2016 - Make Sense of Math

Why I will never tell my students math is easy

The Problem
When I started teaching math, I encountered a problem that I didn't realize I would encounter.  I had many students who just didn't want to try.  They would just sit there and do NOTHING.  I thought that they maybe felt defeated, or that they thought it was too hard for them.  So I did what I've heard many teachers do. I said, "It's EASY, you can do it."  I thought I was giving them encouragement to try, motivating them, inspiring them to pick up their pencil and at least try.  It wasn't until about three years later, that I realized I perhaps was doing the very opposite that I was hoping to do. You see, the problem is that it's NOT EASY for them, and by me telling them that it is easy, they feel so much more defeated.  Now they feel like that can't do something that is labeled EASY.  Now they definitely weren't going to try, because it's one thing to not be able to do something that is hard, but to not be able to do something that is easy, is completely different. 

The Solution
I teach students who are 12-14 years old.  Looking stupid, is the absolute last impression they want to give to their peers. They will choose lazy over looking stupid.  So, after this realization, I started changing my words.  When they aren't working, I let them know that it IS hard.  That I am asking them to do something very difficult, but I believe in them.  I believe that they can try, I believe that they can fail, and I believe that they can learn from their mistakes.  I believe that they can do hard things and it may not be today, or tomorrow, or this week or month, but I believe that they will eventually get it.  And it's OK if it takes them longer than their friend.  It's OK if they are faster than their friend. 

It's wonderful, because if they try and fail, they don't feel stupid, because they failed doing something difficult.  Also, they don't just try and fail, they try and fail and try and fail and eventually try and succeed.  And when they succeed they feel so proud, because they succeeded at doing something difficult. This motivates them to keep trying other hard things. It is a cycle that keeps on giving...to them.  

Banning EASY
Also, this is something that you need to teach your students. Teach them that even if they feel that something is easy, it is not easy for everyone.  So they better not be saying in class that it is easy.  I do not allow the word EASY in my class, and my students know that. 

I challenge you , that if are using words like I was using, to change your mindset.  Tell your students that it is hard, but you believe in them.  Tell them that you expect them to fail, but you also expect them to learn from their mistakes.  You will be surprised how they change their work ethic. 

Save This Article
Save these tips and ideas to your favorite classroom Pinterest board. Come back and reference them for ideas on how to taking memorization out of math. 

Why I will Never Tell My Students Math is Easy



Free Transformations Task Cards



FREE TRANSFORMATION TASK CARDS
CLICK HERE to grab these transformation task cards free from the Free Resource Library. The password will be sent directly to your email provided. 

These 36 transformation task cards are perfect to make sense of and reinforce transformations and coordinate rules.  There are 12 matching sets covering rotations, reflections, dilations and translations.  Each set includes a visual of the transformation, the corresponding coordinate rule, and a written explanation of the transformation.  These are perfect to make sense of transformations as well as to reinforce the concepts.

Uses in Your Classroom
  • Games:  Matching, Go Fish, Spoons, etc, …
  • Exit slips
  • Openers
  • Math Stations
  • Quick formative assessments
  • Putting groups together
  • Pair work or individual work

Questions to Accompany Task Cards
  • Given the visual transformation write a coordinate rule
  • Given the visual transformation explain in words what is happening in the transformation
  • Given a coordinate rule draw a visual transformation that follows the rule
  • Given a coordinate rule explain whether the new figure will be congruent and/or similar to the original figure
  • Given a coordinate rule explain in words what is happening with the transformation
  • Given the written description write a coordinate rule
  • Given the written description draw a graph that follow the rules
Make Sense of Transformations
Higher-order thinking ideas to help students make sense of transformations.  Laminate cards (or place in plastic sleeves) so that students can write on the cards with a dry erase marker while doing the following activities. 

