I’ve been humbled. I can now say I am wrong. For the last 15-20 years I’ve told my students “We don’t FOIL in this classroom”. Actually I have not said this as much as I’ve just never – ever – used the term ‘FOIL’ in my classroom when we were multiplying binomials.
In training’s with teachers I’ve (highly) encouraged them to focus on the distributive property with students and/or use area models for multiplying binomials. I’ve told teachers to stop using the term FOIL altogether in their classrooms. Honestly, I’ve often shamed them for even thinking about the term FOIL ever.
For those of you not in the know….FOIL is an acronym to help organize students thinking about multiplying out 2 binomials. ‘F’ is for multiplying ‘F’irst terms….and so on…For example:
So what changed my mind? What humbled me? What have I been doing wrong?
You’ve been ‘FOIL’ed if you believed for one second I’ve changed my stance on teaching the FOIL method on my classroom.
For those of you reading this post on another day than today, April 1, 2017 – This post was just to see if people would actually believe I’ve changed my stance on teaching FOIL. I have not. I do not think any teacher should teach this method to students. It is a limited method that only works for multiplying binomials. It turns one type of problem where students can use a property they already know – the distributive property – into a ‘trick’. What happens when students multiply a binomial with a trinomial? FOIL will not work, but a deep understanding of the distributive property will.
One thing I may have done in the past is ‘shame’ teachers who use it. I could have been kinder as I told them why I don’t use it and what some alternatives are. Luckily there is a great book from Tina Cardone and the #MTBoS community you can download for free at Nix the Tricks. In the book Tina talks about dozens of math tricks like FOIL you should eliminate from your classroom. She tells why to eliminate them and what to replace them with. Check it out. I promise you will learn a lot.
Since I’ve personally stopped using ‘FOIL’ I’ve noticed my students are so much more proficient at using the distributive property in all situations they encounter. I personally love building off of the partial products/area model for multiplication that students use in elementary school and also use the area model for multiplying polynomials of any size.
The are model or box method can grow with students as opposed to limiting them. I try really hard to not teach rules that stop and don’t work as some point.
I try really hard to not teach rules that stop and don’t work as some point. NCTM has a great article for free on ’12 rules that expire‘ (a.k.a. – things you should not teach). Check it out. Math Rules that Expire from NCTM
This week I met up with 20+ math teachers from around the Minneapolis metro area. Over drinks and chips & queso I heard a teacher almost apologize for her students drawing in the curved arrows instead of using the box method to multiply polynomials. She almost ashamedly said “I let them do this instead of using the box”. In her mind the curved arrows where connected to ‘FOIL’ which she felt was bad. Her shame made me sad. I don’t want any of us to feel that the choices we make in our classroom we have to apologize for. My great hope is that we as teachers continue to be learners. That we take information from our classroom and talk about it with a community of math professionals. We are better together. My hope is we encourage one another and don’t shame one another. I hope that all our students will see multiplying polynomials as an opportunity to use the distributive property.
True Confession. During my first years of teaching (20+ years ago), I had a phenomenal wall display on FOIL. I had cleverly constructed the entire method for multiplying binomials out of tin foil. Yes tinfoil for FOIL> So clever. The time and energy I spent on this display did nothing for my students to understand conceptually what they were doing. What a waste (though I was applauded by principals and many other adults on this display in my room). I could look back in these days with shame. I don’t. I use this Maya Angelo quote often to comfort me in my work as a teacher. I leave this with you to encourage you in your worn work.
Happy April’s Fool Day. Next year I will do a post on why I think teaching ‘cross-multiplying’ is the best thing we can do for students.
Go forth and do better. I’m on spring break – so look for several posts this week.