Bring Basic Math to Life through Visual Learning

Adriana O’ Brien
Wolfram Research
training@wolfram.com

Outline

Importance of Interactive Materials

Introduction to Wolfram|Alpha® and the Wolfram Demonstrations Project™

Wolfram|Alpha in the Classroom

Incorporating Demonstrations into Your Curriculum

Importance of Interactive Materials

Moving Math Education into the Digital Age

Technology-based instruction can reduce the time students take to reach a learning objective by 30–80%, according to the US Department of Education and studies by the National Training and Simulation Association.

Increase of tablets in the classroom.

US tablet market in schools soared by 103% in 2011–12, per the International Data Corporation (IDC).

The number of tablets in England’s schools is expected to reach 260,000 by the end of 2013, up from 100,000 in 2012. The British Educational Suppliers Association (BESA) has predicted that nearly a third of all students will have access to a tablet by 2020.

Source

Real-world applications have always been a part of math standards, even more so since CCSS has dedicated an entire standard to modeling.

STEM job forecast is strong.

From 2000 to 2010, growth in STEM jobs (7.9 %) was three times as fast as employment growth in non-STEM jobs (2.6 percent) in the United States.

Computer and mathematical scientists accounted for 3.4 million jobs in 2008 and are forecast to grow to 4.2 million jobs in 2018.

Georgetown University’s Center on Education and the Workforce stated in the executive summary of its 2010 STEM study that “innovation and technology change have led to demand for STEM competencies beyond traditional STEM occupations” and “STEM competencies are needed in a broader reach of occupations, and their use is growing outside of STEM”.

Source

Effects of Using Interactive Resources

Engages students to make meaningful knowledge for themselves

Makes abstract concepts tangible to aid in the understanding process

Allows math into real-life applications and modeling scenarios that students can create

Introduction to Wolfram|Alpha

stylized[text_]:=Style[text,FontFamily -> "Helvetica", FontSize -> 14];

What is Wolfram|Alpha?

Wolfram|Alpha is a computational knowledge engine, with the goal of making the world’s knowledge systematically computable and accessible.

Wolfram|Alpha will return actual results to your inquiries, not links. It is NOT a search engine.

Example: Properties of Caffeine

(HyperlinkURL["Search", https://www.google.com/search?source=hp&ei=BQukXMLZIoiItQXThqDgCw&q=properties+of+caffeine&oq=properties+of+caff&gs_l=psy-ab.1.0.0l2j0i22i30l8.7855.14149..15815...1.0..1.603.7700.3-11j6j2......0....1..gws-wiz.....0..0i131.Ai39urtCNis])

Wolfram|Alpha

Pro

Wolfram|Alpha Pro gives you a whole new way to interact with Wolfram|Alpha—and immediate access to new, more personal, computational knowledge.

stylized@Grid[{{ImageResize[,400],ImageResize[,400],ImageResize[,400]},{"Go beyond text input and upload images, files, and tabular data","Get richer results with unlimited access to Step-by-step solutions, dynamic interactivity, zoomability, longer computations...","Customize and download images and data that support more than 60 different formats"}},Alignment->Center]

Introduction to the Wolfram Demonstrations Project

What is the Wolfram Demonstrations Project?

Wolfram Demonstrations Project is an open-code resource!

All Demonstrations are made using the Mathematica language.

Covers topics from science, technology, mathematics, art, finance, and a remarkable range of other fields.

Broken down by subject and grade level, and now you can explore by the Common Core State Standards.

Can be authored by anybody.

Finding the Linear Function Rule

Effect of Extra Payments on an Amortizing Loan

Wolfram|Alpha in the Classroom

Example 1: Lesson on Discovering Parabola Shifts

Not engaging

No critical thinking involved

Completely teacher-orientated

With Wolfram|Alpha

Develop a lesson that engages the students

Students critically analyze the results

Student-centered, which fosters long-term knowledge

Button[,NotebookLocate[{URL["\\\\files.wolfram.com\\temp-store\\adrianao\\Educational Outreach\\Lost in Parabola Translation.cdf"],None}],Appearance->None]

Example 2: Lesson on Arithmetic vs. Geometric Sequences

Students not making meaningful knowledge

No problem-solving skills involved

Students told the difference, not discovering the difference

With Wolfram|Alpha

Ask students problem-solving questions

Examples and non-examples solidify the concepts

Develop a lesson that has the students discover the defining characteristics

Button[,NotebookLocate[{URL["\\\\files.wolfram.com\\temp-store\\adrianao\\Educational Outreach\\What Comes Next.cdf"],None}],Appearance->None]

Example 3: Using Wolfram|Alpha’s Step-by-Step Functionality

For a nominal fee, students can have their own private tutor

Order of Operations

Solving a Quadratic Equation

Differentiation Using the Chain Rule

Incorporating Demonstrations into Your Curriculum

Moving away from “telling the students” to “letting the students explore”

Lesson Example 1: Investigating Inscribed Angles

A class discussion of the relationship between inscribed and central angles

Button[,NotebookLocate[{URL["http://www.demonstrations.wolfram.com/InscribedAndCentralAnglesInACircle/"],None}],Appearance->None]

Lesson Example 2: Increasing Estimation Skills

Working in teams to guess the perimeter and area

Button[,NotebookLocate[{URL["http://www.demonstrations.wolfram.com/EstimatingPerimeterAndAreaOfSimplePolygons/"],None}],Appearance->None]

Lesson Example 3: Real-World Modeling

By incorporating real-world modeling, students solidify abstract concepts and build critical thinking skills.

During our Mathematica Summer Camp, students worked toward producing a Demonstration.

Button[,NotebookLocate[{URL["http://demonstrations.wolfram.com/search.html?query=mathematica%20summer%20camp"],None}],Appearance->None]

In Conclusion

Points to Take Away

Interactive resources help students retain and understand the math better

Create activities that put students in the driver’s seat of their own learning

Wolfram|Alpha and the Wolfram Demonstrations Project have a wealth of information to support educators in the digital age

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