Math = Love: The #1 Thing I Won't Teach Next Year: Integer Operations

Thursday, April 24, 2014

The #1 Thing I Won't Teach Next Year: Integer Operations

I realize it's still April.  Our last day of school is May 14th.  But, I'm already thinking about next year.  In fact, I'm thinking a lot about next year.  Things I want to do.  Things I don't want to do.  Things I need to do.  Things I should think about doing.

Here's the deal.  Oklahoma is changing standards next year.  Originally, we were a PARCC state.  Next year is supposed to be our first year of full implementation of Common Core.  Except, we decided to not call it Common Core.  We're calling them the Oklahoma Academic Standards (OAS).  I referred to them as Common Core the other day in the presence of our elementary principal, and I got yelled at.  I'm sorry.  Changing the name does not change what they are.

Then, Oklahoma decided that we don't have the necessary technology infastructure for PARCC testing.  So, we will write our own test that aligns with PARCC and CCSS/OAS.  All was fine and well.  Then, this month, the Oklahoma senate approved a repeal of Common Core.  Instead of teaching CCSS/OAS, Oklahoma is supposedly going to write their own standards that are more rigorous than Common Core.  As a teacher, this is frustrating.  I just want to know what I'm supposed to be teaching.  Will we teach/test CCSS for a few years while writing our own standards?  Or will we jump directly into new standards that haven't even been written yet?  I doubt we will go back to our old PASS standards, but it seems like anything can happen lately.  How can I prepare to provide the best education possible to my students when we keep changing our minds?!?

So, I tell you all this to say, I'm still not exactly sure what I'm teaching next year.  I'm teaching Algebra 1, Algebra 2, and Trig/Pre-Calculus.  But, exactly what those classes will consist of is still up in the air.  I may not have a for-sure set of standards for next year, but I do know this:

Next year, I will NOT spend class time teaching integer operations.

I teach in a school with a history of poor academic achievement.  For the past two years, I have spent at least a week in Algebra 1 on adding, subtracting, multiplying, and dividing integers.  And, I'm sick of it.  This is one of those concepts that is first introduced in 6th or 7th grade in Oklahoma.  I should not have to teach it in high school.  This year, I gave my Algebra 1 kiddos integer speed tests.  64 questions.  4 minutes.  I told them that they were going to take one every day until they passed.  After a week, I gave up.  Not a single student could even finish the test in 4 minutes.

I've got to raise the bar.  Every day in my class is valuable.  And, I could teach so much more if I can regain that week of review.  Because let's face it: reviewing integers is the biggest waste of time.  They've heard the explanation a million times before.  The ones who need the most help are the quickest ones to tune me out.  After all, a negative and a negative make a positive.  Somehow they missed out on the fact that it only works that way when you are multiplying or dividing.  -3 - 7 does not equal positive 10!

This year, I attempted to go back to the basics. We did exploratory activities with algebra tiles.  I saw a few light bulbs go off, but there was not enough light put off to justify the insane amount of time that was spent learning how to use the algebra tiles.  Last year, I made foldables and taught my students memorization tricks.  That didn't work any better.  

Over the course of the year, most of my students seem to (finally!) internalize the rules for integers.  Maybe it was my incessant singing of "Same signs add and keep.  Different signs subtract.  Keep the sign of the bigger number.  Then, you'll be exact" every time someone made a mistake with adding/subtracting integers this year that helped???

When I took Calculus I in college, we had two gateway exams that were in addition to our 3 regular exams.  One gateway exam was over differentiation, and the other gateway exam was over integration.  If I remember correctly, there were 20 questions, and you were required to get 18 or more correct to pass.  Each gateway exam was taken for the first time in class.  If you passed, you were done!  If you did not pass, you were allowed up to four additional chances to take and pass the exam.  These had to be done outside of class time, and they were scheduled with the professor or TA.  If you could not pass the gateway exam, your final grade would automatically be dropped one letter grade.

I want to take the strategy and apply it to integer operations.  I will give the first integer operations test in class.  The tests will be graded and passed back to the students.  Students who score below a 90% must re-test.  Re-tests must happen on their own time.  And, there will be a set date that students must demonstrate mastery of integer operations by.  Ideally, I want 100% of my students to demonstrate mastery of integer operations by the beginning of September.  We start school in mid-August.  This means I will have to get on this ASAP!  

