Monthly Archives: August 2010

Positive Value Classroom Experience

So, you’ve had a few days with your new group of students and things seem to be going well. Well, of course! The first few weeks or so is the honeymoon phase. Most of your students are not showing you their true colors yet. You’re just as guilty. You’ve been so upbeat and positive, but firm and professional. If only the rest of the year could be like these first few days, school wouldn’t feel like, well, school. Let’s talk about ways in which this honeymoon phase can last a little longer, or at the very least, reappear from time to time throughout the year.

First and foremost, let’s understand why the students are so well behaved the first few weeks.

  • They don’t know you yet; therefore, they don’t know what buttons of yours they can push.
  • You don’t know them; therefore, you are providing them with the benefit of the doubt and being non-judgmental.
  • You’re interested in them. You’re asking them questions and trying to get to know them.
  • You’ve set the tone of who’s in charge and where the boundaries are.
  • You’re holding them accountable and making examples out of behaviors that are less than desirable.
  • You’re lesson planning like there’s no tomorrow. You have plans A, B and C. Your organized, with papers and supplies filed in all the right places. Students don’t have a second’s worth of time to be off task or disruptive.
  • You’ve got the classroom looking so nice. Everything in its place, nice and clean, supplies labeled.

There’s nothing like the first of the year. Unfortunately, time does go by and we, as teachers, get very bogged down with paperwork, parent phone calls and meetings. Little time is left to keep the classroom clean, papers filed, supplies organized, or to create a plan A, let alone a B or a C. Since your plans are not as tight as they once were, students now have time in class to engage in conversations and get off-task, some even becoming perpetual classroom disruptions. At this point, you’re just trying to keep your head above water and teach your students the standards. Lest not forget there’s standardized testing, curriculum benchmarks and exams that require us to stay on mark with the curriculum pacing. You’re students start to feel your stress. They don’t know how to take your new demeanor. They start to take things personally, as if you don’t like them. Realize you haven’t had much time to socialize with them or continue to get to know more about them. They see it as, “You don’t care about them”. Behavior starts to deteriorate. You’re falling behind in the curriculum. Student’s grades start to slip. You start to lose respect and confidence in the eyes of the students. Keep in mind; I’m estimating things start to feel this way come, oh, say October.

This is a sad situation that happens to many teachers, classrooms and schools across the nation. Not to add more stress to your pot, but it’s time we need to realize who’s at fault for this rapid decline. It’s you, the teacher. That’s simply the hard, cold facts. It’s painful, I know. However, look at it this way. Imagine you’ve just seen into the future. You see how things “could” end. Now, what can you do to make sure this doesn’t happen to you?

Somehow, someway, you have to make sure that you keep that momentum in place throughout the year. You must stay consistent with your level of expectations for the students, for your performance as an educator, and for the culture you’ve created in the classroom. Simply doing this will keep a gain you a high level of respect from the students. With this comes respect and loyalty, as well as trust. You’re more than halfway there now!

Other ways to keep the focus on the students is to create a “What’s Happening” board. This of course can be called anything you’d like, but the focus is to capture student successes and learning. This can be achieved by posting high quality student work (keep an eye out for posting the same student’s papers time and time again), or out-of-the-ordinary student achievements. I would not say it this way to the students, but this may be reserved for those students who are below desired level, but makes substantial, but maybe intermittent, gains. This is for students who may struggle with concepts and not catch on to things as quickly as their peers. Celebrating these achievements in a public way creates a nurturing classroom culture that can be very motivating for all students. Finally, post pictures of students in the act of learning, doing a lab or an activity, ones that really capture the positive aspects you were requiring for that task. This is a motivator in and of itself. If students know they are only going to be showcased on the “What’s Happening” board by doing what they’re required to be doing, then you’re job has just become that much easier.

The suggestions above are what make teaching fun. Lesson planning, on the other hand, is not so much fun. Let’s face it. Teachers often times have to teach things they aren’t very interested in. Nonetheless, educators must look beyond a particular section or topic, and look at how to build a nice, solid foundation of knowledge for students. Skipping content does not achieve this. I suggest tapping into your resources to help you plan. The recent buzz word is Professional Learning Communities, or PLCs. These are learning environments within schools and districts that are designed to make teachers work smarter, not harder. Within these communities, teachers need to work together to create common items, be it activities, learning experiences, projects, quizzes or tests. Teachers do have to stop reinventing the wheel. This is such a time waster. Utilize your resources so that you can continue to make your plan A, along with your B and C. Last, but not least, two, three, or more heads are better than one, so put your heads together and create solid lessons to keep the level of learning high and the level of student disruptions low.

