Debate: Society's Changing Needs for Math

Charles Fadel

We will describe the rapidly changing societal and employability requirements of the age of exponential technologies and what skills and knowledge are required to stay ahead of the curve. In particular, we will seek to answer "What should be taught in an age of search and A.I.?" and, specifically, the importance of STEM.

Case Studies: Applying Computers to Math Education

Debra Woods

Learning by Making: Learning to Learn

An 18-year history of CBM by repurposing how math is taught from the classroom to online learning will be discussed, with a focus on the strengths, successes, and challenges.

Case Studies: Applying Computers to Math Education

John Perram

I will begin by reviewing current freshman mathematics instruction against the principles of competence-based curriculum design. This will show that the competences are the ability to carry out technical calculations under time pressure without access to any of the resources available in a working environment. I will then outline an alternative in which students learn all the technical content by analyzing a number of applications, with this content structured as interoperable, customizable symbolic, and numerical and graphical code fragments, illustrated with a couple of examples. Based on my experience teaching courses in dynamical systems and analytical mechanics, I will demonstrate that this alternative implies a shift in effort from delivery to preparation and evaluation. I will discuss various impediments to this program and how they might be overcome.

Briefing: State-of-the-Art Technology for CBM

Scott Gray

Making Math is a noLMS system based on an online version of Mathematica. noLMS systems enable learning-by-making combined with formative assessment and social networking. They are a tight integration of an integrated development environment (IDE), for example, Mathematica, content, and learning management. Teaching math becomes more like teaching music: teach them to hear and play the music before getting them caught up in all the notes.

Briefing: State-of-the-Art Technology for CBM

Gary Bitter

"Apps Boom"—Using Math Apps to Teach and Learn Math

The "Apps Boom" has started to embrace the world of education. This session is dedicated to identifying math apps that can be used to enhance the teaching and learning of math. Discussion will include the pros and cons related to the math app topics. The primary goal of the presentation is to provide a scientific basis for the educational value of the math apps available in the market, focusing on what needs to be observed for developing or using an educationally sound math app. The attendees will not only gain insight on what they must be looking for in a math app so as to access the educational value, but they will also have the opportunity to see examples of the math apps available in the market.

Briefing: State-of-the-Art Technology for CBM

Mark Braley

Developing mathematical understanding with ICT in the classroom, focusing on AS and A2 level mathematics, post-16 classroom

How can we use ICT to encourage students to generalize usefully in mathematics and develop their mathematical understanding? Using ideas from Anne Watson and John Mason in the ATM publication Thinkers, I'll give an introduction to the use of TI-Nspire™ and Navigator™, a wireless connectivity system, to prompt thinking and organize discussion in the post-16 classroom. (The practice of using the higher level "thinkers" in the post-16 classroom came from a discussion with Tom Button from MEI on using Navigator for AS and A2 level mathematics. It would be great to share these ideas with an audience of educators!).

Discussion: Engaging the Disenfranchised with CBM

Kyle McCormick

End-users often know the results they seek, but are unaware that mathematics can play any role whatsoever in determining those results. They want outcomes that are accurate and meaningful, regardless of how those outcomes were reached. However, when the method of determining the outcome becomes important, end-users want to be able to probe the process for understanding. Consider the scrutiny a judge gives to damage claims in a court of law, or the temporal nature of threats of terrorism. Increasingly, non-technical users are utilizing computers to make decisions with real, personal consequences. As educators, we must provide superior analytical skills to end-users so that they have the power to use increasingly sophisticated computational tools.

Discussion: Engaging the Disenfranchised with CBM

Bruce Dickson

A whistle-stop tour through a list of successful projects with promise. Some reasons why they work, and a suggested way ahead for all of them.

Debate: Hand versus Computer—Drawing the Line

David Wees

Conceptual knowledge is necessary to be successful at mathematics, but I believe that for many of the algorithms we teach students, there is little difference between using a computer to do the algorithm and using pencil and paper. Some of the algorithms themselves have embedded conceptual knowledge and are of course important to learn, but should be learned for understanding how the algorithm itself works rather than necessarily memorizing the algorithm.

