Demystifying the Hoopla Around Computer Science and Common

Core Mathematics Standards

Julie Tonsing-Meyer & Kian L. PokornyMcKendree University

METC 2013February 12

Background Information

• How many offer Computer Science courses?• What does the curriculum for the computer

science course(s) entail?• To which set of standards has the computer

science curriculum been aligned?• What prior background/training have the

computer science educators had?

Educational Standards in K-12• K-12 standards are set by individual states• Common Core [3] is an initiative to provide a

standard that all states may use– Started in 2009– National Governors Association Center for Best

Practices (NGA Center) and Council of Chief State School Officers (CCSSO)

– Standardize K-12 curriculum, hope all states adopt it• 46 states have adopted it

– English Language arts & Literacy in History/Social Studies, Science, and technical Subjects

– Mathematics

• Computer Science Teachers Association (ACM)[2]– Computer Science K-12 curriculum standard

• Level 1- grades K-6: Level 2 - grades 6-9: Level 3 - grades 9-12– Level 3 divided into 3 distinct courses.

• Computer Science in the Modern World • Computer Science Concepts and Practices • Topics in Computer Science

• 5 strands: – computational thinking (CT), – collaboration (CL), – computing practice and programming (CPP), – computers and communication devices (CD), – community, global and ethical impacts (CI)

Educational Standards in K-12

Educational Standards in K-12

• ISTE [4] – provides National Educational Technology Standards (NETS) for educators.

• Standards for teachers (NETS-T), administrators (NETS-A), students (NETS- S), coaches (NETS-C), Computer Science educators (NETS-CSE).

• NETS-CSE only considers computer science at the secondary school level.

• Divided into 4 principles:– Principle I - content knowledge, – Principle II - effective teaching and learning strategies,– Principle III - providing effective learning environments, – Principle IV - educator’s professional knowledge and skills

Educational Standards in K-12

• ISTE NETS-CSE: Principle I - content knowledge • 4 content areas.

A. demonstrate knowledge and proficiency in data representation and abstraction (4 topics)B. effectively design, develop and test algorithms (6 topics) C. demonstrate knowledge of digital devices, systems, and networks (4 topics)D. demonstrate an understanding of the role computer science plays and its impact in the modern world. (2 topics)

ISTE Topics

Ai. Effectively use primitive data typesii. Demonstrate an understanding of static and dynamic data structuresiii. Effectively use, manipulate, and explain various external data stores: various types (text, images, sound, etc.), various locations (local, server, cloud), etc.iv. Effectively use modeling and simulation to solve real-world problems

Bi. High-level programming language, construct programs involving simple and structured data types; compound Boolean expressions; and sequential, conditional, and structures iterative control ii. Design and test algorithms and programming solutions to problems using advanced data structuresiii. Analyze algorithms by considering complexity, efficiency, aesthetics, and correctness.iv. Knowledge of two or more programming paradigmsv. Use two or more development environmentsvi. Knowledge of varied software development models and project management strategies

ISTE Topics

Ci. Demonstrate an understanding of data representation at the machine level

ii. Demonstrate an understanding of machine-level components and related issues of complexity

iii. Demonstrate an understanding of operating systems and networking in a structured computer system

iv. Demonstrate an understanding of the operation of computer networks and mobile computing devices

Di. Demonstrate an understanding of the social, ethical, and legal issues and impacts of computing, and attendant responsibilities of computer scientists and usersii. Analyze the contributions of computer science to current and future innovations in sciences, humanities, the arts, and commerce

Number of topics in each strand of CSTA courses

Strand CS in the Modern World

CS Concepts and Practices

Computational Thinking (CT)

11 11

Collaboration (CL) 4 3Computing Practice & Programming (CPP)

12 8

Computers & Comm. Devices (CD)

10 5

Community, Global &Ethical Impacts (CI)

11 8

Computer Science in the Modern World: 6. Analyze the representation and

trade-offs among various forms of digital information.7. Describe how various types of data are stored in a computer system.8. Use modeling and simulation to represent and understand natural phenomena.9. Discuss the value of abstraction to manage problem complexity.10. Describe the concept of parallel processing as a strategy to solve large problems.11. Describe how computation shares features with art and music by translating human intention into an artifact.

Computational Thinking (CT)

1. Use predefined functions and parameters, classes and methods to divide a complex problem into simpler parts.

2. Describe a software development process used to solve software problems (e.g., design, coding, testing, verification).