By incorporating these things into your daily or weekly routines, you’ll see  you’re not falling into the dark abyss most teachers find come the third or fourth month.  My final suggestion would be to print, or retype, and post the bulleted items I listed at the beginning of this post. Stick them in a location in the classroom that is highly visible to you. I would even suggest reading these over every Sunday night or Monday morning as you put your mind in focus for the week.

Let me know throughout this semester if you’ve found these ideas helpful. Good luck as you transition out of this honeymoon phase.


Error Analysis

Interestingly enough, as a teacher you’re concerned with students getting correct answers when it comes to math problems. However, a student’s wrong answer can tell you a great deal about what they know and understand.

 Have you ever graded a test, multiple choice or single answer, and found a large portion of students submitted the same wrong answer? If it’s a multiple choice question, hopefully all choices were designed with common student errors in mind. By doing so, you create the opportunity to group students post-test into groups according to the mistake they made.

 This next instructional strategy I’m about to explain is not my own. In fact, I’m not certain who initially came up with this idea, but it is one that I, and fellow teacher s, have used and found very informative. What you do before and after this strategy is up to you as the teacher. This idea simply gives you an idea of how to collect data about what students know and understand.

 Let’s start with a simple concept like solving one-step equations. Provide students with a questions such as x – (-3) = -7. We know the answer to be -10, because subtracting 3 from both sides is the correct step in isolating the variable for this problem. We see this equation to be x + 3 = -7 by use of the definition of subtraction that states a – b = a + (-b). Only after we “clean up” the question are we able to see what operation we need to undo during the solving process. This particular problem is a quite difficult for 7th and 8th grade students who are just learning how to solve equations. Common mistakes are to add 3 to both sides, producing a -4 solution. Other mistakes are to correctly perform the operation to solve only to apply integer operations incorrectly. If students did indeed subtract 3 from both sides, they could come up with -4 or 10 as incorrect solutions. If we play the role of the student when designing question, we can perform error analysis during classroom instruction.

 Using this particular example, we arrived at solutions of -10, -4, and 10. The value of 4 could be justified as an incorrect response if students did not apply integer rules correctly when solving the simpler, yet equivalent, equation x + 3 = -7. Provide students the original question, x – (-3) = -7, and have them solve this equation and show their work. Have the potential answers of -10, 10, -4, and 4 posted around the room inconspicuously. Once students have found an answer, and before you have disclosed the correct solution, have students get up and stand by their response. Give them one or two minutes to discuss as a group how they found their common answer. Next, have one member from each answer group explain to the whole class how they arrived at their answer. After all students have listened to all of the groups’ responses, they must then decide to agree with their original group, or decide to join a new group. They must provide an explanation to why they are choosing to join a new group by stating the mistake they made in their solving process that arrived at a new answer.

 This can be applied to any multistep problem, on in which common misconceptions or error may occur. There may be anywhere from 2 to 5 possible responses students may have, depending on the error they made. Do your best not to make any judgment calls prior to students forming groups and making their final decision on an answer based on each group’s explanation. This provides students the opportunity to evaluate their steps and problem solving process against others in the class. This is a level of analyzing that most of the time does not happen when we, as teachers, simply mark a student’s paper for incorrect responses. Once students become accustomed to this type of discussion and error analysis, they will become leaders in their own education.

 I will caution you on stopping the discussion at disclosing the correct solution for the problem. I encourage you to provide students the reason as to how they could have arrived at the incorrect solutions where predetermined.  You will find students with incorrect answers that do not fall into the anticipated incorrect responses. Take this opportunity to allow the student to perform their own error analysis on their work and have them explain their mistake.

 This is a powerful tool that creates analytical students and better test takers. Of course, it’s important for students to understand how to arrive at correct solutions for problems. However, students can gain a great deal more information from learning what they did incorrectly. It’s important for students to know when they got a question incorrect, but to maximize learning; students must understand how they got a question incorrect.

Please share ways in which you have utilized, or will utilize, this stategy.

Have a Plan

So the first day of school is here! Do you have a plan … for everything? As a teacher, the one skill you can never under utilize is creating a plan for events that have not yet happened. Think of this as an extra level of planning that is just as important as planning the lessons for instruction themselves. Having a plan for what “might” happen will make your life so much easier when the need arise. What am I talking about? I’m referring to the following situations, of which most veteran teachers have experienced at some point in their teaching career:

