Differences between the ACT and SAT:
http://www.math.com/students/kaplan/satoract.html
A good analysis of who does better on the ACT vs. the SAT.
http://www.nytimes.com/2007/11/04/education/edlife/guidance.html?_r=1&pagewanted=2
Sunday, July 11, 2010
Friday, July 2, 2010
Computer Science at the Highschool Level
From the collegeboard, there is a Pre-AP Teacher's corner that has quite a bit of info and resources. This is the one for preAP computer science.
http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/22778.html
I really like the book she describes: an online book on "How to Design Programs" (http://www.htdp.org/2003-09-26/ ) with the following table of contents (below). It talks through a logical, step by step approach to learning how to approach a problem for programming and the text looks like it is written to the student instead of to the teacher. It prepares the student for more in-depth java or any other language:
Processing Simple Forms of Data
1 Students, Teachers, and Computers
2 Numbers, Expressions, Simple Programs
2.1 Numbers and Arithmetic
2.2 Variables and Programs
2.3 Word Problems
2.4 Errors
2.5 Designing Programs
3 Programs are Function Plus Variable Definitions
3.1 Composing Functions
3.2 Variable Definitions
3.3 Finger Exercises on Composing Functions
4 Conditional Expressions and Functions
4.1 Booleans and Relations
4.2 Functions that Test Conditions
4.3 Conditionals and Conditional Functions
4.4 Designing Conditional Functions
5 Symbolic Information
5.1 Finger Exercises with Symbols
6 Compound Data, Part 1: Structures
6.1 Structures
6.2 Extended Exercise: Drawing Simple Pictures
6.3 Structure Definitions
6.4 Data Definitions
6.5 Designing Functions for Compound Data
6.6 Extended Exercise: Moving Circles and Rectangles
6.7 Extended Exercise: Hangman
7 The Varieties of Data
7.1 Mixing and Distinguishing Data
7.2 Designing Functions for Mixed Data
7.3 Composing Functions, Revisited
7.4 Extended Exercise: Moving Shapes
7.5 Input Errors
8 Intermezzo 1: Syntax and Semantics
8.1 The Scheme Vocabulary
8.2 The Scheme Grammar
8.3 The Meaning of Scheme
8.4 Errors
8.5 Boolean Expressions
8.6 Variable Definitions
8.7 Structure Definitions
II Processing Arbitrarily Large Data
9 Compound Data, Part 2: Lists
9.1 Lists
9.2 Data Definitions for Lists of Arbitrary Length
9.3 Processing Lists of Arbitrary Length
9.4 Designing Functions for Self-Referential Data Definitions
9.5 More on Processing Simple Lists
10 More on Processing Lists
10.1 Functions that Produce Lists
10.2 Lists that Contain Structures
10.3 Extended Exercise: Moving Pictures
11 Natural Numbers
11.1 Defining Natural Numbers
11.2 Processing Natural Numbers of Arbitrary Size
11.3 Extended Exercise: Creating Lists, Testing Functions
11.4 Alternative Data Definitions for Natural Numbers
11.5 More on the Nature of Natural Numbers
12 Composing Functions, Revisited Again
12.1 Designing Complex Programs
12.2 Recursive Auxiliary Functions
12.3 Generalizing Problems, Generalizing Functions
12.4 Extended Exercise: Rearranging Words
13 Intermezzo 2: List Abbreviations
III More on Processing Arbitrarily Large Data
14 More Self-referential Data Definitions
14.1 Structures in Structures
14.2 Extended Exercise: Binary Search Trees
14.3 Lists in Lists
14.4 Extended Exercise: Evaluating Scheme
15 Mutually Referential Data Definitions
15.1 Lists of Structures, Lists in Structures
15.2 Designing Functions for Mutually Referential Definitions
15.3 Extended Exercise: More on Web Pages
16 Development through Iterative Refinement
16.1 Data Analysis
16.2 Defining Data Classes and Refining Them
16.3 Refining Functions and Programs
17 Processing Two Complex Pieces of Data
17.1 Processing Two Lists Simultaneously: Case 1
17.2 Processing Two Lists Simultaneously: Case 2
17.3 Processing Two Lists Simultaneously: Case 3