3. Explain how sequence, selection, iteration, and recursion are building blocks of algorithms.

4. Compare techniques for analyzing massive data collections.

5. Describe the relationship between binary and hexadecimal representations.

Computer Science in the Modern World

Collaboration (CL)1. Work in a team to design and develop a software artifact.

2. Use collaborative tools to communicate with project team members (e.g., discussion threads, wikis, blogs, version control, etc.).

3. Describe how computing enhances traditional forms and enables new forms of experience, expression, communication, and collaboration

4. Identify how collaboration influences the design and development of software products.

Computing Practice and Programming (CPP)1. Create and organize Web pages through the use of a variety of web programming design tools.2. Use mobile devices/emulators to design, develop, and implement mobile computing applications.3. Use various debugging and testing methods to ensure program correctness (e.g., test cases, unit testing, white box, black box, integration testing)4. Apply analysis, design, and implementation techniques to solve problems (e.g., use one or more software lifecycle models).

Computer Science in the Modern World

5. Use Application Program Interfaces (APIs) and libraries to facilitate programming solutions.6. Select appropriate file formats for various types and uses of data.7. Describe a variety of programming languages available to solve problems and develop systems.8. Explain the program execution process.9. Explain the principles of security by examining encryption, cryptography, and authentication techniques.10. Explore a variety of careers to which computing is central.11. Describe techniques for locating and collecting small and large-scale data sets.12. Describe how mathematical and statistical functions, sets, and logic are used in computation.

Computers and Communications Devices (CD)1. Describe the unique features of computers embedded in mobile devices and vehicles (e.g., cell phones, automobiles, airplanes).2. Develop criteria for purchasing or upgrading computer system hardware.3. Describe the principal components of computer organization (e.g., input, output, processing, and storage).4. Compare various forms of input and output.

5. Explain the multiple levels of hardware and software that support program execution (e.g., compilers, interpreters, operating systems, networks).6. Apply strategies for identifying and solving routine hardware and software problems that occur in everyday life.7. Compare and contrast client-server and peer-to-peer network strategies.8. Explain the basic components of computer networks (e.g., servers, file protection, routing, spoolers and queues, sharedresources, and fault-tolerance).9. Describe how the Internet facilitates global communication.10. Describe the major applications of artificial intelligence and robotics.

Computer Science in the Modern World

Community, Global, and Ethical Impacts (CI)1. Compare appropriate and inappropriate social networking behaviors.2. Discuss the impact of computing technology on business and commerce3. Describe the role that adaptive technology can play in the lives of people with special needs.4. Compare the positive and negative impacts of technology on culture (e.g., social networking, delivery of news and other public media, and intercultural communication).

5. Describe strategies for determining the reliability of information found on the Internet.6. Differentiate between information access and information distribution rights.7. Describe how different kinds of software licenses can be used to share and protect intellectual property.8. Discuss the social and economic implications associated with hacking and software piracy.9. Describe different ways in which software is created and shared and their benefits and drawbacks (commercial software, public domain software, open source development).10. Describe security and privacy issues that relate to computer networks.11. Explain the impact of the digital divide on access to critical information.

Computer Science in the Modern

World

Computer Science Concepts and Practices Computational Thinking (CT)1. Classify problems as tractable, intractable, or computationally unsolvable.2. Explain the value of heuristic algorithms to approximate solutions for intractable problems.3. Critically examine classical algorithms and implement an original algorithm.4. Evaluate algorithms by their efficiency, correctness, and clarity.5. Use data analysis to enhance understanding of complex natural and human systems.6. Compare and contrast simple data structures and their uses (e.g., arrays and lists).7. Discuss the interpretation of binary sequences in a variety of forms (e.g., instructions, numbers, text, sound, image).8. Use models and simulations to help formulate, refine, and test scientific hypotheses.9. Analyze data and identify patterns through modeling and simulation.10. Decompose a problem by defining new functions and classes.11. Demonstrate concurrency by separating processes into threads and dividing data into parallel streams.

Computer Science Concepts and Practices

Collaboration (CL)

1. Use project collaboration tools, version control systems, and Integrated Development Environments (IDEs) while working on a collaborative software project.

2. Demonstrate the software life cycle process by participating on a software project team.

3. Evaluate programs written by others for readability and usability.

Computer Science Concepts and Practices

Computing Practice and Programming (CPP)1. Use advanced tools to create digital artifacts (e.g., web design, animation, video, multimedia).

