An Instructional Shift

I am working this summer as a common core coach for the state of Tennessee.  It has been an amazing experience.  Tennessee contracted with the Institute for Learning to train 700 coaches across the state.  This summer, we will train 34,000 teachers.  This is the largest training ever hosted by the TN Department of Education.  I have learned so many things such as:

• High level tasks matter
• Enacting tasks in the classroom is vital to student learning
• Accountable Talk in the classroom ensures productive discussions
• Learning how to ask students assessing and advancing questions is necessary
• The practice standards for mathematics are long overdue
• The common core is a great thing!!

I am so excited about the common core and the changes it will bring to instruction and student learning.  The standards and practices in themselves are not magic, but the shift of focus from multiple choice assessment to conceptual understanding will benefit student learning.  To help teachers in the classroom, I have compiled a list of math tasks in a tab at the top of the page.  Please feel free to comment on them and add to the list.

Zombie Attack and Exponential Growth (What to do after state testing…)

After the End of Course test I am always scrambling to find activities for my students.  I did this zombie activity in my class last year, but this year several other teachers and I teamed up and collaborated to put together this very cool activity.  (To be honest, my contribution was only the worksheet.)

On day one, we showed the movie Contagion.  We discussed the r not value and how viruses spread. 

 

We prepared small cups of water, numbering them on the bottom.  We filled the cups half way with water and put a few lemon drops in one of the cups.  Each student received a cup. 

 

The students were then told to share water with one other student.  This involved two students getting together and one of them emptying their content into the other cup.  We asked them to transfer the water from one cup to another three times to make sure the liquids mixed.  After this, the students equally distributed the water between the two cups.  This constituted sharing with one other person.  We repeated this two to three more times (depending on the size of the class).  After this we added a few drops from this pH test kit. 

If the water turned yellow, the student was infected.  We then discussed what students shared water and who they shared with.  In both classes the students were able to discover who initially had the virus (lemon juice).  We confirmed this with the numbers on the bottom of the cups.  Doing this part of the activity really helped students understand exponential growth and how viruses spread.  We handed out the following zombie attacks packet and had the students work through the exponential growth using different scenarios.

Next year, the plan is to have the entire STEM academy join in the fun.  We would like the STEM English teachers to have their students research creative stories that include exponential growth and decay or the spread of bacteria.  The science teachers will add their expertise and critique the film from a scientific plausibility stand point.  We asked the history teachers if they would have their students research past epidemics and the effects on society.  As we collaborated as a STEM academy, the excitement grew and new ideas sprouted.  I’m excited to see the great collaboration that will happen next year after the End of Course test.  This is just evidence that learning doesn’t stop after state testing.

Assessment For and Of Learning

I have learned so much over the past few months while attending common core training.  Tennessee is currently training teachers to act as facilitators this summer and train their peers.  I am working as one of the common core coaches in Algebra 2.  This is the first professional development where classroom practices and activities have been modeled for me.  Instead of someone standing at the front of the room lecturing me about how not to lecture in class, I have opportunity to be the student and see common core tasks implemented.  I am learning so much about advancing and assessing questions.

Recently we had a discussion regarding assessment for learning and of learning.  I have always known there is a difference and I assumed my formative and summative assessments were addressing this.  I have since changed my opinion.  With the switch to common core, I need to incorporate tasks into my classroom.  These tasks are similar to the one I used before training. This baseball task was open-ended and provided multiple solution paths.  The real meat to this task comes in the discussions and questions that come after the students complete the task.  By asking the right questions, a teacher can assess a students learning and know where a student may lack the understanding.  I must admit that this is the part I need the most help with implementing successfully.  (I promise to write more on questioning later.)  By doing this task in class and allowing the students to work in groups, you are allowing learing to take place.  A student may not understand all the avenues to find a maximum, but through a group discussion, they may be reminded of alternative methods.

Assessment of learning happens when a student takes an assessment and receives a grade or feedback to evaluate themselves.  I do believe that learning happens from this, but often we as teachers make this the end.  This is more reflective of a PARCC assessment or final state test.  Some groups are calling these Problem Based Assessments (PBA) and other call them Constructed Response Assessments (CRA).  (All we need in education is more acronyms.)  A better example of a PBA involves taking the original task used and modifying it by asking the student to:

• Write the equation in vertex form and identify the key values in terms of the story.
• Write the equation in factored form and identify the key values in terms of the story.

