The Problem with FOIL
Monday, January 15, 2018 by Tammy White | Parent Support
Even though a student could use this post as a “how to” guide for multiplying binomials, this is intended to be a “look for” post for parents who are working with algebra students at home.
Let’s look at a typical example…
Multiply (3x + 2)(x – 5)
Traditionally, there is one method taught – FOIL.
Multiply the First terms, then the Outer terms, then the Inner terms, and finally the Last terms.
There is nothing magical about FOIL. It’s just one way to organize work. The big idea is that each term in one binomial needs to be multiplied by each term in the other one. (Think “sharing is caring!”)
But there are different ways to organize work that may make more sense to the person doing the work. Many times, a student thinks they need permission to do it a different way.
(If your teacher isn't flexible about the approach, show it to them privately first. Most will give full credit if the mathematics is correct. What may seem like "inflexibility" is really just an attempt to avoid confusion.)
It’s more important to understand the mathematics under the algebra than to follow a set of steps without understanding what is going on.
If a student can write out their process and can correctly justify their thinking when asked “why did you do that?”, let them find a way to organize the work however it makes sense to them.
Teaching “rules” about how to do things implies that there is ONE way to do a thing, which...
1) isn’t true, and
2) actually prevents learning mathematics.
Most students stall out when they need to apply the FOIL algorithm to multiplying polynomials with more than 2 terms.
A student who doesn’t understand what FOIL is really doing won’t attempt a problem like (x+5)(3x
+ 2x + 4) without someone else showing them how to do it.
A better outcome comes when they were encouraged to organize multiplying binomials differently, asked to explain why they think it will work, and then praise the creativity and grit for figuring out a “new” way to solve the problem. An empowered student will trust her intuition and attempt a new problem on her own.
Here are some approaches I’ve seen done when students forgot FOIL and had to figure out another way…
A distributive property approach…
Think of (3x + 2) as a single number and "distribute" it to the x and to the -5.
(This one gets a bit tricky when they need to distribute “backwards” on the second line. If your student is using this approach, watch for errors here.)
The vertical method of organizing work is familiar to students because it looks like the way they learned how to multiply 2-digit numbers in elementary school.
The old skill from earlier grades:
Same technique applied to (3x + 2)(x – 5):
Let’s “level up” now…
Multiply (x + 5)(3x
+ 2x + 4)
What happens when a student who memorized FOIL is now asked to move up to the next level…
However, students who have been empowered to organize their work in the way that makes sense to them, usually attack this problem on their own.
They may still make some mistakes and that’s ok. Mistakes are attempts and that means there will be a successful solution at some point soon.
What we want to teach kids to avoid is the habit of up before starting. ANY attack strategy is better than giving up before trying something.
I’m sure there are more than two ways to multiply a binomial and a trinomial, but let’s compare the two methods we've been looking at here.
First, a distributive property approach and then a vertical approach…
Both approaches arrived at the same solution.
There is a bigger benefit to not forcing kids to do their work one way - their approach may shine light on their misconceptions. For example, when forced to use FOIL on a problem like
(3x + 2)(x – 5),
they might multiply the first terms, 3x and x, the last terms, 2 and -5, and arrive at their solution of 3x
- 10. When I see that, I suggest the vertical approach and that will help them see why there is a middle term.
If you have any questions or if you've seen another approach to multiplying polynomials, please share it with me! My email is TammyWhite@OnlineGeometryTutor.com.
If you would like to join my mailing list to get notifications of future blogs and access to free tutoring videos, click here.
Thanks for reading!
Is Your Student a "Master Procrastinator"?
Wednesday, January 3, 2018 by Tammy White | Parent Support
I’ve shown this video to my classes at the beginning of each semester since I first saw it.
LOL! (Seriously – if you didn’t watch, you missed a funny video.)
We all procrastinate. But chronic academic procrastination will impact a student negatively. It will increase stress, create conflict at home with grades drop, and possibly take a student off-track to graduate on time.
There is a lot of research out there on this topic. A recent study I found was a bit of a dense read, but the gist is that they found that the students who self-reported that they were supported at home, felt empowered, had clear boundaries and expectations, and knew how to use their time constructively, tended to not procrastinate their academic tasks and had a high commitment to learning.
Well, gosh. That seems a bit obvious, doesn't it?
Parents want to support their kids and they want them to do well in school. But we are all busy and we all procrastinate to some extent. What are some specific
, realistic actions that parents take to minimize student procrastination without it becoming a source of conflict every evening?
It’s not your job (or the teacher’s job) to make your student do their work and turn it in. If you think that, you’ve got to let that go. Now. (This post may cause a subtle paradigm shift and you might have questions. Please ask them! Email me at TammyWhite@OnlineGeometryTutor.com.)
Some teenagers are happy to let adults take control of their academic organization for them. It may have been necessary when they were little, but now it’s enabling and keeping them from developing the skill to organize a task or project that they will need later.