Reflections:
  Have students connect corresponding points and notice that the lines are parallel but not the same length.  Ask them if this will always be the case. Have them justify their reasoning.  They can draw additional reflections and continue to analyze.  Have them practice reflecting over lines that are not the axes.  Challenge them to write a coordinate rule for their new reflection.  Again, have them analyze lines connecting corresponding points, are they still parallel?  How do the lines compare to the line of reflection?  They should notice that the lines are perpendicular.

Rotations:
  Have students connect only one set of corresponding points to the center of rotation and measure the created angle with a protractor.  Students should be able to verify that this is the degree of rotation.  Also, guide the students to notice that the length of their lines are also the same length.  You can move deeper into this idea by using compasses. Ask the students if corresponding points will always be the same distance from the center of rotation.  Have students justify their reasoning.   Students can practice rotating the figure varying amount of degrees. 

Translation:
  Have students connect corresponding points and notice that the lines are parallel, and the same magnitude (length)  Will this always be the case? Will the lines always be parallel and the same length?  Have them justify their reasoning.  Have them draw more translations and continue to analyze and justify their reasoning. 

Dilations:
  Have students connect corresponding points and extend the lines until they intersect.  Students should notice that these lines intersect at the center of dilation.  Challenge them to draw a new dilation with a different center of dilation and check their thinking.  

CLICK HERE to grab these transformation task cards free from the Free Resource Library. The password will be sent directly to your email provided. 
 
Save This Article
Save these tips and ideas to your favorite classroom Pinterest board. Come back and reference them for ideas on how to effectively teach transformations.

Free Transformation Task Cards




Why you should say no to teaching f.o.i.l. with a no symbol


What is F.O.I.L.?
Tell me if this scenario sounds familiar.  You are planning your classes for next week and you notice that your students will need to learn to multiply binomials.   You are so excited, because you have a great trick to teach your students, and it's SO easy, right?  If your kids can just remember the acronym F.O.I.L., then they'll have the concept learned in no time.  This may have been the way you learned to multiply binomials, you know your students will catch on in no time.  Many teachers use F.O.I.L. to teach multiplying binomials such as (x + 3)(x + 4).  The F. represents FIRST, multiply first terms. x(x) = x2  Next comes O. = outside terms x(4) = 4x, then I.= inside terms 3(x) = 3x then L. = last terms 3(4) = 12.  Combining the terms we have  x+ 4x + 3x + 12 =  x+ 7x + 12.  Voila...you can multiply binomials.  O.K. I hope I'm not convincing you to use F.O.I.L.  I'll give you some credit, F.O.I.L., is usually easy for the kids to learn and memorize (if they can memorize), however teaching F.O.I.L. has many, many downfalls.   Let me explain why I NEVER will teach my kids F.O.I.L.

Why I Will Never Teach F.O.I.L.
1)  F.O.I.L., has no mathematical basis.  Your quick memorizers may attach quickly to F.O.I.L. and zoom through their 20 practice problems that you have assigned them.  However, ask them to explain why F.O.I.L. works and they will stare at you blankly.  Generally, if students do not understand why an algorithm works they will not be able to retain the concept, or they will not be able to apply the concept to new skills.  Also, if you are just teaching a shortcut, are you really teaching pure mathematics?

2)  What about the students who can't memorize?  F.O.I.L., is based on the assumption that all students can memorize the acronym, what each letters stands for, and when to apply it.  If you haven't learned already, you soon will, all kids are not great memorizers.  The ability to memorize should not be a requisite for being a mathematician, rather the ability to reason and problem-solve.  As a teacher you should work to develop reasoning and problem-solving skills in your students at every opportunity.  Teaching F.O.I.L. does not to do this.  

3)  The  MOST important reason I will never teach F.O.I.L. is that students suddenly get stumped when in their next math class they have to multiply polynomials like the following : (x + 2)(x2 + 3x + 4)  or even a little more complicated (x2 + 2x + 1)(x2 + 3x + 4).  In fact, many students who learn the F.O.I.L. method try and apply this to these polynomials, and the result is disastrous.