17.4 Function Simplification
17.5 Designing Functions that Consume Two Complex Inputs
17.6 Exercises on Processing Two Complex Inputs
17.7 Extended Exercise: Evaluating Scheme, Part 2
17.8 Equality and Testing
18 Intermezzo 3: Local Definitions and Lexical Scope
18.1 Organizing Programs with local
18.2 Lexical Scope and Block Structure
IV Abstracting Designs
19 Similarities in Definitions
19.1 Similarities in Functions
19.2 Similarities in Data Definitions
20 Functions are Values
20.1 Syntax and Semantics
20.2 Contracts for Abstract and Polymorphic Functions
21 Designing Abstractions from Examples
21.1 Abstracting from Examples
21.2 Finger Exercises with Abstract List Functions
21.3 Abstraction and a Single Point of Control
21.4 Extended Exercise: Moving Pictures, Again
21.5 Note: Designing Abstractions from Templates
22 Designing Abstractions with First-Class Functions
22.1 Functions that Produce Functions
22.2 Designing Abstractions with Functions-as-Values
22.3 A First Look at Graphical User Interfaces
23 Mathematical Examples
23.1 Sequences and Series
23.2 Arithmetic Sequences and Series
23.3 Geometric Sequences and Series
23.4 The Area Under a Function
23.5 The Slope of a Function
24 Intermezzo 4: Defining Functions on the Fly
V Generative Recursion
25 A New Form of Recursion
25.1 Modeling a Ball on a Table
25.2 Sorting Quickly
26 Designing Algorithms
26.1 Termination
26.2 Structural versus Generative Recursion
26.3 Making Choices
27 Variations on a Theme
27.1 Fractals
27.2 From Files to Lines, from Lists to Lists of Lists
27.3 Binary Search
27.4 Newton's Method
27.5 Extended Exercise: Gaussian Elimination
28 Algorithms that Backtrack
28.1 Traversing Graphs
28.2 Extended Exercise: Checking (on) Queens
29 Intermezzo 5: The Cost of Computing and Vectors
29.1 Concrete Time, Abstract Time
29.2 The Definition of ``on the Order of''
29.3 A First Look at Vectors
VI Accumulating Knowledge
30 The Loss of Knowledge
30.1 A Problem with Structural Processing
30.2 A Problem with Generative Recursion
31 Designing Accumulator-Style Functions
31.1 Recognizing the Need for an Accumulator
31.2 Accumulator-Style Functions
31.3 Transforming Functions into Accumulator-Style
32 More Uses of Accumulation
32.1 Extended Exercise: Accumulators on Trees
32.2 Extended Exercise: Missionaries and Cannibals
32.3 Extended Exercise: Board Solitaire
33 Intermezzo 6: The Nature of Inexact Numbers
33.1 Fixed-size Number Arithmetic
33.2 Overflow
33.3 Underflow
33.4 DrScheme's Numbers
VII Changing the State of Variables
34 Memory for Functions
35 Assignment to Variables
35.1 Simple Assignments at Work
35.2 Sequencing Expression Evaluations
35.3 Assignments and Functions
35.4 A First Useful Example
36 Designing Functions with Memory
36.1 The Need for Memory
36.2 Memory and State Variables
36.3 Functions that Initialize Memory
36.4 Functions that Change Memory
37 Examples of Memory Usage
37.1 Initializing State
37.2 State Changes from User Interactions
37.3 State Changes from Recursion
37.4 Finger Exercises on State Changes
37.5 Extended Exercise: Exploring Places
38 Intermezzo 7: The Final Syntax and Semantics
38.1 The Vocabulary of Advanced Scheme
38.2 The Grammar of Advanced Scheme
38.3 The Meaning of Advanced Scheme
38.4 Errors in Advanced Scheme
VIII Changing Compound Values
39 Encapsulation
39.1 Abstracting with State Variables
39.2 Practice with Encapsulation
40 Mutable Structures
40.1 Structures from Functions
40.2 Mutable Functional Structures
40.3 Mutable Structures
40.4 Mutable Vectors
40.5 Changing Variables, Changing Structures
41 Designing Functions that Change Structures
41.1 Why Mutate Structures
41.2 Structural Design Recipes and Mutation, Part 1
41.3 Structural Design Recipes and Mutation, Part 2
41.4 Extended Exercise: Moving Pictures, a Last Time
42 Equality
