I recently shared an article on the expiration dates on certain strategies or concepts used in the classroom, and so many of you had such great comments on that article that I wanted to discuss it a bit further.
The strategy that brought the most feedback was on the Butterfly Method. While this method is very effective in raising standardized test scores, it does nothing to help the students when they move on. Today, I want to give you three tips on how to deal with it.
Tip #1 - Don’t criticize the teachers who used it.
If your students’ previous teacher used this method, don’t criticize them for what they did in their classroom. There are a couple of reasons for this:
- It undermines the students’ confidence in their teachers overall. You know that you have your students’ best interests at heart and you should also assume that about their previous teachers. They wanted their students to achieve their best, and they were trying to help them do that.
- It undermines the student’s confidence in themselves. If you tell them that they are doing something the wrong way, they are going to be insecure and wonder what else they do that isn’t right. You don’t want your students to be nervous and insecure because then they aren’t as willing to try new things.
Tip #2 - Compliment them on what they remember.
As I have said many times, always take the time to build your students up with what they already know before trying to teach them something new.
Use what they learned in the past to connect it to the new concept. For example, if you are comparing fractions, they likely learned to use the Butterfly method to find common denominators. How can you use that to move on to more complicated ways of doing the problems?
I like to use sticks of gum. I break them up into halves and thirds and divide them among the students with a few students getting whole sticks. They then have to combine their pieces with students who have the same size as theirs to get a whole.
Show them how this is the same as the butterfly method they learned previously but can be used with much more complicated problems. You aren’t asking them to forget what they learned, but rather you are teaching them how to build on it.
Tip #3 - Drive the Vocabulary
If you just listen to your students, most of the time they will use the exact vocabulary that their previous teachers used in teaching them these methods. Once you know the vocabulary they used, you can build on it and teach them the correct mathematical terms for what they are doing.
Again, don’t undermine the teachers. I like to tell my students that the teachers used those words because the students were little, but now that they are high-schoolers or middle-schoolers, it’s time to use the bigger, more technical, terms.
You can also show them why the Butterfly method no longer works by giving them examples of negatives. Ask them where the negative goes on the butterfly. Then let them try it with three fractions and see what happens. They quickly see that it doesn’t work for the higher-level problems.
As always, I encourage you to talk to your students and help them to see how many things they’ve learned and how capable they are of learning newer, higher-level things. As you build them up, they will almost always give their best effort.
Please comment below and let me know if you struggle with this in your classroom and how you’ve overcome it.
I believe this is an example as to why elementary and middle school math teachers need to have degrees in math. The foundation of understanding and manipulating fractions is crucial for success in Algebra courses and many students are at a disadvantage if their foundation is lacking.
I went over fractions yesterday, I used three different ways to check for proportionality. I started with what they knew, the dreaded butterfly, however, after some success we moved to a different method.
Hi Kathy,
I don’t think the elemtary teachers should have degrees in math. I don’t even have a “degree” in math and I teach high school. I think what would be more productive is communication and collaboration. All levels of teachers should have time to meet and discuss topics such as tricks and how they should or should not be used. Collaboration is key and I find that there is very little done between grade levels and between primary and secondary.
I, too, don't have a degree in math (30 hours, but no degree--my degree is actually in French!), and I am beginning my 45th year teaching math, math, and more math! I love your comment, Liz. Communication and collaboration are soooooo much better than even the best PD.
I can understand using the butterfly method. I would even show it to kids. However, at any and all times, I would emphasize with the kids that this has nothing to do with proportions, when an equal sign is in the middle. And, this is when I see kids mess up with the butterfly method. They get it confused with proportions then really mess things up. "If" they can keep the butterfly method separate from proportions, I could even see the definite benefit from showing the butterfly method. But, until then, the kids shouldn't even consider it.
I think I use the word butterfly for cross multiply. What does butterfly mean to you guys? I don't think I'm familiar with the method you guys are talking about.
I, too, would like to know if what I'm thinking is meant is really what is meant . . .
I dislike the use of the words "butterfly method" and the "check method". The students remember the phrases and even the picture but do not remember the calculations associated with it or why they are even using it. I tried to convince my pre-algebra co-teacher from using it but was met with strong opposition.
What I do appreciate from this topic are the 3 steps shared when experiencing this situation in the classroom. They are valid and valuable strategies that I will endeavor to utilize.
I tell my students that I don't care what method they use as long as they can get the correct answer. I will often show different methods and let students choose which they feel most comfortable using.
Jeanette, can you please re-post the link to the original 'expiration date' article?
Absolutely Pam. I added it to the article above.
https://www.nctm.org/Publications/Mathematics-Teaching-in-Middle-School/2015/Vol21/Issue4/12-Math-Rules-That-Expire-in-the-Middle-Grades/
The use of the term "butterfly" fosters confusion for students who do not have a firm conceptual understanding of equivalence of fractions. "Butterfly" has been used widely for both comparison of fractions and solving proportions. It is necessary for students to understand the underlying concept of equivalence in both instances. When comparing fractions to determine their relationship to each other, "butterfly" finds the numerators of the fractions with the same denominator created from finding the product of the two original denominators. For example, when comparing 2/3 to 3/4, using "butterfly" yields 8 and 9 making 2/3<3/4. In actuality, comparing the fractions should be written 8/12 and 9/12. Since the denominators are the same, we can compare the numerators to determine the relationship between the fractions; 8/12 < 9/12 or 2/3 < 3/4. In proportions, you know the two fractions are equivalent, but you are missing a value within one (or both) of the fractions. For instance, when solving 3/4 = x/20, most begin with "butterfly" getting 60 = 4x. In reality, it should be written 60/120 = 4x/120. We want equivalence, and since the two denominators are equal, we need to find the value if x to make the two numerators equal. Thus, we need to solve 60=4x. It is only from understanding conceptually what is being done, that true learning can occur. Without conceptual understanding of the need to work with fractions having common denominators in problems involving proportionality and comparison of fractions, "butterfly" becomes a trick that has the potential to be applied at inappropriate times, such as when multiplying or dividing fractions.