Interaction: But who’s multiplying

Myers: Hello, and welcome once again to Interaction, wherein we examine some of the leading topics of the day with a group of people who are unlikely ever to agree on anything. This evening, our topic is mathematics and its education. Many have wondered about the continuing relevance of mathematics education in a modern, computerised world. If your mobile telephone has an app for that, does your brain need one as well? Well, that is why we have a panel with us today, as well as to see if they will agree with one another or come to blows with the display screens. Joining us in Los Angeles, CA, USA, we have the director of the Los Angeles local chapter of the Mathematics Teaching Brigade, Mr Phil Winfield.

Winfield: Hi.

Myers: In London, England, UK, we have the associate editor of the Journal of Mathematical Brain Functions, Ms Rebecca Kildenstein.

Kildenstein: Good evening.

Myers: From Chicago, IL, USA, the president of the organisation Parents for Useful Mathematics Education, Ms Thessala Dominiko.

Dominiko: Hi.

Myers: And joining me here in Warwickshire is the Charlie P Cambrick professor of mathematics at the University of the West End, Mr Ron Carron.

Carron: Hello there.

Myers: Thank you all for joining us today. Phil, going to you first, since its founding, your organisation has been in the forefront of the fight for improved mathematical education in the United States. What specifically do students need to learn?

Winfield: Well, Debbie, mostly we are looking for students to learn the basic arithmetic operators: addition, subtraction, multiplication, and division. Being able to do these quickly, or at least being able to estimate the results, is an important skill in the modern world. For students in high school, we are also expecting a knowledge of basic algebra: solving equations, understanding logarithms, and the like, as well as a deeper understanding of the rationale behind all these methods – that is, why we do what we do, so as to understand how a mathematical system works.

Myers: Well, some noble sentiments there. Rebecca, is it reasonable to expect all students to be able to learn these abilities?

Kildenstein: It is, Debbie. However, we must also be aware that different students learn in different ways, and so the approach that works for one may not work for another.

Myers: Certainly an important consideration. Thessala, your organisation believes that mathematics education should be directed differently. In what way?

Dominiko: Well, it’s very well and good to say that students should learn multiplication and logarithms. But the fact of the matter is, everyone has computers now. Everyone has computers, and calculators, and even calculation apps on our cell phones. Mathematics teachers need to recognise that and adjust accordingly.

Myers: Some different thinking there. Ron, as a professor of mathematics, do you believe that students are entering university with the appropriate mathematical education?

Carron: Well, yes and no. You see, many of those who are entering university with the intention of studying mathematics or a mathematical field, such as science or engineering, do have a proper understanding of a variety of mathematical fields, from algebra and geometry right up to calculus. But students who plan to study other fields tend to have lower scores in, for instance, algebra and geometry. And we at many universities around the country are trying to fight the perception that mathematics is only useful for certain fields. Everyone needs to understand mathematics, especially when we all have bills to pay, taxes to compute, and decisions to make.

Myers: Well, that’s an important point. Mathematics is, at its heart, a decision making tool. Thessala, do you believe that calculators and computers are really sufficient replacements for the intuitive problem solving skills that mathematics are all about?

Dominiko: Certainly. As the professor just pointed out, everyone needs mathematics. But not everyone needs to be able to learn how to compute logarithms mentally. There’s simply no need for most people.

Winfield: That’s not what we’re expecting, though. We’re expecting an understanding of what logarithms are. Students should understand that the logarithm is the inverse of exponentiation, and what its applications are. For instance, loudness is not perceived in a linear fashion, and so we measure sound intensity with decibels, rather than a linear scale.

Myers: All right. Well, let’s move on to our viewer questions. As you know, you can send us your questions in a variety of formats. These include telephone, text message, E-mail, snail mail, and facsimile, and the various numbers and addresses are appearing on your screen now. And they are being represented on the faces of a two dimensional projection of a multidimensional hypercube. How cute. Well, we now go to our first question, and it’s an E-mail from Sandra in Madrid, Spain. Sandra asks what algebra is good for. Ron?