2. Use tools of abstraction to decompose a large-scale computational problem (e.g., procedural abstraction, object-oriented design, functional design).

3. Classify programming languages based on their level and application domain

4. Explore principles of system design in scaling, efficiency, and security.5. Deploy principles of security by implementing encryption and authentication strategies.6. Anticipate future careers and the technologies that will exist.7. Use data analysis to enhance understanding of complex natural and human systems.8. Deploy various data collection techniques for different types of problems.

Computer Science Concepts and Practices

Computers and Communications Devices (CD)

1. Discuss the impact of modifications on the functionality of application programs.

2. Identify and describe hardware (e.g., physical layers, logic gates, chips, components).

3. Identify and select the most appropriate file format based on trade-offs (e.g., accuracy, speed, ease of manipulation).

4. Describe the issues that impact network functionality (e.g., latency, bandwidth, firewalls, server capability).

5. Explain the notion of intelligent behavior through computer modeling and robotics.

Computer Science Concepts and Practices

Community, Global, and Ethical Impacts (CI)1. Demonstrate ethical use of modern communication media and devices.2. Analyze the beneficial and harmful effects of computing innovations.3. Summarize how financial markets, transactions, and predictions have been transformed by automation.

4. Summarize how computation has revolutionized the way people build real and virtual organizations and infrastructures.5. Identify laws and regulations that impact the development and use of software.6. Analyze the impact of government regulation on privacy and security.

7. Differentiate among open source, freeware, and proprietary software licenses and their applicability to different types of software.

8. Relate issues of equity, access, and power to the distribution of computing resources in a global society.

CSTA topics covered by NETS-CSE

Strand CSTA Topics Covered by NETS-CSE

CT 22 13 = 59% (5-A, 5-B, 3-C)

CL 7 0 = 0%CPP 20 6 = 30% (2-A, 3-B, 1-D)

CD 15 8 = 53% (1-A, 7-C)CI 19 14 = 74% (14-D)Total 83 41 = 49%

• Computer Science concepts left out of the NETS-CSE. – Theoretical computer science, artificial intelligence,

security, parallel processing, and the use of predefined functions and classes

– no mention in the NETS-CSE and arise in 18 of the 83 topics in the CSTA recommendation.

• CSTA provides a complete covering of NETS-CSE– NETS-CSE is a subset of CSTA K-12

CSTA topics covered by NETS-CSE

Common Core Mathematics

• CCM for high school is divided into the six categories: subdivide into 22 content units with between 1 and 4 subcategories each, for a total 55 topics.– Number and Quantity overview, (4 units, 9 topics)– Algebra Overview, (4 units, 11 topics)– Functions overview, (4 units, 10 topics)– Modeling, (1)– Geometry overview, (6 units, 15 topics)– Statistics and Probability overview, (4 units, 9

topics)

Number and Quantity overview1. The Real Number System• extend the properties of exponents to rational exponents

• Use properties of rational and irrational numbers.2. Quantities• reason quantitatively and use units to solve problems3. The Complex Number System• Perform arithmetic operations with complex numbers

• represent complex numbers and their operations on the complex plane

• Use complex numbers in polynomial identities and equations 4. Vector and Matrix Quantities • represent and model with vector quantities.• Perform operations on vectors.• Perform operations on matrices and use matrices in applications.

Common Core Mathematics Topics

Algebra Overview1. Seeing Structure in Expressions• Interpret the structure of expressions• Write expressions in equivalent forms to solve problems2. Arithmetic with Polynomials and Rational Expressions• Perform arithmetic operations on polynomials• Understand the relationship between zeros and factors of polynomials• Use polynomial identities to solve problems• rewrite rational expressions3. Creating Equations

• Create equations that describe numbers or relationships4. Reasoning with Equations and Inequalities• Understand solving equations as a process of reasoning and explain the reasoning• Solve equations and inequalities in one variable• Solve systems of equations• represent and solve equations and inequalities graphically

Common Core Mathematics Topics

Functions Overview1. Interpreting Functions• Understand the concept of a function and use function notation• Interpret functions that arise in applications in terms of the context• analyze functions using different representations2. Building Functions• Build a function that models a relationship between two quantities• Build new functions from existing functions3. Linear, Quadratic, and Exponential Models• Construct and compare linear, quadratic, and exponential models and solve problems• Interpret expressions for functions in terms of the situation they model4. Trigonometric Functions• extend the domain of trigonometric functions using the unit circle• model periodic phenomena with trigonometric functions• Prove and apply trigonometric identities

Common Core Mathematics Topics

Modeling

Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social, and everyday intuitions can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data.