How To Teach Multiplying Polynomials
So, if you should not teach F.O.I.L. what should you use?  The answer is simple, you should teach mathematics, not tricks.  If a students happens to discover the F.O.I.L. method you applaud them and let them explain to you why it works.  If they understand why, they will have no problem with advanced polynomial multiplication, because they discovered it and understand it.

I teach the multiplication of polynomials using two methods, sometimes simultaneously, sometimes consecutively.  I use algebra tiles so students can see the geometric connection, and I teach the distributive property.  If you have not used algebra tiles in your classroom before, the time to start is NOW.  Using algebra tiles is a hands-on method that reaches all students, and can easily challenge the top-learners as well in your classroom. You can purchase algebra tiles; however, they are kind of pricey.  You can download some FREE algebra tiles here for your students in my FREE RESOURCE LIBRARY (the password will be sent to the email provided.) They are available in color and as black-line versions to print on colored paper. 

In a different post I will cover how to teach with Algebra Tiles, but if you would like to get started today THESE TASK CARDS are a great addition to your classroom.


Teaching the distributive method is also VERY effective.  Students who understand the distributive property can apply this concept to multiplying polynomials with various terms.

Set your students up for success, not just in your class, but for their future math classes.  Say adios to F.O.I.L. and starting working with algebra tiles.  Your students will thank you.

Save This Article
Save these tips and ideas to your favorite classroom Pinterest board. Come back and reference them for ideas on how to effectively teach multiplying binomials. 
 
Why you should say no to teaching f.o.i.l. with a no symbol





Stack of books Why I don't grade papers at home

The Mistake
I was in my third year of teaching and we had a new technology teacher.  This teacher has a fantastic personality for teaching.  All students love him from day one, and he has an ability to connect with them immediately.  He had just left a job at a bank, and this was his first year teaching.  He did what many first year teachers do.  He worked, and worked, and worked.  He came early, he left way late and he was very, very tired.  He came to me one day after a few months and mentioned to me that the school director wanted to meet with him.  He was a little nervous, and didn't know what she was going to say.  I gave him some assurance and let him know that our director was fantastic, and I'm sure anything that she had to say was just to help him.  The next day I asked him what the meeting was about, and he told me that she was worried about him.  She was worried that he was working way too hard.  She gave him some ideas to grade more efficiently and not have to work so hard.  You see, our very experienced educator knew something that only the best teachers know. Let me explain further, because I made the same mistake. 

Getting B's
Years ago I attended a commencement ceremony, and something was spoken that made a huge impact on me, though not the exact words, the message was along these lines. "Congratulations to all those who have graduated with A's, you have worked really hard, studied countless nights and you deserve those grades, but I would like to congratulate even more those who graduated with B's. Getting B's because you have made your family a priority, B's because you also are a parent, spouse, friend, and neighbor."  I thought, Yes, that is what is important. 

I started out teaching trying to be the "straight A" teacher, and as a result everything else suffered....even my students.  I stayed late hours at school....then I would go home, eat....and continue working.  I worked, worked and worked. Interestingly enough this often backfires on teachers.  I was so stressed, wasn't sleeping, and my patience in the classroom greatly diminished.  

Systems
As the years went on, I realized that what I was doing wasn't working. So, instead of planning curriculum over the summer, I spent time reading, studying and planning systems so that my classroom could run more efficiently, and I told myself that I would leave school everyday at 4:00, and I would not work at home.  I didn't stick to my plan 100% at first, but I did better. Each year, I perfected my systems and stuck better to my plan. I noticed something interesting...I actually became a better teacher. I had more patience for my students, and I noticed that I began to value every minute while at work.  I learned to use my time wisely. I then began applying this with my students. I began to value my time with them even more, and when my students were in my class, they thought and problem-solved until they walked out the door. I took it as a compliment when they said their head hurts from thinking so much.