That said, we do need to help kids learn how to prioritize, organize, and get stuff done. And that’s a little harder than just getting in the habit of reminding them or handling it for them.
Customizing a strategy to help your student be more organized, is part of what I do as your student’s tutor, but I don’t do it for them. I coach them on what they need to do and I hold them accountable to do it.
SUPPORTIVE or CONTROLLING? How You Say It Is Important!
Teenagers are supposed to rebel a little. It’s age appropriate for them to need to control their environment. The way some kids exert their control is to not comply by choosing to not do school work. If you decide to help your student with procrastination, it will be more successful if your goal is to empower them instead of control the situation. How something is presented to any of us can determine whether we’ll be open to cooperate, right?
“We’re going to work together to make this organization thing easier for you.”
“You’re doing it wrong and I’m going to check up on you to make sure you do it right.”
Take a moment to think about how to bring this up with your teenager in a way that will sound like a good idea to them without triggering a defensive response.
USE THE STUDENT PLANNER
Many schools provide planners like this one…
Most students at our school use the planner only for the hall passes. The basic planner can be a “tricked out” with a few printable inserts to make it a little more useful. (Click here to get a free PDF download of these inserts.)
The weekly layout in our school’s planner doesn’t leave a lot of room for writing assignments.I created this insert for my students that can be printed and attached at the top of a weekly page so it can be flipped up to see what’s written underneath.
The planner is also a communication tool between the teachers and parents. It also needs to be a shared document between you and your student otherwise the accountability component is lost.
Set up a procedure at home where kids know they need to leave their planners open to the current week on the kitchen table where you will see it.
Clarify that you aren’t checking up on them, but just want to help them establish the habit of filling in assignments with start dates and due dates.
Adults do something similar when we hire a personal trainer – it’s easier to stay focused on a goal if we have someone set up to hold us accountable.
If there was no assignment for a class that day, the student can ask the teacher to sign off on the planner to verify that for you.
HOW TEENAGERS SEE DUE DATES
It’s a DUE date, not a DO date!
After 20+ years of teaching, I’ve learned that many teenagers interpret the concept of a “due date” as a “now I have to DO it” date.
Some kids literally had no idea something was “due” until it was put into the gradebook as “missing”. I get it. They probably didn’t write it down anywhere. And if they did, there is only one date associated with that task – and once that date arrives, it’s too late to do it and turn it in on time.
I included the “Start Date” and "Days I Need to Do It" columns on the weekly assignment planner insert. Granted, a hard-core procrastinator can still ignore these dates, but writing these dates down in the planner might just engage the Rational-Decision-Maker in the brain.
STUDENTS NEED TO USE TEACHER WEBSITES
If the teacher has an active website, assignments may be posted there, too. Ask your student to copy their teachers’ websites onto one page of their planner. (There is a planner insert for that, too!)
HOW TO HANDLE MISSING WORK
Students (and parents) already check grades online frequently. If you check and see something, causally (even though your Panic-Monster is probably fully engaged) ask your student to check.
"I think you're missing some things in your math class. You might want to check online and check your planner."
"How are you going to handle that?"
Resist the urge to tell them how to handle it. Ask questions instead. Leading questions, maybe, but use questions to coach them to formulate their own plan. The goal is to teach them how to put together an action plan on their own so they can feel confident about their ability to dig themselves out of hole they created. They know you are there to support them, but you aren't doing it for them.
Missing work may be due to a learning gap on that skill, not procrastination. As their tutor, if I know there is missing work, my first response will be address the problem as a potential learning gap, not as an organizational issue. Once the learning issue is addressed or ruled out, I’ll reteach the new organizational habits to support what you are doing at home.
An advantage of using school planners is that they have the “End of Grading Period” dates printed in them. Most teachers make those dates “firm” due dates, so your student needs to be aware of them.
If a teacher accepts late work, they need time to process it. Many teachers will use weekends to catch up on grading. Others will make sure their grades are current before they leave on Friday afternoon.
I made this insert for my students to put in their planner that would have the late work policies summarized for each class in one spot.
A good approach is to ask your student to set a personal due date to turn in late work on Wednesdays or two days before the “absolute late work due date” set by the teacher if they set one.
Why two days?
Because of the DUE vs DO teenage-brain-habit of thinking. If a teacher is accepting late work, that last due late work date is firm. Teachers have to cut off the flow of papers landing in their inbox because they have their own firm due dates for entering grades.
NO LATE WORK ACCEPTED? DO IT ANYWAY
OK - this next point may be controversial, but it’s critical for breaking the habit of procrastination.
If the teacher doesn’t accept late work, your student needs to do it anyway.
I’m serious about this - and it's not intended as a consequence for a bad decision. Students cannot skip assigned work. The expectation must be that all assigned work has to be done, even if it won't be graded.