Students who make less than a 90% on their integer operations test will be provided with a list of websites, online games, flash cards, etc. that they can use to practice with.  I will also be available to help them before school, after school, or at lunch.  Students who have not demonstrated integer mastery by the beginning of September will be required to log 1 hour of integer practice in my classroom each week until they pass.  This time can be spent before school, during lunch, or after school.  This is going to be absolutely 100% non-negotiable.  Students who do not log their hour of practice in my classroom will be given mandatory lunch detention until mastery is achieved.

This accomplishes multiple things.  It communicates to students that integer operations are an important concept for algebra success.  It communicates that this is something that students should have learned in middle school.  It also communicates that if they didn't learn it in middle school, then I am here to help them.  I care so much about their success that I am willing to inconvenience myself to help them master their integer operations.  I am identifying a weakness that I see in the students at my school as a whole.  And, instead of lamenting the weakness, I'm acknowledging it and providing practice opportunities and support.

I want students to take control of their own learning before that first gateway exam.  I will provide them study materials, practice tests, and links to online resources.  They can assess their own needs.  My students are capable of so much more than I give them credit for.  It's time I let them show me what they can achieve when they set their mind to it.

For my Algebra 2 students, I think their gateway exam needs to cover exponent rules.  I should not have to spend a week reteaching exponent rules to Algebra 2 students.

Have you ever done anything like this with your students?  Do you see any changes I need to make?  I'm very open to constructive feedback.  My teaching style is slowly morphing, and I think it's a good change!


P.S.  This blog post did not go where I planned for it go at all.  I started writing this post to tell you about an awesome new game I learned about at my last Math Teachers' Circle meeting.  I will be using it to emphasize integer operations and the order of operations.  That'll have to wait until tomorrow, though!                

23 comments:

  1. This a lot of similarities to standards based grading. Do you use SBG in your classroom?

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    1. I used SBG for several Algebra 2 units this year. I'd love to do SBG with my Algebra 1 students, but I need to do a lot more research and reading before jumping in!

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  2. I agree! I teach Algebra 2 and I gave summer study packets at the end of last school year because I was tired of teaching solving, graphing and writing linear equations. I tested the students on it on the second day of school. I love the ideas of having to do the remediation! I definitely have copied this post for our Math Dept. meeting this week!

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    1. Summer study packets sound like an awesome idea! That may be something I look into doing in the future. When I took English in high school, we would have summer reading and journaling assignments to do.

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  3. Such a great idea!!!! You stated that, "Students who make less than a 90% on their integer operations test will be provided with a list of websites, online games, flash cards, etc. that they can use to practice with." Will you please share your list of websites, online games, flash cards...? Please! I think this is an awesome idea and I'd like to do something similar next year as well.

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    1. Definitely! I'll be compiling resources this summer, and I'll try to get it posted before school starts! I'm thinking I'm also going to have to type out a letter explaining this new policy/program to students and parents since it will be an entirely new way of doing things in my school district. I'll be sharing that, too!

      Thanks for stopping by my blog!

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  4. In the past, I too had timed integer quizzes (only 10 questions). I also did timed perfect squares & square roots 1 to 15. However, with Common Core, I don't have time to for this, nor is it part of my standards. We (the teachers at my school) are teaching how to use the "technology." What I mean is, using a calculator. We give them the best tool that is able to be used on the standardized test and show them how to use it WELL.

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    1. I've tried to emphasize good calculator use, too. But, this year, I had a group of students who REFUSED to use the calculator. It drove me insane. In my mind, if you know integers are a problem, you will use your calculator religiously to avoid simple errors and mistakes. This group of students would rather guess at the answer than take the time to type it in.

      Eventually, I started telling them whether they would need a calculator that day and requiring them to get it out. I found that if the calculator was already out on their desk, they would be much more likely to use it.

      My goal for next year is to get them to practice integers without calculators outside of my classroom. Inside my classroom, we will use the tools WELL. There's just not enough time to do otherwise!

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  5. I feel your pain! I teach middle school and I have similar frustration when it comes to BASIC math facts. I DO have the responsibility of teaching integer operations, but when my fabulous fifth graders struggle with fact families, it holds us back on all of the other important concepts we need to learn. I like these ideas. ...I think I may have to apply them to basic fact knowledge at the beginning of the year.

    Smack Dab in the Middle

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    1. I like the idea of using this with basic math facts, too. I have quite a few high school students who never memorized their multiplication tables. When we get to factoring, they get extremely frustrated. What two numbers multiply to -27 and add to -6? All of a sudden, they realize that multiplication has a purpose!