Discussion: Implementing the Change to CBM

James Tanton

Implementing change within the rigid mindset

If educators insist that certain standard topics remain in the curriculum—no matter what—then CBM has an interesting challenge. Can CBM be introduced into a rigid framework and offer convincing first steps to change? Let's examine one standard topic, 10th grade quadratics, and explore concrete possibilities.

Discussion: Implementing the Change to CBM

Alison Clark-Wilson

Digital technologies and mathematics education, The JMC Working Group Report

Against a background of widespread concern about the U.K.'s ability to meet the increasingly technological skill needs of major sectors of the economy, the Joint Mathematical Council of Great Britain established a working group to consider the role that digital technologies might and should have in mathematics education now and in the future. The session will present the key findings of the working group and its recommendations.

Discussion: Implementing the Change to CBM

Douglas Butler

By letting the computer do the spade-work, topics such as 3D lines and planes, complex numbers, differential equations, and the central limit theorem can all come back into the mainstream—but pedagogy, firm understanding, and effective teacher training remain paramount.

Discussion: How Will Assessment Work for CBM?

Tom Button

Mathematics in Education and Industry (MEI) is working with OCR to develop a new unit for A-Level Further Mathematics, which will require the use of computers with CAS-enabled software for teaching, learning, and assessment. We plan to work closely with a small group of schools and colleges, supporting them to begin teaching the unit in the academic year 2012/13, with first assessment in summer 2013. This presentation will address:

• Introducing computer-based mathematics within the current assessment system
• The impact of the assessment on classroom practice
• The importance of involving classroom teachers in developments

Discussion: How Will Assessment Work for CBM?

Douglas Stein

Whether we like it or not, the political accountability pressures on teachers to demonstrate "value-added" in the classroom tend to force them to keep at least one eye on the summative end-of-year tests. Since most summative tests (typically multiple choice plus handwritten computation–possibly with a hand calculator) ignore CBM, which makes it difficult for any but the most confident and strong-minded teachers to consider using CBM instead of "drill-and-kill". A new generation of assessments that are based on performance tasks using CBM tools and concepts coupled with computer-assisted formative instruction that develops and guides students' ability to engage in modeling activity can make it "safe" to restructure math education to be truly CBM-friendly.

Discussion: Math (STEM) Needs for Industry

Toshiaki Kurokawa

This talk will give some experience and survey on the educational sessions for Design Thinking both for academia and industry. Originated from design studios, Design Thinking has now come into engineering, science, and business schools and service science, management, and engineering. Industries have also become interested and are involved in this activity.

Debate: The Role of Government

Rosamund Sutherland

Against a background of widespread concern about the U.K.'s ability to meet the increasingly technological skills needs of major sectors of the economy, the JMC established a working group to consider the role that digital technologies might and should have in mathematics education, now and in the near future. Within this brief presentation, I shall discuss some of the recommendations from this report.

Discussion: Different Cultures, Different Math?

David Stern

I am very partial to the thought that the subject of mathematics is a universal language that transcends culture, but my own person experience has shown how different parts of the world have very different mathematical cultures. I will mention how interesting insight into a country's mathematical culture can be obtained by asking what good maths students study at university. This leads into my current area of work in Kenya, where we are trying to use technology to change the mathematics culture.

Discussion: Different Cultures, Different Math?

Simon Walsh

Exploratory learning with locally generated content

Traditional education models are failing too many. The old way is as inaccessible as it is ineffective. This is why we have been working in partnership to build a Virtual School, which will apply the best in technology and learning theory to make a high-quality, comprehensive primary and secondary school education available to children throughout the world for free.

While mathematics is a universal subject, one of the key challenges has been to develop math resources that are localized for each country. The process has lead us down many routes and has involved input from math experts on the ground from places as far afield as Africa, India, and the U.K.