  • What if the busses are late arriving to school in the A.M. or the P.M. and you have students straggling into your homeroom/first period or staying with you for an extended period of time in your last period?
  • What happens when your students receive textbooks 2 weeks late? Teaching still must happen. Are you prepared to teach without having a book for students to refer to?
  • How are students going to go to their locker? If you work in a newer school where the hallway width is minimal, including hundreds of lockers, every student will not be able to access their locker during the same change of class. Would designated locker times alleviate over crowding and tardiness? How would these locker times be assigned? By grade? By teams? By location in the building? By top locker/middle locker/bottom locker? How will this be conveyed to students? What penalty will be in place if students go at a time that is not theirs?
  • You have just gone over the procedure for walking to the next class/auditorium/gym/cafeteria. The time has come for students to transition, and students cannot go according to the procedure. Reason could be there are too many students in the hallway at some point along the path students were going to take; the procedure involved going outside, but now it’s raining; or it simply is not the most efficient route. What is your Plan B? Plan C? How will you communicate this to all individuals effected by this change, i.e. students, fellow teachers, and administrators?
  • What happens if there is a fire or inclement weather on the first day? (This HAS happened to me on the first day, in fact a fire and a tornado watch.) How will the emergency procedures be handled by the school, your grade, and your team?
  • What happens if a parent wishes to accompany their child on their first day of school and your administrative staff has permitted this? Are you prepared to have a parent visitor?

These situations are on top of the usual situations you have a plan for, such as

  • Where are students going to sit on the first day? I recommend not allowing them to sit where they want. Having a plan, whether it’s using number cards with matching number on the desk, a seat assignment displayed, or other random seating technique, it’s the first instance where students see that you are organized and one step ahead of them.
  • How will you pass out materials?
  • How will you collect materials?
  • How will students turn in assignments?
  • What will you do if students do not have the proper supplies, i.e. paper, pencil, or book?
  • If you allow students to borrow materials, what is your plan for administering the return of these items?
  • What will be your plan for students leaving and returning to your classroom?
  • Teaching students the importance of keeping their area, and entire classroom, clean and orderly starts on the first day. What activities do you want students to do on a per class period basis to ensure this happens? Will you reward students who do their part?
  • How will students move from one location to another? Will you require them to be in a straight line? (highly recommended) Will there be traffic pattern requirements, such as only walking on the right-side of the hallway or one-way hallways?
  • How will students have assigned tables/area at lunch? How will you collect students after lunch? I recommend lining them up and checking their area to insure cleanliness.
  • How will you dismiss students?

These are just a few questions to ask yourself and work out at least one plan before the first day students arrive. Plans can always be modified as needed, but it’s not best practices to keep changing plans simply because they do not work the first go around. Students will often see this as a sign of weakness and become the culprit in sabotaging your plans. Consult fellow teachers on your team, hallway, or school, as well as administrators to get assistance in creating solid plans that will create an environment that is structured and focused on learning.

Working Systems in Groups

Once the three methods of solving systems of equations have been taught, graphing, substitution and elimination, a wonderful review activity is for students to work in groups of 4 solving systems together, discussing solutions and methods chosen. I did this activity over a two day period as a review for the cumulative chapter test in algebra honors.


  • To have students become more proficient in solving systems of equations, both abstract and in context
  • To have students discuss their method of solution and analyze its efficiency
  • To have students utilize technology in solving systems of equations


  • Graph paper, ruler, graphing calculator, pencil, paper


     Divide students into groups of 4, if necessary a group of 3 will sufficient. Create small name plates to identify the job(s) of each student reading Graphing, Substitution, Elimination, and Calculator. Give each group a set of system of equations, with the first day focusing on the abstract and the second day focusing on the system problems in context. Each member of the group works out the problem, showing all necessary work for their method. The calculator person will have no work to show except the solving of each equation for y. After each person determines the solution, they compare results. As a team, if a member did not come to the correct answer, or if the group as a whole disagreed on the answer, discussion would occur. Each member would analyze other student’s work, ask for assistance from group members or lend support to group members if they can. The goal is to get students discussing the mathematical process for each of the methods of solution. After an answer has been agreed upon and work corrected as needed, students will then discuss which method, or methods, was/were the most efficient. It’s important that students do not get stuck utilizing the same method over and over again, simply because they don’t know how to do the other methods. There are instances where one method is more efficient than others. For each question, each member will write to why their method was the most efficient, or not efficient. For each question, the jobs rotate. This is to insure that each student gets the necessary practice on all methods.

The Impact of Common Core Standards

Let’s get the discussion going on the effects of the Common Core Standards on mathematics education and how the Bill and Melinda Gates Foundation are impacting public education. Here are a few items to get you caught up on the topic. This could drastically impact the education of students for decades.

Do you think this a positive or a negative shift?

What do foresee to be the immediate effects this year?

What are your concerns as educators?

NCTM – Common Core Standards

San Diego 2010 – Common Core Standards Initiative Video (NCTM)

Bill Gates\’ School Crusade – Bloomberg Businessweek

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