Work Smarter, Not Harder
I'm not necessarily saying that you need to work less and you will be a better teacher, rather, the point I am trying to make is that you need to work smarter.  You need to work very efficiently and effectively while at school.  While at home, you need to work hard at not working :) It's tough to relax and spend time on other things when you feel like you have a long to-do-list.  However, you need to trust that doing so will truly make you a better teacher.

I have learned that what we do at school is important, very important, but what we do at home is more important.  When teachers set their priorities straight, your teaching and classroom will improve because you will be happier and less stressed.  Set a goal and try to change something today to act according to your priorities. 

Save This Article
Save these tips and ideas to your favorite classroom Pinterest board. Come back and reference them for ideas on how to take back your personal time. 

Stack of books Why I don't grade papers at home


3 keys to grading in the math classroom with 3 markers

 
Grading in the Middle School Math Classroom
Grading in my math classroom is something that I change to try and improve every year. My system is not perfect but I have learned some important aspects that I believe can benefit other teachers.

Focus on Growth
First, your grading system should focus on growth while still holding students accountable to minimum standards.  High students measured on a growth system will progress significantly more than if they are only measured on reaching standards. Low students will also progress more through a growth-based system because they will not get discouraged and give up which often happens through an achievement-based system.  Setting up a growth based system in your math classroom can be difficult.  Some ideas are allowing for retakes on exams after remediation.  Expecting your higher students to reach higher standards.  There should never be a ceiling for standards in your classroom.  There should always be room for growth.  In math,  you don't necessarily need to push students to the next grade level mathematics.  Instead of further, think deeper.  Have the students dig down into the core of mathematics.  This will definitely get them thinking critically.

Set Minimum Standards
Second, you should set minimum standards that all students can and need to reach by the end of the year. You can set this standard by thinking about what is absolutely necessary for your students to know in order to be successful on the next level.  You should not require mastery until the end of the year. Students progress at various rates and you should account for that in your grading system.  In my school we have what are called "non-negotiables."  We have 5-7 "non-negotiables" for each subject/grade.  These are standards that every single student needs to reach by the end of the year in order for them to be successful at the next level.  A great way to set "non-negotiables" is to talk with the teacher that teaches the next level and ask them what does every single student need to know coming into your classroom in order to be successful. They will be able to guide you in thinking about these minimum standards.

Knowledge not just Accountability
Third, the majority of the grade should reflect knowledge and not just accountability. Accountability can definitely be weaved into your system, and it may need to be to motivate students. However, accountability should have a significantly less weight on a grade than knowledge. For that is your primary purpose as a teacher, help students acquire knowledge.

Change is OK
One last thought, don't be afraid to change your system in the middle of the year if your system is not working.  No need to wait it out until the end of the year.  I have changed a couple times in the middle of the year, I was really worried.  I took the time to talk to my students, explain why what we were doing wasn't working, and the plan moving forward.  They were really receptive, in fact more receptive than I even expected.

I would love to hear how you grade in your math classroom. 

Save This Article
Save these tips and ideas to your favorite classroom Pinterest board. Come back and reference them for ideas on how to grade in the middle school math classroom

3 keys to grading in middle school math with 3 markers




Starting the year off right in your math classroom image of cup with pencils and calculator


Back to School in Middle School Math
I was 9 months pregnant at the start of the school year.  The director of the school let me decide if I wanted to start the year or start my maternity leave at the beginning of the year.  I took about 2 seconds to make my decision, "I'll start the year!" I declared.  I knew how important the first weeks of school are, and I knew that if did not establish some important routines and habits at the beginning of the year, the students and I would suffer the entire rest of the school year.  So there I was, two weeks before my due date, teaching 6 classes of 7th graders per day.  My days were exhausting, but I knew that these weeks were essential for success.  I focus on two aspects, and only two aspects at the beginning of the year: relationships and routines.