Three reasons why this expectation is critical…
- The skills on that assignment are part of the curriculum and will be on the next exam, the final exam, and possibly on high-stakes exams like the SAT or ACT. NOT doing assigned work, especially a math assignment, may create a learning gap that will become a bigger problem later.
(Honestly, as a tutor that specializes in closing these gaps, you’d think I wouldn’t suggest this, but honestly, I’d prefer it if your student didn’t need my services. That would mean they have no learning gaps, are confident learners, and are on track to reach all their academic goals. That is what I want for all my students. THAT is what I want for your child.)
- If a student knows they will have to do the assignment anyway, for no credit, it’s a loose-loose for them. They loose free time AND they loose points. It’s likely that they will do assignments on time in the future.
- The ability to follow-through is valuable a character trait to nurture, even if it won't be graded. Completing the task is what's important.
Parents – after the work is finished, ask your student if they are willing to turn it in the teacher with an explanation that they know it will not be graded.
If they are uncomfortable with it, don’t push it, but ask each time there is an assignment that is too late to grade. When they are willing to do it, this is an empowering activity. That’s when you know your son or daughter has taken ownership over their academic work.
If you have questions about how to customize a plan for your student or about how online tutoring works, please feel free to contact me at TammyWhite@OnlineGeometryTutor.com.
Thank for reading!
The 4 Most Effective Ways Parents Can Help a Student Do Better in Math Class
Tuesday, December 26, 2017 by Tammy White | Parent Support
A new term is about to begin, so it’s a good time to reflect on what motivates teenagers to work at school. Teachers can do some things, but honestly, nothing I’ve done as a classroom teacher is more effective than what parents can do from home to motivate their kids to learn.
These are the TOP 4 STRATEGIES I’ve seen my parents use that worked…
#1: High expectations that are clear and communicated frequently.
My students tell me exactly what their parents expect. However, the parents who based their goals on growth, instead of grades, had students who did not give up when things became difficult.
For example, say “I expect you to work on it until you learn it because I know you can”, instead of “Earn a C in the class”.
The first phrase clarifies that learning is expected, while the second phrase communicates that you grade is more important than how it was earned.
For more about how to encourage a growth mind set at home, check out the parents page at Mindsetworks.com.
#2: Work with a Professional Tutor
Tutoring options range from basic homework help to working with a professional tutor. Parents decide what will work for their student, but working with a professional tutor is the best choice for students who have struggled with learning gaps.
- “Homework support” online may be an app that solves problems, which will increase homework completion, but it’s like copying someone else’s work.There are also people kids find through social media who charge to do homework problems, too.However, there is no learning going on here.Over time, learning gaps widen.
- Hiring an older student for homework support can be helpful, but it depends on the tutor.
- Often, “homework support” is really the older student telling the younger student what to do – which again, is great if the goal is to get work completed, but it may not teach the student how to start problems on their own.And it doesn’t build understanding or encourage different problem-solving approaches.
- This kind of tutoring is a crutch.As a teacher, when one of my kids won’t work in class because they are “saving it for their tutor”, I know parents are wasting their money.Again, there is no learning happening and old gaps widen.
- Work with me! (A shameless plug, I know.) But honestly, working with a professional tutor who approaches their it like I do, is like having a personal trainer for math. I find and close learning gaps while teaching the curriculum just ahead of the classroom teacher. At school, while other students may get lost during a lecture, my student will have already been introduced to the content and will understand what the teacher is doing. Assignments become the practice they are intended to be. My students know how to analyze their errors and grow in understanding because they know mistakes make them stronger. Learning happens.
#3: Stay in the Loop & Follow Up at Home
- Students work harder when they know parents and teachers are communicating.
- Double check that your school and teachers have your email address and phone number.
- If your school uses an online gradebook, set it up so that you receive notifications.
- Ask for a copy of the class syllabus to keep at home.
- If your teacher has an active website, make sure your student is checking it frequently.
- Email teachers as needed, but not more than once a week if it can be helped. Emailing is more time-efficient than calling. Teachers can reply to emails when kids are in the room. (Note - if your cell phone doesn’t have a local area code, teachers may not be able to return that call from their classroom phones. Many schools require that they use a phone in the main office.)
- IMPORTANT – if you get a message from a teacher that there is a problem, act on it at home immediately! It may only need to be a conversation. However, if a teacher takes the time to contact you, it’s because they need your help to get your student back on track. If you do nothing, teachers may stop contacting you because that wasn’t an effective strategy from their perspective.
THE MOST EFFECTIVE SHORT-TERM INTERVENTION…
#4: Take the Phone
I have seen kids do some miraculous academic transformations in short periods of time just to get their phones back.
And, if that phone has become a chronic distraction in the classroom, consider replacing that smart phone with a less expensive “burner” phone. Many teachers do require that some things be done online, but because of equity of access, if they don’t have computers in the classroom available, kids have access in the library, in computer labs, or teachers will adjust due dates if access to a computer is an issue.
Please feel free to contact me if you think I might be able to help your student in geometry this semester.
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