Trying to Think Algebraically

It’s been more than six weeks since I participated in a week-long Common Core institute put on by Pearson Education. I have 21 days worth of lessons done so far for Unit 1 and have moved on to Unit 2. Unit 2 is supposed to last 4 weeks according to the ISBE Scope and Sequence and I already have an opening 3-Act math activity similar to this planned to introduce the lesson and a few direct instruction lessons planned after that for solving equations.

Now, I’m trying to create lessons and activities where students will have to write and solve equations in order to work through the task. However, it’s been tough to come up with activities outside of rates or ratios. I looked in my textbook to see what word problems/scenarios were in there and here were two of the problems I found:

book problem 2

book problem

First, question #38 is so contrived, it made me laugh as a math teacher. If Chris and Nora can determine that “Chris has saved twice the number of quarters that Nora saved plus 6 and the number of quarters Chris saved is also five times the difference of the number of quarters and 3 that Nora has saved,” they should also be able to just count the number of quarters they each have without having to write and solve an equation. Dan Meyer has a weekly “Makeover Monday” in which he takes a bad textbook question and he and his Twitter followers give the question a “makeover” to try and create a 3-Act math activity out of it. I’m not sure if this one can be saved.

When I look at question #52, it starts off looking a little better. When we go shopping as a family, there are times where we find unit prices in order to find the better deal. This is probably one of the few times my wife uses math in a real-life situation. But once I read through the entire problem, I thought, “Why would any market give you the price of apples, pumpkins, blueberries, and winter squash, but not give you the prices of potatoes or zucchini?” Also, when you are told the prices, why would the prices of potatoes be given as “$1.50 less than half the price of apples?” I’ve never seen a price list anywhere that writes prices this way.

Now I’m back to where I started, looking for situations in my life where I use algebra. I think the hard part is that I do it automatically, without thinking about inverse operations. I also have to remember that I may not be able to come up with multiple tasks/scenarios to model each standard, especially enough to last four weeks. As time goes on, I think we will all come up with one or two activities that work really well, share them with each other, and accumulate weeks worth of intriguing, engaging activities.


A Conversation With My Children

I have the luxury of having a stepson who loves math and does really well and a stepdaughter who hates math and struggles daily, giving me insight into both ends of the spectrum on student performance. While preparing my Common Core lessons, I began to see that, although my Common Core lessons will look quite a bit different than my old lessons, it is very possible my kids will probably still feel the same way about math as they do now. During a recent trip to get ice cream, I talked to the two of them about my new lessons to get a better idea of why they feel the way they do about the subject of math.

When I met my wife, my stepson Logan was in kindergarten and Kenzie was in third grade. Since that time, it was very apparent that Logan was talented when it came to math, and Kenzie was going to fight her way through it year after year. This year, Logan will be in sixth grade, but taking a seventh grade math class, while Kenzie will be in eighth grade and in eighth grade math.

During our trip for ice cream, I asked them:

  1. What are your feelings about math and math class?
  2. Why do you think you feel that way?

Kenzie was the first to respond and said she hated math class and the subject of math. However, she did say she likes to  “add, subtract, multiply, and divide.” So I asked her why she didn’t like the other stuff in math and she replied, “It’s really hard to read a problem and figure out what to do. I’m really bad at that and usually get the wrong answer.” In my experience, this is true of Kenzie. She would rather you tell her what to do in any situation in life than to sit and figure it out on her own.

When Logan answered he said, “That’s the part I like about math. I like to figure stuff out and get the answer.” Since I have known him, Logan has always been this way. He loves to solve puzzles and is always asking questions about anything in like that he doesn’t fully understand.

When thinking about Common Core and how it is going to “fix” student understanding of math, I start to question how that will happen. Since we are moving toward a more inquiry-based style of teaching and learning, I feel Logan will excel. It’s possible he will like math even more than he does now. However, Kenzie will struggle even more. If her biggest problem with math is figuring out what to do and math classes will now be filled with those situations, she will have to fight even more to understand.