42.1 Extensional Equality
42.2 Intensional Equality
43 Changing Structures, Vectors, and Objects
43.1 More Practice with Vectors
43.2 Collections of Structures with Cycles
43.3 Backtracking with State
http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/22778.html
I really like the book she describes: an online book on "How to Design Programs" (http://www.htdp.org/2003-09-26/ ) with the following table of contents (below). It talks through a logical, step by step approach to learning how to approach a problem for programming and the text looks like it is written to the student instead of to the teacher. It prepares the student for more in-depth java or any other language:
Processing Simple Forms of Data
1 Students, Teachers, and Computers
2 Numbers, Expressions, Simple Programs
2.1 Numbers and Arithmetic
2.2 Variables and Programs
2.3 Word Problems
2.4 Errors
2.5 Designing Programs
3 Programs are Function Plus Variable Definitions
3.1 Composing Functions
3.2 Variable Definitions
3.3 Finger Exercises on Composing Functions
4 Conditional Expressions and Functions
4.1 Booleans and Relations
4.2 Functions that Test Conditions
4.3 Conditionals and Conditional Functions
4.4 Designing Conditional Functions
5 Symbolic Information
5.1 Finger Exercises with Symbols
6 Compound Data, Part 1: Structures
6.1 Structures
6.2 Extended Exercise: Drawing Simple Pictures
6.3 Structure Definitions
6.4 Data Definitions
6.5 Designing Functions for Compound Data
6.6 Extended Exercise: Moving Circles and Rectangles
6.7 Extended Exercise: Hangman
7 The Varieties of Data
7.1 Mixing and Distinguishing Data
7.2 Designing Functions for Mixed Data
7.3 Composing Functions, Revisited
7.4 Extended Exercise: Moving Shapes
7.5 Input Errors
8 Intermezzo 1: Syntax and Semantics
8.1 The Scheme Vocabulary
8.2 The Scheme Grammar
8.3 The Meaning of Scheme
8.4 Errors
8.5 Boolean Expressions
8.6 Variable Definitions
8.7 Structure Definitions
II Processing Arbitrarily Large Data
9 Compound Data, Part 2: Lists
9.1 Lists
9.2 Data Definitions for Lists of Arbitrary Length
9.3 Processing Lists of Arbitrary Length
9.4 Designing Functions for Self-Referential Data Definitions
9.5 More on Processing Simple Lists
10 More on Processing Lists
10.1 Functions that Produce Lists
10.2 Lists that Contain Structures
10.3 Extended Exercise: Moving Pictures
11 Natural Numbers
11.1 Defining Natural Numbers
11.2 Processing Natural Numbers of Arbitrary Size
11.3 Extended Exercise: Creating Lists, Testing Functions
11.4 Alternative Data Definitions for Natural Numbers
11.5 More on the Nature of Natural Numbers
12 Composing Functions, Revisited Again
12.1 Designing Complex Programs
12.2 Recursive Auxiliary Functions
12.3 Generalizing Problems, Generalizing Functions
12.4 Extended Exercise: Rearranging Words
13 Intermezzo 2: List Abbreviations
III More on Processing Arbitrarily Large Data
14 More Self-referential Data Definitions
14.1 Structures in Structures
14.2 Extended Exercise: Binary Search Trees
14.3 Lists in Lists
14.4 Extended Exercise: Evaluating Scheme
15 Mutually Referential Data Definitions
15.1 Lists of Structures, Lists in Structures
15.2 Designing Functions for Mutually Referential Definitions
15.3 Extended Exercise: More on Web Pages
16 Development through Iterative Refinement
16.1 Data Analysis
16.2 Defining Data Classes and Refining Them
16.3 Refining Functions and Programs
17 Processing Two Complex Pieces of Data
17.1 Processing Two Lists Simultaneously: Case 1
17.2 Processing Two Lists Simultaneously: Case 2
17.3 Processing Two Lists Simultaneously: Case 3
17.4 Function Simplification
17.5 Designing Functions that Consume Two Complex Inputs
17.6 Exercises on Processing Two Complex Inputs
17.7 Extended Exercise: Evaluating Scheme, Part 2
17.8 Equality and Testing
18 Intermezzo 3: Local Definitions and Lexical Scope
