I watched a “simple” math question explode into a thread of insults, and it all could have been avoided. I say simple because the question, whether someone believes it was a trick/misleading or not, should not have led to an all out verbal assault.
I’m sure you’ve seen this math question floating around social media.
8 ÷ 2(2+2) = ?
There are two solution camps for this problem, and neither wants to budge.
| Answer is 16 | Answer is 1 | |
| 8 ÷ 2(2+2) = ? | 8 ÷ 2(2+2) = ? | |
| 8 ÷ 2(4) = ? | 8 ÷ 2(4) = ? | |
| 8 ÷ 2 * 4 = ? | 8 ÷ 2*4 = ? | |
| 8 ÷ 2 is the next step | 2 * 4 is the next step | |
| 4 * 4 = 16 | 8 ÷ 8 = 1 |
One of two reactions tends to come after seeing the answers people post.
- Who cares?
- If you didn’t get my answer, you’re an idiot.
It usually doesn’t go left this quickly, but after each person questions the other about how they got they answer, insults follow. Those who aren’t arguing usually don’t care or believe both are right and that we should be happy that people care about math.
So, what’s the problem? One of these answers will be marked incorrect on an exam. If we take both solutions as being correct, what happens when the steps to solve this question are applied to surgical procedures, medicine, money, architecture, transportation, or anything else? That’s a lot of variation and could result in tragedy.
Here’s the irony: Each group tells the other that the correct way to solve the equation is by using the order of operations – PEMDAS – parenthesis, exponents, multiplication, division, addition, and subtraction.
And…both are correct in following what they learned. The issue is that there seems to have come a time in which there was a change in what was considered the proper way to solve this equation.
Until recently (within the past generation), we were taught something that has been termed “implied multiplication by juxtaposition.” It allowed us to group things together that seemed to demand solving first. The same way we would read the term 3xy as one unit is the same way we would see 3(xy) as one unit. That means that the group of individuals (myself included) who got the answer of “1” read “8 ÷ 2(4) = ?” to require us to multiply 2 * 4 first because what we see is as an implied unit. So, when we see the original problem, we see:
8 ÷ 2(2+2) = ? —> 8 ÷ [2(2+2)] = ?
You may be thinking (or arguing), as many did on the post, that calculators come up with “16.” That should settle it, right? Who argues with calculators?
Well, the calculators that we had stated that “1” was correct. Those of us who were required to buy specific graphing calculators for our classes had the method we learned reinforced by our little desk computers, too.
The Math Doctors discovered that Texas Instruments produced calculators that placed higher priority on implied multiplication over explicit multiplication in graphing models like the TI-81. The TI-83 did not have the priority included. link
This is an archived manual of the TI-81. It’s available in different formats, but I chose this one. https://archive.org/details/ti_guidebook_en/page/n33/mode/2up
I screenshot these in case there is trouble finding them again online. Please notice that implied multiplication comes before multiplication and division in the order of operations. They are not the only calculators with this function programmed. I use this example because this was included in my required school supplies.
As someone who bought math books just to practice problems as an adult, this bothered me. I wasn’t bothered because they changed the method. I could have accepted it if someone had simply told us we no longer use implied multiplication. I accepted the fact that we no longer type two spaces after periods, so I think I could handle this. What bothered me was the way people responded on the post.
- Women laughed at our explanations and stated we were trying to argue with calculators. (Again, our calculators supported our answers and the way we were taught, also. I guess “Google” was supposed to override everything.)
- We were told to help our children with everything but math.
- Intelligence was insulted.
- On and on
I wonder if any those women realize that their attitudes contributed to more problems. If we, as a community, are supposed to support teachers and help our students, telling us to “leave the education to the teachers” places all burdens on them, and they’re absolutely never allowed to make any errors. It also creates more distance between parents and teachers as well as parents and children because parents are painted as “uneducated” or unable to help. That’s simply not the case.