Routines
In my mathematics classroom, routines include teaching students how to justify their work, participate and create proper classroom discussions, giving and receiving constructive criticism, and math talk.  I also include the same routines needed for any classroom: starting your class, ending your class, grading homework, group work, pair work, test routines, obtaining materials, etc...  My first week of school often consists of problem solving/logical tasks.  These tasks are approachable for any level, as well as a contain a high ceiling to challenge all students.  I use these tasks to launch and discuss the above mentioned routines.  As a math teacher, I always am checking and guiding my students thinking, while this is a very important task for every other week of the school year, it is not your goal this week.  Don't dismiss their thinking, do take time to discuss their thinking, but remember your goal is to teach routines.

Relationships
Your students need to know that you care about them, both as students and humans. Work hard to learn their names and something unique about them. I have my students fill out a getting to know you form. I ask them how they feel about math as well as things they like to do and some of their goals.  I am pleasant with them, and do not take the "scary teacher" approach.  This does not mean that I allow them to be disruptive or disrespectful.  I work to set proper boundaries and firm limits.  However, within these limits I allow them to create relationships with each other and with me as their teacher.  I notice things about them, and let them know that I noticed.  For example, "Ashley, I noticed that you got a haircut."  "Tony, I noticed that you have new shoes."  Noticing helps the students realize that I do care about them.  Just a note, as a junior high teacher I am very careful to say, "Ashley, I love your new shoes,"  because Ashley may not want her junior high math teacher loving her shoes, that could be considered "uncool."  As the weeks turn to months, I really get to know my students, and I work to use the correct language with each of them.

Successful First Week in Middle School Math
The first week of school is absolutely critical to the success of your classroom throughout the year. As a teacher, during the first week  it is easy to get stuck on pretests, sending homework, being the "boss", etc...  Remember, routines and relationships should be your goal.  Forget about the other things, and the rest of your school year will be much more successful.  

Save This Article
Save these tips and ideas to your favorite classroom Pinterest board. Come back and reference them for ideas on how to have a successful first week back to school in middle school math. 


Starting the year off right in your math classroom image of cup with pencils and calculator






Let your students think


The Problem
Early in my teaching career I noticed a certain struggle with most of my students. I thought the problem was theirs, and I couldn't figure out why they had this certain struggle. I finally mentioned this struggle to the school principal. In the most loving way possible she helped me understand that I was the problem, I was creating this struggle in my students.

The problem was that my students didn't know how to think for themselves. When given a math problem, they didn't know how to start. Essentially they would give up or ask for help. And when they asked for help, guess what I did, I told them how to do it. This is what a good teacher does, right? Wrong! 

The Solution
A good teacher does not tell students what to do. A good teacher gives guidance and direction, but does not tell. A good teacher judges the frustration level of the student and lets the student struggle without reaching their breaking point.

In a math class, a teacher who tells students what to do often starts sentences with, "Just do this" or "First do this, then this, then this." or " Here, let me just show you, give me your pencil." A good teacher who does not tell will start sentences in a math class like this, "What do you know?" "What do you not know?" "What is the question asking?" "How do you think you should start the problem?" "What do you think the next step is?" A good teacher asks questions to the students and let's them think. The more your students think to solve problems, the better math students they will be.

A good teacher knows how to push their students without causing them to reach their breaking point. Every student's breaking point is different and you have to know your students. When you sense that they are reaching their breaking point, have them take a break. You may need to give them a little more direction, but do not give in and tell students what to do.

The Reward
Teaching like this takes a great deal of patience on the part of the teacher.  You may think that you do not have the time to teach like this. You actually don't have the time NOT to teach like this. You may have to put forth more time at first. However, your students will require less review, and in a few months they will be less needy.  They will learn to think for themselves and be less dependent on you as the teacher.

Let your students think and they will thank you later.

Save This Article
Save these tips and ideas to your favorite classroom Pinterest board. Come back and reference them for ideas on how to let your students think. 

Tips for secondary math teachers. Let your students think. Head clipart with gears in brain space.





Back to Top