Carron: Well, that’s a good question. Algebra is good for identifying unknowns and solving for them. So let’s suppose that you make a certain amount of money per month. You have several different expenses to pay each month, like the rent, the electricity, and groceries. Now suppose that you want to get a mobile telephone. You’d like a smart phone with a data plan, but you’re not sure whether you can afford it. So you sum up your expenses and call them E. Your income is I. The remaining money you have each month is then x. So you then have E = I + x, and therefore x = E – I. If x is greater than the monthly cost of the plan you want, you can afford it. These are the sorts of decisions that everyone needs to be able to make.

Myers: Thessala, is this the sort of approach that you would like students to learn?

Dominiko: Of course. You don’t need to know how to subtract two numbers. So if that’s what mathematics teachers were teaching, we would have no problems whatsoever.

Winfield: That is what we’re teaching. This kind of critical thinking is essential in today’s world. The emphasis is now less on what numbers are and more on what they mean.

Dominiko: That’s not true at all. You still teach the multiplication table. What is the point of that? There’s no need to continue teaching the multiplication table.

Winfield: I would disagree with that. There is still a need to make rough calculations quickly. When you’re in a store, and you’re buying several of the same item, you need to know about how much it’s going to cost. When you’re at a restaurant, you need to know how large of a tip to leave.

Myers: All right. Let’s leave that aside for a moment and continue on to our next question. Lewis from Southampton, England, UK, are you there?

Lewis in Southampton: Yes. Hi.

Myers: Hello Lewis. What is your question?

Lewis in Southampton: What is fourteen times two?

Winfield: Twenty eight.

Kildenstein: Twenty eight.

Lewis in Southampton: Ha ha! Gotcha! It’s twenty four!

Carron: No it bloody isn’t.

Lewis in Southampton: Ha ha! I stumped you! You experts don’t know – aaaaaaah! [voice recedes into faintness]

Myers: This demonstrates the value of knowing how to multiply. Our next question is a text message from Leticia in Staten Island, NY, USA. She asks “omg i no how 2 x numbrs n stuff isnt that awsum”. Rebecca, is that indeed awsum?

Kildenstein: It certainly is. I recommend she proceed to spelling.

Myers: Well, I believe that would be considered a “zing”. We have time for one more question, and it’s from Kelly in Talham, MA, USA. Kelly, are you there?

Kelly in Talham: Yes. Hi.

Myers: Hello Kelly. What is your question?

Kelly in Talham: I’ve seen a lot of news reporters, and a lot of articles, make misstatements about mathematics. Especially when it comes to probabilities. Wouldn’t it be important to get our media to understand mathematics if we want our children to understand it?

Myers: A very interesting question that. Phil, would you agree there?

Winfield: Yes, I think she was right.

Kildenstein: I thought that was a guy.

Carron: Yeah. So did I.

Winfield: I thought it was a girl.

Dominiko: It sounded like a girl, yeah.

Myers: Regardless, Kelly had an important point.

Carron: It really sounded like a dude to me.

Winfield: No, the voice was too high.

Kildenstein: Some guys have high voices. Who’s that one singer who sounds like a girl?

Carron: Mariah Carey?

Kildenstein: No, the one who sounds like a girl but isn’t.

Myers: But back to the question about –

Dominiko: Natalie Merchant.

Kildenstein: No, the one who isn’t a girl.

Dominiko: But she got a sex change, right?

Kildenstein: What? No!

Dominiko: I thought Natalie Merchant got a sex change.

Carron: Who’s Natalie Merchant?

Myers: If I could –

Winfield: Is she still making albums?

Dominiko: Yes, but as a guy.

Kildenstein: No she’s not!

Carron: Not making albums, or not a guy?

Kildenstein: She’s not a guy, and she’s still making albums!

Carron: Who the hell is she?

Winfield: How old is she now?

Kildenstein: It doesn’t matter! She’s –

[Sound cuts out abruptly.]

Myers: Well, I’m afraid we’re going to have to end things there, with a red button push. We may never know how important it is to have a news media that understands mathematics. So we’ll say so long for this week and thank Mr Ron Carron, Ms Thessala Dominiko, Ms Rebecca Kildenstein, and Mr Phil Winfield for joining us today. Next time, we’ll be discussing social media and how it is changing the way people interact. We’ll be joined by the owner of a leading social media company, the author of a book about social media, and someone who is leading the push in the area of antisocial media. So be sure to join us from Warwickshire next week at this same time. Till then, good night.

Dominiko: Well, there was one singer who got a sex change, right?

Winfield: Pretty sure that was Justin Bieber.