My hope for my classroom is that I am able to challenge those students who already do well in math and also entertain those students who dislike math. I feel that if I can create fun activities that students similar Kenzie would enjoy doing, I may be able to create an environment where analysis and learning can take place. I know this for sure, the way I taught my class before didn’t work for kids like Kenzie. Students like Logan could show up, do the work, and get an A. Students like Kenzie were uninterested, rarely learned much, and were always behind. Maybe the hope for Common Core is that, since there are fewer standards, the extended amount of time will help struggling students take their fragile knowledge and turn it into a deeper understanding.

Making Parents Aware of Common Core

As I continue to prepare for next school year, I keep coming back to the idea that most parents are unaware what Common Core is and how it is going to affect their students. I decided I would email a letter to all parents who had a working email address in my district’s student management software.

But, what I am going to say?

“Dear parent,

Math class will look different in almost every way for your child next year.


Andy Harridge”

Although it is accurate, that really tells them nothing. I was hoping I could find someone else’s flashy, informative parent letter through Google. All I read was wordy, dull letters that teachers could understand, but the average parent would have stopped reading after one paragraph.

So now I’m back at square one. I felt that in the letter/email, the following things needed to be covered:

  1. This is a national change to education. The change is being made to better prepare students for college and the workforce.
  2. Lessons are going to be much more student driven than teacher driven. Students will be coming up with ideas, concepts, and definitions through exploring instead of me telling them all of this through a lecture.
  3. In my class, homework is going to be much less of drill and practice and more writing of explanations. Instead of 20-30 questions per lesson, students will have very few, if any items to answer.
  4. Tests and quizzes will be given more often and will tell me what I need to reteach and who needs to be retaught.  Students will have an opportunity to retake a quiz or test if they did not master the material the first time. Like homework, tests and quizzes will be made up with fewer questions and more explanations.

My finished product looks like this: (here is a copy of the letter in Word)

Dear parent or guardian,

My name is Andy Harridge and I will be your student’s math teacher for this 2013-14 school year.  During this school year, you will see many differences between my math class and what math class looked like when we were in school. These changes are due to the nationwide movement towards the Common Core State Standards. These changes are being made to better prepare students for college and the workforce. Currently, 45 states have adopted these standards, with full implementation and testing to be done during the 2014-15 school year.

The first change you will hear about from your student will be how classroom lessons look. Lessons will be much more student driven than in the past with students coming up with ideas, concepts, and definitions through exploration instead of me telling them all of those things through lecturing. There will also be much more application of concepts to real-world scenarios than was done in the past.

Another change that students will notice is that homework is going to take less time. Instead of students doing 20-30 practice problems every night, students will have very few problems, if any at all from day to day. The homework problems the students will have to do will involve more explanation and writing instead of getting one correct numerical answer.

The third change in my classroom will be on tests and quizzes. Tests and quizzes will be given more often and will tell me what needs to be retaught and what students need the reteaching. Students will have an opportunity to retake a quiz or test if they did not master the material the first time. I will use a grading system that encourages students to do well the first time, but also improve on the second try of a quiz or test. Like homework, tests and quizzes will be made up of fewer questions, but will involve more writing and explanations.

If you have any questions at any time, please reply to this email and I will respond to you as soon as I can.


Andy Harridge

I have not emailed parents yet. If you have any things you think I should change or any opinions on this, please comment. I’m hoping I didn’t create yet another wordy, dull letter that parents are going to stop reading after the first paragraph.

My Assessments Have to Change

In my previous seven years of teaching, my class looked like this:

  1. I teach half of the chapter.
  2. I give a quiz.
  3. I teach the second half of the chapter.
  4. I give a test.
  5. Next chapter – return to step 1.

Throughout those seven years, I feel I was fairly successful with about two-thirds of my students. The problem with my class, though, was that the other third never had a second chance to learn the material. Most of the time, the students that earned a low grade on their mid-chapter quiz, also earned a low grade on the chapter test. This trend then continued chapter after chapter until the semester final, on which those students really never had a chance.