      Also - I've really been enjoying your blog lately, Heather!

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  6. I feel your frustration. Those in power have no idea what they are doing and this is why education in this country is such a mess. I teach 6th grade and there are soooo many common core standards for this grade that it is impossible to teach all of them before our state tests at the end of April. Especially since I spend many weeks reviewing 4th and 5th grade concepts which haven't been mastered but are necessary for the work they need to do in grade 6. I can't imagine making CC standards more rigorous. Good luck.

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    1. I agree! I am overwhelmed when I look at CCSS. They say we're not supposed to have to reteach anything, but that's just not a reality in my school district. It seems like there a lot of us in this boat together!

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  7. Did you create your integers timed sheets or find them? I teach 7th grade and I am trying to remediate my students on integers before they get to your level. I am looking for ANYTHING that I can use to help them. Any and all suggestions are truly appreciated!

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    1. I found them somewhere on the Internet. But, I don't remember exactly where. The files are on my school computer. So, I'll try to find them and link to them next week. Send me an e-mail at mathequalslove (at) gmail (dot) com, and I'll gladly send them to you. I think there are five different versions of the speed quiz if I remember correctly!

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  8. Sarah, I totally agree that integers are one of those basic skills that so many kids struggle with! I love your idea of giving them a chance in class, resources and then they have to take over. In our state, all grades given must be linked to a standard for that class--so in Algebra or Geometry there are no integer standards! ugh! They just bomb other concepts because they can't do basic math. :( I look forward to hearing how this goes in your classroom next year! Great idea--thanks for sharing!!

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    1. Thanks! I'll keep everybody updated! Your grading policy sounds very interesting! We have nothing like that at all in Oklahoma.

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    2. @ Alicia...Can you still practice the skill? Instead of a grade, you can offer constructive feedback to your
      students.

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  9. I have been teaching 8th grade for 28 years and struggle with the same issues with basic facts.I feel like I have tried every trick in the book. This year my principal told my department that he wanted us to give multiplication timings everyday to our students. We all started out doing it, but when they finished the timing they never studied or even looked at the facts they missed. After 2 1/2 months I finally gave up because it took so much time and I saw very little improvement. I was doing much more work than the kids for sure. When we started our perfect squares and square roots I gave the kids flash cards that were small and portable that they were to study. Again they didn't look at them. This changed when I started giving them 3 minutes to quiz a partner in class. Wow who knew peer pressure could do so much. I cannot tell you how much my students have improved! I'm flabbergasted. Why don't you try pairing kids with other students in a timed situation as well as your other ideas. I agree with having them do it on their own time. The kids help each other with ways to remember some of the facts. One of my students couldn't remember the square root of 256. Her partner gave her a hint, "It's how old you are when you can get your license." For some reason that stuck and helped her remember the answer. I hope you see the results that I have.

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    1. I love the flashcard idea! I had my students make flashcards at the end of last year to review for our standardized test, and they did seem to help. I'm already starting to make a list of the things I want my students to have down cold.

      Multiplication Facts, Perfect Squares, Perfect Cubes, Common Decimals and Their Equivalent Fractions, For my trig kids next year - the unit circle.

      Having them quiz and coach each other would be awesome! I can already imagine spending a little time on this each week paying off great dividends over the course of a year. Or in my case, the next several years. Because I will see all of my Algebra 1 students again in Algebra 2!

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  10. This is a great idea. I'm teaching Algebra 1 as well as Pre-Algebra this year, and integers are one of the most important concepts. Another concept I'm thinking about implementing this with would be solving multi step equations. Was this the first test grade your students receive? Also, I have been trying to find more resources to help remediate my students. Where did you find yours?

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  11. How did this year pan out in reality? Which ideas did you incorporate? Could you make it into a blog post? (Maybe "What Worked and What Didn't"?) :D I'd love to hear!

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    1. Well, I didn't teach integer operations. But, I didn't follow through with quizzing my students and holding them responsible on their own. I had enough on my plate with trying out SBG for the first time.

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    2. Yes, SBG does take a lot of time and effort. I just started it with a class, and I'll have to see how it works out. I find that teaching integer operations can be a waste as well because even if they get it in the beginning of the year (and that's *if*), when they start doing examples from other topics that involve integer operations, they go back to making their old mistakes. Some of my students just use a calculator for everything....

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