18.1 Organizing Programs with local
18.2 Lexical Scope and Block Structure
IV Abstracting Designs
19 Similarities in Definitions
19.1 Similarities in Functions
19.2 Similarities in Data Definitions
20 Functions are Values
20.1 Syntax and Semantics
20.2 Contracts for Abstract and Polymorphic Functions
21 Designing Abstractions from Examples
21.1 Abstracting from Examples
21.2 Finger Exercises with Abstract List Functions
21.3 Abstraction and a Single Point of Control
21.4 Extended Exercise: Moving Pictures, Again
21.5 Note: Designing Abstractions from Templates
22 Designing Abstractions with First-Class Functions
22.1 Functions that Produce Functions
22.2 Designing Abstractions with Functions-as-Values
22.3 A First Look at Graphical User Interfaces
23 Mathematical Examples
23.1 Sequences and Series
23.2 Arithmetic Sequences and Series
23.3 Geometric Sequences and Series
23.4 The Area Under a Function
23.5 The Slope of a Function
24 Intermezzo 4: Defining Functions on the Fly
V Generative Recursion
25 A New Form of Recursion
25.1 Modeling a Ball on a Table
25.2 Sorting Quickly
26 Designing Algorithms
26.1 Termination
26.2 Structural versus Generative Recursion
26.3 Making Choices
27 Variations on a Theme
27.1 Fractals
27.2 From Files to Lines, from Lists to Lists of Lists
27.3 Binary Search
27.4 Newton's Method
27.5 Extended Exercise: Gaussian Elimination
28 Algorithms that Backtrack
28.1 Traversing Graphs
28.2 Extended Exercise: Checking (on) Queens
29 Intermezzo 5: The Cost of Computing and Vectors
29.1 Concrete Time, Abstract Time
29.2 The Definition of ``on the Order of''
29.3 A First Look at Vectors
VI Accumulating Knowledge
30 The Loss of Knowledge
30.1 A Problem with Structural Processing
30.2 A Problem with Generative Recursion
31 Designing Accumulator-Style Functions
31.1 Recognizing the Need for an Accumulator
31.2 Accumulator-Style Functions
31.3 Transforming Functions into Accumulator-Style
32 More Uses of Accumulation
32.1 Extended Exercise: Accumulators on Trees
32.2 Extended Exercise: Missionaries and Cannibals
32.3 Extended Exercise: Board Solitaire
33 Intermezzo 6: The Nature of Inexact Numbers
33.1 Fixed-size Number Arithmetic
33.2 Overflow
33.3 Underflow
33.4 DrScheme's Numbers
VII Changing the State of Variables
34 Memory for Functions
35 Assignment to Variables
35.1 Simple Assignments at Work
35.2 Sequencing Expression Evaluations
35.3 Assignments and Functions
35.4 A First Useful Example
36 Designing Functions with Memory
36.1 The Need for Memory
36.2 Memory and State Variables
36.3 Functions that Initialize Memory
36.4 Functions that Change Memory
37 Examples of Memory Usage
37.1 Initializing State
37.2 State Changes from User Interactions
37.3 State Changes from Recursion
37.4 Finger Exercises on State Changes
37.5 Extended Exercise: Exploring Places
38 Intermezzo 7: The Final Syntax and Semantics
38.1 The Vocabulary of Advanced Scheme
38.2 The Grammar of Advanced Scheme
38.3 The Meaning of Advanced Scheme
38.4 Errors in Advanced Scheme
VIII Changing Compound Values
39 Encapsulation
39.1 Abstracting with State Variables
39.2 Practice with Encapsulation
40 Mutable Structures
40.1 Structures from Functions
40.2 Mutable Functional Structures
40.3 Mutable Structures
40.4 Mutable Vectors
40.5 Changing Variables, Changing Structures
41 Designing Functions that Change Structures
41.1 Why Mutate Structures
41.2 Structural Design Recipes and Mutation, Part 1
41.3 Structural Design Recipes and Mutation, Part 2
41.4 Extended Exercise: Moving Pictures, a Last Time
42 Equality
42.1 Extensional Equality
42.2 Intensional Equality
43 Changing Structures, Vectors, and Objects
43.1 More Practice with Vectors
43.2 Collections of Structures with Cycles
43.3 Backtracking with State
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