Teaching Framework and Principles for the App++

The red team will consist of the first through third grade teachers and the blue team will consist of fourth through seventh grade teachers.

Members of each team should teach parts of each grade in a team bracket in order to promote continuity over longer periods of time in order to establish better teacher/student relationships and teaching goals.Common Core guidelines will help each team focus on long term goals for the course. The rate and amount of detail of Common Core suggestions covered should be set by the team members as is the choice of technical apps that best suits the team goals. Team members of each class group are the best judges of how to adjust to maximize learning for a particular situation.

Students instinctively know when a teacher is in control of a class. Having a unified team of teachers enforces the control problem.  Numerous internet sources from individuals, teacher associations, and university research offer good suggestions of written expectations for the class and consistent discipline for offenders.

Teach mathematics by learning the rules. Learning to think about what numbers do rather than what they represent is crucial. This is a central view of the recommended text for the class: “Mathematics A Very Short Introduction” by Timothy Gowers (Fields Medal); Oxford University Press (about $12). The text is often referred to in the App++ and teachers will need to help students read Gower’s text. Mathematics must be read slowly and very carefully. Each word counts.

The App++ uses only basic Swift concepts in order that special computer science teachers are not required, only the regular mathematics teachers. The structure of the course will encourage students to think computationally.

Some schools will desire to teach more advanced coding. The first problem is that Xcode ( development center for maxOS) is too large for the iPad. However, the recently released SwiftUI allows access to crucial features of Xcode on the iPad which can be exploited.

The second problem is that advanced features of the Swift language not addressed by the App++ must be covered and will require the aid of an experienced Swift programmer. At this stage one can avoid class objects and concentrate on structs and enums objects. One sends messages to an object by the dot syntax. That is the object is followed by a dot and then some message. These messages are  developed by apple engineers and are carefully tested and optimized.

Two Recommended Code Books

Two code books (there are many) that are useful are:

A. iOS 15 Programming Fundamentals by Matt Neuburg (O’Reilly)
B. SwiftUI Essentials iOS edition by Neil Smyth (Payload Media)

Both books only address the Playground that is in Xcode. Book A gives a comprehensive development of the fundamentals of the Swift language. Check page 690 for a brief but insightful discussion of SwiftUI. Book B is useful for the new material needed and the examples of SwiftUI.

Additional Code to Access SwiftUI on the iPad

The following additional code on the iPad will allow a portion of the SwiftUI available on the Playground in Xcode to be produced on the Playground on the iPad.

Add at the top of your Playground on the iPad the following statements:

• import SwiftUI
• import PlaygroundSupport
• import UIKit

 If an error for example says the variable rotation is not in scope, then below the struct name (say ContentView)

struct ContentView: View {
enter:
@State private var rotation: Double = 0
var body: some View {

Add rest of program (as in book B examples), then at the very end add:

PlaygroundPage.current.setLiveView(ContentView( ))

If the struct has another name, insert it in place of ContentView. This last statement will then show a view where you can see the effects of the SwiftUI using VStack, HStack, Colors, and animations.

Further development is available through the following program.

Dr. McKnight of Montgomery County Public Schools asked Apple to develop a summer coding program for middle school students. It has been very successful. It is based on using the iPad to design apps in Keynote and then prototype them to Swift using Apple’s Everyone Can Code guides.

Books To Aid Teaching

The following books should be available in the school library to aid teams teaching the App++ course. The list is by no means exhaustive. 

1. Art of Problem Solving: pre-Algebra by Rusczyck, Patrick, Boppana; ApOS
2. Introduction to Algebra by Rusczyk; ApOS
3. Mathematics for Secondary School Teachers by E. Bremigan, R. Bremigan, Lorch; Mathematical Association of America.
4. Teaching School Mathematics: Algebra by Wu; AMS
5. Algebra by Gelfand and Shen; Birkhäuser
6. Algebra by Higgins; Oxford University Press
7. Statistics by Hand; Oxford University Press
8. Probability by Haigh: Oxford University Press
9. Creative Mathematics by H. S. Wall; University of Texas Press
10. Real Number System by Olmsted; Dover
11. Making Mathematics Come to Life by Ivanow; AMS
12. Geometry A Metric Approach with Models by Milliman and Parker; Springer
13. Choose several books from the Series of Math Books by the National Council of Teachers of Mathematics – for example Common Core Mathematics in a PLC at work and Algebra: Patterns, Functions, Casebook.