Passion Drives Our Profession

A couple of weeks ago, I had an unpleasant interaction with someone who works at a hedge fund. He was a friend of a friend and we were sharing a cab and our conversation started off as most conversations with people you meet for the first time. How long have you lived in the city? What do you do? Well I told him I was a middle school math teacher and he told me he worked for a hedge fund. He made an implication that the pay must not be good, and I answered awkwardly, “I guess”. When we got to the destination I offered to pay using my card, since I didn’t have cash and that he could pay me back with cash he had. He responded along the lines of “No I got it, you’re a teacher.” Implying I didn’t have the money to pay a $15 cab ride. This infuriated me but I held my tongue and let it go.

This interaction with this unpleasant person reminded of the poem “What Teachers Make” by Taylor Mali. I had the pleasure of seeing him perform it live at our network end of the year conference. (If you are not familiar click on the following link: http://youtu.be/RGKm201n-U4) The main point of his poem is; our profession has nothing to do with what we make in dollars, but the passion we have to push our students to do their absolute best.

It is our passion for the subject we teach and the passion we have to make a change. It is about the student who struggles to pass every test, and to make them not give up. It is about having a student realize that every step they take is an improvement and they are doing their best. It is about pushing the A+ student to continue to work hard, to continue to be their best in every situation. It is about having our student’s believe and be confident that they can succeed and reach their goals if they put their mind to it.

Our profession is driven by passion. It is what is in our minds and our hearts driving us forward. It is the change we are making in each student’s life that gets us to do our very best. It has gotten harder, with the pressure of state tests and curriculum changes. But every now and again we need to be reminded why we have accepted the challenging role as an educator.  We have become educators to help, to challenge, to inspire, to create, to make kids love to learn, to make kids believe they can achieve anything they put their minds and their hearts to. We are living proof that we chose a profession based of what we love, not because of the money earned.

Take a moment before you begin the school year and think about why you have chosen to be a teacher. Get pumped up, be excited, be passionate about the lessons you are about to give and the challenges you will overcome.

Take a look at the two links below, including the one from Taylor Mali above. They are my favorites and always get me ready to take on the school year, school week, even just a school day. Some are about teaching in general and others are just great nerdy math links that have inspired some lessons.

10-Year Old Inspires Teachers

Rita Pearson: Every Kid Needs a Champion 

Arthur Benjamin: The Magic of Fibonacci Numbers 

Vi Hart: Anti-Pi Rant 

Vi Hart: Origami Proof of the Pythagorean Theorem 

There is one more piece of advice I would like to pass on from one of my colleagues. It was my first year and I showed my colleague a note I received from a student that said in short “thank you”. My fellow teacher told me to keep it and any other notes in a box for a reminder of why I am a teacher.  I have put every note, card in a shoebox and when I am having a tough week, I look through some of those notes. They are the best pick me up and a great reminder of why I stay up late, get up early, work my absolute hardest, and why I love my job.

The Importance of the Mathematical Practices and its Connection to George Polya

The Common Core’s Standards for Mathematical Practices are one of the, if not the most important standards teachers need to incorporate in their lessons. These standards are the epitome of problem solving. Our goal as math educators is not only for our students to understand the content, but to learn the life skill of problem solving and reason. We want our kids to be able to attack any type of problem (not just math) with confidence and a set of skills to guide them. The Standards for Mathematical Practices lay out this foundation for us.

These standards share a similarity with George Polya’s Steps for Problem Solving. Most math educators have heard and have used these steps, but they seemed to have been forgotten in recent years with the implementation of the common core. However, his work still lives on within these standards.

Each of the standards for mathematical practices are necessary for success in solving problems. The first standard, make sense of problems and persevere in solving them is vital to problem solving.This is a challenging standard for our students to demonstrate on their own. Some students are too quick to give up on a problem the moment they finish reading it. This first standard for mathematical practices encapsulates all of Polya’s four steps. Each of these steps aid students to understand and solve the problem. As educators we have to keep in mind that we cannot rush this process of understanding. Too often, due to time constraints and other outside factors, teachers move too quickly through problems without having their students really sink their teeth into a problem. Albert Einstein stated “If I had an hour to solve a problem, I’d spend 55 minutes thinking about the problem and 5 minutes thinking about solutions.” It is the understanding of the problem and coming up with a process to solve it is the most difficult. As teachers we need to be conscious of our pace and make sure that we are not moving along before our students understand the majority of the problem. For our students to reach this first mathematical standard, we need to be good models and slow it down, and demonstrate how to grapple with a problem. Polya’s first two steps are the longest, and that is because these steps are to understand the problem.

The second and third practice require students to analyze and defend their solutions. These standards focus on communicating the solution to a problem. We want students to question solutions and processes in our class. We want them to be able to reason abstractly and quantitatively and to construct arguments to prove their solutions. In order for our students to meet these important standards they need to communicate with each other. The most challenging part of this is for a student not to be afraid of asking a question. It is our job as educators to create and safe environment for students to ask questions. The only way our students can improve on these important skills is to make sure communication is happening in the classroom. It may be helpful to demonstrate a productive conversation or to point out good questions and good responses other students have made in class. These two standards really focus on proving their solution or other’s solution is viable. Standards two and three are directly related to Polya’s fourth step, looking back. In this step students need to make sure their answers make sense. To do this they must reason with themselves, and others, and construct an argument to why their solution is valid.