This not only assesses if the students understand quadratics and their real life applications,  it ensures that the students can represent quadratics in multiple forms. 

My goal for next year is to incorporate one good task per class every two weeks.  I would also like to include PBA style questions for summative assessments.  I’m trying to be careful with outside resources for common core.  I want to make sure the tasks I select are rigorous and appropriate.  What good resources have you found for common core?

Quadratic Introduction: Baseball Math

I recently was selected to be common core coach for TN for Algebra 2. I have tried to incorporate the philosphy into my classroom. I handed out the worksheet below and put the students in small groups. I had not spent any time in Algebra 2 on quadratics and I wanted to see what they remembered from Algebra 1. I asked them to work individually first. After approximately five minutes, I let them work together to answer the questions. I was amazed with what they could figure out without me having to teach a lesson. After 10 minutes, I asked different groups to come to the smartboard and present their findings. I had some students use their graphing calculators to find all of the answers. I know this seems bad to some teachers, but it was helpful for students who could not remember quadratics from Algebra 1. It provided them with a way to be successful. I had one group who remembered the quadratic formula and used it and found the vertex by hand.  You can get the worksheet here.

 

I love teaching quadratics becasue of the real life applications.  I need help with finding real life like the one above.  I really want questions that can be solved using different methods.  I’m trying to prepare for the new common core tasks.  Does anyone have any good resources and wouldn’t mind sharing?  Thanks.

When Teaching Hits Close to Home

This has been one of the most difficult years I have spent in education. I have considered leaving the classroom more than once. I should have known this semester would be difficult when the guidance department informed me that several of my students were hand selected for my class.

One of the problems with being a proponent of Standards Based Grading in a school that does not unilaterally embrace it is that you provide multiple opportunities for students who struggle. Students who have never experienced success in the classroom show great gains when the philosophy of mastery learning and multiple attempts at mastery permeate the classroom. What’s the problem with that? You get more at risk students than you can possibly handle. You get more special cases and more troubled students than you can possibly handle. Word gets out when kids and their successes are the driving force in your classroom. Be warned.

I became jaded and slightly cynical and a little burned out. I felt like a failure that I could not reach each one of these students who had become jaded with public education. To add insult to injury, I was awarded Southeast Tennessee Teacher of the Year this semester. I felt unworthy of this honor.

It is amazing how God can humble you and rekindle your passion and calling for students. It is heart wrenching how He chooses to do it. My own son started experiencing neurological issues last summer. It was obvious to all; and students started making comments to him at school. Sixth grade is difficult enough without adding obvious facial tics to the list of awkward middle school attributes. My son is on medication and the tics are gone,but one of the side effects is the inability to retain information and difficulty processing information. He describes it as working through a fog. My once honors student who scored advanced on standardized tests is struggling to remember to write his name on papers. He forgets to turn in assignments. He still rocks a standardized test and is currently earning A’s and B’s on most tests, but he is struggling with the day to day workings of school.

After a tremendous grade drop this nine weeks, he begged me to take him off his medication. He told me he would rather face the teasing of kids over his tics than to disappoint me or his father with these poor grades. I told him I would talk to his teachers about accommodations, and his response was that he didn’t want his medication to be an excuse. I’m so proud of this young man. We go back to his doctor and my hope is that we can find a new medication or adjust the dosage. In the mean time, my son and I have been blessed with some amazing teachers in his classrooms. They were all quick to work with us on this issue. My son is not lazy and I believe they would attest to the fact that this is not typical behavior for him.

As an educator, it was difficult for me to ask for any special consideration for my son. I was reminded that there are several students out there just like my son. Most of those students do not have a teacher for a mom. Several of them do not have advocates in the house. A few of them do not have encouragers in the house. I teach for them. I teach for the student who has never experienced success. I teach for the child who used to be successful, but for different reasons, can’t seem to achieve. I teach for my son.

So, please give me the at risk kids. I want the students who struggle and hate math. I want the young man who doesn’t understand why he needs Algebra 2 to graduate. I want the young lady whose home life doesn’t foster learning. I know it will be difficult and I know I won’t always be successful, but I can plant a seed. I write this for myself so I can remember. The next time I’m frustrated that a student turns something in late, forgets to put their name on a paper, or needs to retest another assessment, I will remember my son and the grace his teachers showed him. He is not another at risk kid. He is my son.