Do you know how we could have avoided 400+ comments of mud slinging, hurt feelings, and confusion? (I unfollowed after a while, so the number could have been higher.)
- Someone, preferably the original poster who was aware of the correct answer, could have said, “This is why this answer is accepted now.”
As someone who liked math enough to consider it for a major, I researched to find out about the changes. But…it seems that by the time I responded, no one noticed or cared about my comment. Oh, well.
Before I comment on the spiritual lesson I got, I just want to leave you with this video. It seems, only the teachers in North America have been pushing for straight PEMDAS to eliminate implied multiplication. So, I’m not sure where this will lead us, especially since I thought math was a language on which we could all agree. Even though there are many ways to solve a problem, we should all arrive at the single, correct answer. (I guess not.)
So, the intense arguments got me thinking about the interactions I see in some forums (Christian and otherwise). There are times to take the “It could be 16 or 1” approach, and then there are times to take the “There is only one answer” approach. As I thought about what was setting off the intense discussions, I considered Jude.
Jude 3 tells us to contend earnestly for the faith. Contending is an intense action verb. Picture yourself wrestling or using your bare hands to protect your children from someone trying to take them. That’s how we’re supposed to verbally handle the faith. Of course, there are appropriate ways to do so, and the forum will affect how we speak. But I wondered how many Believers feel a burning desire to do so.
Now, I don’t want to confuse this with arguing with any and everyone about whatever religious topic comes up. I also don’t believe that many issues require this kind of reaction. I am all for Believers reasoning together, but some of the discussions I see going on and on (and on and on) aren’t core issues. Sometimes, it’s just a matter of preference or one person finding a situation challenging and insisting everyone else do what he does because the action is tempting him.
I believe this kind of focus is important for salvation issues, such as the deity of Christ. If we believe wrongly about Christ, it won’t matter how much alcohol we avoided, how many hours we volunteered at church, or how much we tried not to sin because we would, ultimately, still be lost and hellbound. Paul tells us the Gospel we are to believe in 1 Cor 15:1-4. These are non-negotiables. There is no believing Jesus committed sins but could atone for ours. There is no denying His virgin birth or resurrection. Likewise, we don’t claim Jesus is a created being (some teach) while saying He is the Creator (John 1, Col 1, 1 John 1).
What we believe matters.
What we teach other people matters.
What we reinforce matters.
For me, watching the thread on the math problem sparked several thoughts and reminders:
- It is difficult to reteach someone who has learned something improperly, especially if what they believe is part of their makeup. People are reluctant and resistant to change. However, if they desire truth, they are usually willing to listen.
- Supremacy of Scripture. The Bible is impartial and unaffected by how we feel. Even though both the person who has learned a false gospel and the person who has learned the true Gospel will use the Bible as their text, it should be something we appreciate because we already have an understanding that the Bible is the final authority on what is correct and what is incorrect.
- Seasoned speech – Just as the argument and hurt feelings could have been avoided if someone had taken the time to listen and then explain where the error was in the math problem, correcting a false Biblical view will require the person to see the seriousness of the situation, know how to adjust their speech to be heard, and the wisdom given by God to help the misled one see the truth.
That’s it, actually. We’re supposed to know what we believe and why. We should be able to explain to others. However, we aren’t instructed to verbally beat them into submission. It’s not our job to talk until they cry “uncle.” Sometimes, we’re so focused on winning the argument that we don’t see the damage we’re doing to the hearer in the process. Give people the truth and allow the Holy Spirit to do the convicting.
***10/12/2022 - We've had some interesting discussions and comments. Unfortunately, they don't transfer across platforms in blogs (or I haven't figured out the correct way to do it). Dave Peterson, the Math Doctor who wrote the article referenced above, mentioned a phrase I'd never heard called "theological triage." I looked it up and spent about a week reading, listening, and learning about it. (It doesn't take that long to understand the concept. I just wanted to know more.) Here's a very short explanation.***