but it often struggle with a lack of student engagement. They are afraid to play with the program and want to follow directions.

Directions…I firmly believe that many students are too programmed to seeing math as a list of directions. Each problem comes with a set of instructions to solve. This view quickly leads to a lack of retention and demonstrates no understanding when they see a test as fifty different systems and not as fifty variations of the same over arching rule set. Students who follow this method are not inclined to play with numerical concepts or experiment with mathematical logic. The study is a chore and one that must be done for some reason about the future. Standardized tests somehow reinforce this line of thinking though it leads to poor test takers for they are not flexible in problem solving and struggle with new questions.

How does one change the student mindset so that math becomes the profoundly interesting study that it is and not a painful exercise in drilling and boredom? Games are a great avenue if they are properly designed. They need to encourage thinking through play. People are not afraid of mistakes when they play and are interested in the rules of the game for they are the source of the challenge. I believe Whole is a great game in that it allows for plenty of experimentation but the parameters are key parts of the mathematical system. There are a wealth of other great games and plenty of avenues to make more for your class.

When students develop a strong understanding of how numbers and patterns work, then they will be intrigued by the possibilities of geogebra and embrace the challenge of complex problems. My personal goal for this upcoming year is to enact a system for students that build that strong foundation. I plan on using some of the Visible Thinking concepts, the most important of which is to make students write about what they are doing and why. This process will challenge them to think past the step of directions and provide me with another avenue to help guide them.

Technology will have its place for the is little more powerful than pen and paper.

The post Technology is just another tool. appeared first on Algebrawesome.

]]>The post What is it to be a good teacher? appeared first on Algebrawesome.

]]>I don’t know if I will ever be able to qualify myself as a master teacher and I don’t always integrate new methods with my own for the most successful class but I do know that I am a very good teacher. Why? It is not test scores and all that painful stuff. I know for the same reason you know and the same reason we all came to teaching. My students are always present for class and view it as something they want to be part of. My only secret is that I am myself and I care about those students. Class should be a time to learn and I insist that we do learn but it does not always have to be about quadratics or rational functions. The world is beyond our wildest dreams of understanding and kids are desperate to know as much as they can about all parts of it. If you find a time in class where it they need to focus on what it is to be a good friend or how to draw a straight line or appreciate their history or how to tie a bowline, then that is right and good thing to do. We, as teachers, are there to guide young people into being the best that they can be. None of us will be successful with all of our students but we all will resonate with some of them. Identify the part of yourself, that best part, that commands the most attention. The best part…therein lies another key.

I did steel work for many years before teaching. I was dirty and cussed like a sailor. As soon as I knew that I would be in the classroom I changed my language and worked on being a decent role model for students. Teaching has inspired me to be a better person because I can then be a better model for my students. I could more effectively guide them through the mean and awful parts of ourselves. Each of us has walked a different path and fought different personal battles along the way and so each of us has a wealth of guidance to offer in the classroom.

I guess this is all a somewhat round about way of saying is work on being the best person and teacher that you can be. Whatever you or I do that inspires people to improve is what we should be doing. Move forward, improve your craft, and keep your strengths in sight.

The post What is it to be a good teacher? appeared first on Algebrawesome.

]]>The post The moon is huge and that’s amazing. appeared first on Algebrawesome.

]]>The post The moon is huge and that’s amazing. appeared first on Algebrawesome.

]]>