Number Sense and Math Reasoning Inventory

I have two children of my own. Often, they end up becoming guinea pigs when it comes to math instruction (or just about anything). As a secondary teacher, I feel qualified to teach integration, quadratic functions, or any other topic beyond Algebra 1. When my son brought home his first set of flash cards from school, I was at a loss. The only tool up my sleeve was memorization by repetition. Needless to say, we spent many hours drilling and crying (ok, I was the one crying). My younger son watched and didn’t speak, but he was absorbing. Little ones are like sponges and sometimes that is not good.

A few days after the flashcards disappeared, my then 6-year-old said, “Mom, I know why 3 x 5 is 15.” I was curious. His response shocked me. He explained that if he counted by three’s 5 times, he would end at 15. He also told me that he could do it the other way and count by five’s 3 times. Of course, I knew this, but in my pursuit to push my older son to memorize faster, I skipped the understanding. What my 6-year-old was developing was number sense.

One of the complaints I most often hear from high school teachers is that students do not have number sense. I’m not sure how you measure number sense or how to teach it, but you know it when you see it and you definitely know when it is lacking. I need students to understand that 3/4 – 1/4 is 1/2 without having to perform an algorithm. Sometimes I think we become too engrained in teaching algorithms without understanding. My hope is that the new common core assessments will force teachers to fix this.

Recently a colleague introduced me to a website, Math Reasoning Inventory, that encourages formative assessment for understanding and building number sense. Maybe some of you already use it and can offer feedback. I have not seen anything like it in mathematics before and am excited about how this could change elementary mathematics education. The site encourages teachers to conduct interviews with the students on mathematics problems. The focus is not only the correct answer, but how a student achieved that answer. For example, if a student is asked to calculate 7000 – 70, using a standard algorithm would be considered an inappropriate strategy. I have to say I love this! Students forget algorithms and cute tricks, but true number sense and understanding will always work. I encourage you to look at the website and provide feedback below. I would love to have students at the secondary level who had been evaluated with this method. 

Number sense is hard to define and harder to assess, but I believe that the Common Core will help us achieve what is so necessary for mathematical success.

A Calculus Wedding

We had a wedding in Calculus.  I gave the students a copy of an invitation the day before, asking them to come dressed in black and white to observe the occasion.  I purchased a cake for the event and provided a bouquet of flowers for the bride.  On the day of the wedding, students arrived in suits and dresses.  I was really surprised with the effort the students put into this event.  I thought they would think it was cheesy, but I guess they know me by now and expect nothing less.  One student went as far as to  borrow a wedding dress from the theater department.

I allowed the students to vote for a female student to represent Deriva, the Derivative and a male student to represent Integroom, the Integral.  Each person was allowed to select an attendant.  I played the wedding march and directed the ceremony, officially wedding the Integral and the Derivative using The Fundamental Theorem of Calculus.  The wedding was all the buzz of the school and several students in Pre Calculus came to ask me about it.

 This is my first year teaching Calculus and AP Calculus.  I think it is important for the class that we establish an identity in the school so other students see the importance of being in such a rigorous class.  My goal next semester is to order t-shirts for us.  Does anybody else have any good ideas for setting the AP Calculus class apart?

Constructed Response Assessment for Common Core

I recently was invited to attend training for the new constructed response assessment for common core for 6th – 8th grade mathematics.  My system has decided that the high school teachers will help the middle school teachers grade the assessments.  We are doing this for two reasons.  The first is to gain knowledge of what is to come in 2014 for us and the second is it takes a long time to grade them.  I personally was anxious to see how my own child (a 6th grader) was going to be assessed.

I knew I would love the new common core, but I had no idea how much.  As I sat and listened to a 6th grade math teacher speak about how the common core had changed her classroom, I had to hold myself back from shouting “amen” and “preach it, sister.”  Each grade has two focus standards that all lessons revolve around.  For sixth grade, one of them is “understand ratio concepts and use ratio reasoning to solve problems.”  (How many time have you said:  “If my kids could only understand fractions…”)  This teacher stated that she no longer teaches her students ‘cross multiply and divide’.  She said that is an algorithm or trick we teach them, but it does not lead to a deep understanding of ratios and proportional reasoning.  (I was crying for joy inside!) 