We can also make a connection between the second and first standards for mathematical practice. To understand the problem more deeply we must be able to have number sense, to reason abstractly and quantitatively. These are not just skills for math, they are skills for life. We want our students to be able to understand the difference between quantities given certain contexts. For example the difference between a 2% raise or a 5% raise, or the difference between one million dollars and one billion dollars.

The fourth standard is important and vital to Polya’s second and third step, developing and carrying out a plan. For a student to meet the fourth standard they must be able to model with mathematics, which includes drawing models or using manipulative. This standard cannot be reached if there is not enough exposure to using a model when solving a problem. When there is an opportunity for a student to use something physical to represent the problem, it will help with understanding the problem even more. Students should be exposed to manipulatives in math in the elementary grades, and when they reach the middle school level, they should be reminded they can model the problem by drawing or using a manipulative. A way to promote modeling with mathematics is intentionally including it in the lesson and having manipulatives easily available for students to use.

The fifth standard, use tools strategically, is a valuable skill our students need to learn. This involves knowing how to use all the math tools correctly and knowing when to use them. This not only is important in the math classroom, but it is an important life skill. This goes hand in hand with the previous standard in retrospect to Polya’s steps for problem solving.

Attending to precision is the sixth standard. We want our students to be accurate with their answers. In order to meet this standard, they must be able to meet the second standard, to reason abstractly and quantitatively. To be precise, students must realize their answer is reasonable. This is in Polya’s fourth step, to look back at the work and reason whether it is viable.

The last two standards are vital to problem solving. These both involve looking for structure and patterns to solve a problem. At the middle school level having students discovering regularity in repeated reasoning is prominent in solving problems. A way we can have our students meet this standard is to create discovery lessons, where students find patterns and repeated reasoning to solve similar problems. For example, having students discover exponent rules is a great way for them to recognize patterns in repeated reasoning to learn the rules. The important piece of these two standards is it is repeated reasoning. Students are supposed to make sense of the problem and reason with what they are doing to solve the problem. a further look into Polya’s work involve questions at each step, which is guiding the student through reasoning.

These standards need to be incorporated in the classroom as much as possible. As teachers we need to be conscious of including them in our lessons and take any opportunity to address them in the classroom. I have the standards hanging up in the classroom, and when it is relevant I will point out what standards that have been met. For example, if I hear students discussing and defending their solution with reasoning, I would address the class and explain how the conversation was a great example of the third mathematical practice. I also found it helped to list which practices students would be addressing in my lesson plan. In addition to having the practices on the wall, I have my students paste Polya’s four steps in the back of their notebook along with questions they should ask themselves for reference when they are stuck. It is a great tool for students to persevere through difficult problems.

These practices are not just for mathematical problem solving; they are life skills. Each practice is a skill used in everyday life, no matter what profession. This is why we teach mathematics. To have our students be prepared in the real-world. For our students to be able to reason and critique in social and academic situations. These standards can be applied to numerous real-world situations. The first and second practice alone are not just related to mathematics. They can be connected to different situations and different academia. In social sciences, people need to be able to listen, reason, critique, and argue different points.

It is unfortunate that teachers are being pressured for our students to only master the content. If we take a step back, our students can master the content through the skills we are teaching them. Not all problems on each topic will be the same. However, if we can get our students to recognize the content, and use the mathematical practices and Polya’s steps to solve the problem we as teachers are successful. Our job as math educators is not only to teach our students the content, but to develop these necessary skills so they can be successful in the future.

Too Impulsive With Curriculum Changes

I am entering my fourth year teaching 6th, 7th, and 8th grade math and it will be the third year in a row that our curriculum has changed. I have started from scratch each year with new material, and have not had any continuity.  I am able to incorporate some of the lessons that I created in previous years into the new curriculum, however becoming familiar with the problems and the order takes time. 

Our previous curriculum was Math In Focus (which I really enjoyed), which promoted more problem solving and cooperative learning will change to Eureka math. The problem is continuing to switch curriculums and not giving the current one a chance. We cannot execute a curriculum to be successful within the first year. It takes time for a teacher to be familiar with the matierial in order to improve their lessons. In order for a teacher to mold a curriculum to be their own and for it to be conducive to their class, it takes more than a year.  We can’t expect our students to be successful if the teacher is not able to improve and really be familiar with the material given to them.

Another problem is that we are assuming that student’s success is all about the curriculum being used. This is false.  A curriculum is a guide for a teacher. A curriculum provides materials and problems for students and teachers to work with. A curriculum is not a rule book that needs to be followed exactly. A teacher’s job is to use that curriculum as a guide and make it their own. The textbooks, workbooks, and the manipulatives are all supplemental to the structure of the teacher’s lesson. If the curriculum keeps changing, a teacher is not able to improve on his/her lessons.  The teacher has to start over and will not be able to focus on improving lesson from the previous year.

When picking a curriculum, the administration should involve the teachers. Since they are the ones using it everyday, they should be invovled in the decision. In addition, as educators we should not be so reactive. Everytime there is a new article on a new style of pedagogy or on the common core, adminstration and sometimes teachers are to quick to believe it and change what they are doing. The constant change will hinder the teachers from moving forward, which will in turn hinder our students. We need to give the curriculum we choose a chance, and not be so impulsive because we are not receiving immediate results. We have had a big change with common core, and it takes time. We can’t rush. When we rush, we stress, which gets passed on to our students.

It is time to let our teachers take the reigns and have them create lessons that are unique and conducive for their students. We need to give curriculum a chance and and not make impulsive decisions.