During each chapter, I had very little information as to what any of my students knew and didn’t know. Then, once the quiz or test was graded and returned to the student, I did very little with the data I had obtained. The students had no opportunity to learn the material and retake the assessment and I did very little to change my lessons to reach those that had not yet learned the material. Basically, my belief was that a bad grade would motivate those students to try harder and do well on the next assessment, which rarely happened.

So, with Common Core bringing about change in the way I teach, I felt it was a great time to change the way I assess and use assessments. Thought Twitter and other websites I read, formative assessment has become a buzzword. I knew I would first have to get some information about formative assessments and how to implement them. I was fortunate enough to come across a great book Embedded Formative Assessment by Dylan William. I was also shown the website New Jersey Center for Teaching and Learning(NJCTL) by my colleague Wendy. From this site, you can download SMART Notebook lessons with SMART Response questions within each lesson.

The last month or so of last school year, I used the NJCTL lessons and I feel the students did much better on the mid-chapter quiz and end-of-chapter test. About four or five times per lesson, I could assess student understanding of the lesson and move on or reteach if I needed to. I used 80% as the marker for whether or not I would move on. I saw two problems with my process, though:

  1.  It was usually the same students who were in the 20% that didn’t get the question.
  2.  Because I was using SMART Response, most of the questions were multiple choice. There were some students that guessed on every answer, or, used the multiple choice to eliminate bad answers. When asking for explanations of answers, some students told me they knew what the answer wasn’t, so they could then determine the correct answer. They were unsure about the right answer, so, they may not have known the correct answer or how to get the correct answer.

First, I’ve decided this year to use much more formative assessment during my lessons. I’m going to try to use less SMART Response and more cooperative learning for my formative assessment. Within those cooperative learning groups, I’m going to require more explanation and much less “just-give-me-the-answer” types of questions. I’m going to try to take some very basic notes each day through Google Docs to keep track of which students struggle with what concepts and strategies I tried to help them. This will help me year after year when teaching those lessons.

Second, I’m going to allow students to retake any assessment that I give this year. The past three years, I’ve offered credit recovery to students who have failed a chapter test. They would have to complete a folder on Compass Odyssey and then I would change their grade from an F to a D-.  I’ve only have a few take me up on in though. This time, I wanted to find a way where a B could become an A or a D could become a C. While reading Embedded Formative Assessment, I found a great matrix that encourages students to do well the first time, but to also to improve on the second try.

Grade Table

I have never tried this before, so this will be interesting for me. I will be sure to share how I feel this worked this year.

Lastly, I’m going to stop putting a grade on student assessments. I’ve made my first two assessments(Unit 1 – Interim Assessment 1-3 and Unit 1 – Interim Assessment 4-6) and made an area for me to comment on each set of questions of the same type. I want students to actually listen to my feedback instead of just focusing on their grade. In Embedded Formative Assessment, there is discussion of a study done by Ruth Butler and her colleagues in which students were given a grade, feedback, and both on an assessment. The students who just got feed back had the most improvement. The students who got a grade and the students who got a grade and feedback both improved much less and at the same rate. Dylan William also had a very interesting point about this study: 

“When students were given both comments and scores, which did they look at first?” Everyone realizes, of course, that it was the score. What is more interesting is what the students looked at next: somebody else’s score.

-Wiliam, Dylan. “Providing Feedback That Moves Learning Forward/Practical Techniques.” Embedded Formative Assessment. Bloomington, IN: Solution Tree, 2011. N. pag. Print.

Once students have been given their assessment and we have talked about their feedback, I will then post their grades by ID number so they will then know their grade. Again, I’ll share the results of this practice as well.

Overall, my class will look different in every way next year. I’m pretty worried about how I’ll adjust, but that comes with teaching. I’m hoping as I create more lessons, I’ll feel more comfortable with this new style of teaching and assessing. By Christmas break, I’m hoping to be able to post on here how successful everything has been and how I should have made these changes years ago.