Common core has identified six key principles for mathematical practices.  This is what the students are assessed on.  The content is interwoven into the these six practices. 

• Make sense of problems and persevere in solving them.
• Reason abstractly and quantitatively.
• Construct viable arguments and critique the reasoning of others.
• Model with mathematics.
• Use appropriate tools strategically.
• Attend to precision.
• Look for and make use of structure.
• Look for and express regularity in repeated reasoning.

The teacher I observed had a poster on her wall for each practice.  She said she constantly refers to them when working on problems with her students.  As we began to grade the sample assessments, it was obvious that the eight mathematical practices were vital to earn a successful score on the assessment.  I loved that the students did not have to work the problem using on method, however, they did have to show their work and reasoning.  As a grader, you could not assume anything.  If a student did not show how he or she arrived at an answer, they did not receive credit for several of the categories above.  If it was necessary to perform a process more than once, like finding the slope of a line, the student would have to calculate the slope using the same method each time, while showing their work, to receive credit for the repeated reasoning practice.

Overall the grading of the assessments reminded me of the Advanced Placement Calculus training I went through and how that test is graded.  Students have to justify arguments and show their work.  Answers are no longer enough and your method for finding the answer must be mathematically sound.  The sixth grade teacher told us that she spend a class period with her students looking over the sample tests and the scoring rubrics and discussing why some students didn’t receive full credit.  One of the benefits for students was that they discovered they could work the same problem using different methods and still receive full credit as long as they showed and explained their work.  

I would strongly encourage you to contact your state to gain access to any practice assessments and grading rubrics released.  In TN, the items are password protected or I would share them.  (I like my job and want to keep it   I plan on encouraging our Algebra 1 teachers to begin implementing the 8th grade assessments we have access to online.  Overall, I learned a lot from the training and I have high hopes for the future math students.  It will take a few years to see the results, but I believe mathematics education is finally moving in the right direction in the United States.

Roller Coaster Fun

The STEM academy at my school is starting a Science Olympiad team this year.  To recruit members, the engineering teacher and I collaborated for a roller coaster project during class.  We took our students to the auditorium and put them in groups of three or four.  We gave them a handout explaining the details of the activity.  The students were asked to create a mock roller coaster using the supplies they were given.  They were told the roller coaster would be evaluated using the following equation:

The students had to first discuss how each of the variables in the equation would affect the final score.  The goal was to achieve the highest score, while creating an aesthetically pleasing roller coaster.  After the student finished the roller coaster, they were asked to create their own equations that would give them a higher score.  They had to defend why they weighted each item as they did and why they put it in the numerator or denominator. 

We supplied each group with a piece of foam tube for track, four notecards, four straws, a styrofoam cup, and a roll of tape, and a razor blade.  The students were allowed to use items in the room as supports, but not as actual parts of the roller coaster.  The passengers were marbles of varying weights.  The students had a great time and it was amazing to see the differences in  each roller coaster.  I definitely see expansion ideas for this project.  Next time, the engineering teacher and I will create a store for the supplies and make the students purchase their supplies with a limited budget.

Calculator Boot Camp

I based this idea on something I stole from samjshah.  Sam does an algebra boot camp for his calculus students during the first week of school.  If you have taught calculus before, you know that the calculus is easy, but most students struggle with the algebra involved in it.  I transferred  this idea to my Algebra 2 students.

The Algebra 2 standards in TN are overwhelming.  After teaching it for 2 years, I  found that most of my time was spent teaching students how to use the graphing calculator.  My students do not use a graphing calculator in Algebra 1.  This is their first exposure to this type of technology.  This year, instead of repeating the same steps everyday and getting frustrated, I decided to do a calculator boot camp the first week.

On the second day of school, I give the students this lab on how to graph a function and change the window.  It will also address how to utilize the table feature of the TI-84.  On day two, students will work on finding zeros on the TI-84 and finding maximums and minimums on a graph.  On the third day of the boot camp, students will learn how to input data into a table and find the measures of central tendencies.    My plan is to give the students an assessment at the end of boot camp to test their calculator skills.  My goal is that students have the basic skills to navigate the calculator and to give them the confidence to explore the calculator on their own.  I will post on my success with this after the first week of school.