Common Core Mathematics Topics

Geometry overview1. Congruence• experiment with transformations in the plane• Understand congruence in terms of rigid motions• Prove geometric theorems• make geometric constructions2. Similarity, Right Triangles, and Trig.• Understand similarity in terms of similarity transformations• Prove theorems involving similarity• define trigonometric ratios and solve problems involving right triangles• apply trigonometry to general triangles

Common Core Mathematics

Topics

3. Circles• Understand and apply theorems about circles• find arc lengths and areas of sectors of circles4. Expressing Geometric Properties with Equations• translate between the geometric description and the equation for a conics• Use coordinates to prove simple geometric theorems algebraically5. Geometric Measurement and Dimension• explain volume formulas and use them to solve problems• Visualize relationships between two dimensional and three-dimensional objects6. Modeling with Geometry• apply geometric concepts in modeling

Statistics and Probability overview1. Interpreting Categorical and Quantitative Data• Summarize, represent, and interpret data on a single count or measurement variable• Summarize, represent, and interpret data on two categorical and quantitative variables• Interpret linear models2. Making Inferences and Justifying Conclusions• Understand and evaluate random processes underlying statistical experiments• make inferences and justify conclusions from sample surveys, experiments and observational studies

Common Core Mathematics Topics

3. Conditional Probability and the Rules of Probability• Understand independence and conditional probability and use them to interpret data• Use the rules of probability to compute probabilities of compound events in a uniform probability model4. Using Probability to Make Decisions • Calculate expected values and use them to solve problems • Use probability to evaluate outcomes of decisions

CSTA topics covered by CCM

Strand CSTA Topics Covered by CMM Complementary

CT 22 4 = 18% 3 = 14%

CL 7 0 = 0% 0 = 0%

CPP 20 2 = 10% 2 = 10%

CD 15 0 = 0% 0 = 0%

CI 19 0 = 0% 0 = 0%

Total 83 6 = 7% 5 = 6%

CSTA topics covered by CCM

• 5 of the 6 topics are covered by the CCM Modeling category and 1 by the Statistics and Probability category. – Topics in CSTA that we have equated to the CCM Modeling

either directly use the phrase simulation and modeling or refer to the application of computer science tools.

• 5 topics categorized as complementary, – They require a mathematical topic as a prerequisite and

enhance understanding of the mathematical topic. • CSTA K-12 standards are complimentary to the CCM

standards. – Little redundancy, and not mutually exclusive. – both have the modeling of real world problems in common.

CCM and NETS-CSE

• CCM consists of a 6 categories and NETS-CSE has 4 areas with a total of 16 topics. Only one of the NETS-CSE topics, “Effectively use modeling and simulation to solve real world problems,” is covered by the CMM modeling category

Hoopla Project

• Form small groups (4-6 participants per group)• Using index cards containing the CSTA

standards, align the cards with the Common Core Math Standards to identify where the connections or overlaps exist Computer Science in the Modern World.

Results

• What overlaps were discovered?• Where are the disconnects between the two

sets of standards?

Conclusions: What will they know?• The new Common Core which may become the

standard for ALL states does not view Computer Science as necessary

• Standards provided by ISTE and CSTA do not agree– ISTE expects teachers to know about half of what

CSTA expects their students know.• Common Core Mathematics and CSTA appear to

compliment each other– Both agree on Modeling used to apply topics in

empirical situations.

• [1] ACM K-12 Task Force Curriculum Committee. A Model Curriculum for K-12 Computer Science. 2003, ACM, New York. http://csta.acm.org/Curriculum/sub/ACMK12CSModel.html , retrieved 10/12.

• [2] ACM K-12 Task Force Curriculum Committee. A Model Curriculum for K-12 Computer Science. 2011, ACM, New York. http://www.csta.acm.org/Curriculum/sub/CurrFiles/CSTA_K-12_CSS.pdf, retrieved 10/12.

• [3] Common Core Standards Initiative. http://www.corestandards.org/, retrieved 10/12

• [4] International Society for Technology in Education, National Educational Technology Standards for Computer Science Educators, http://www.iste.org/docs/pdfs/nets-cse.pdf?sfvrsn=2, retrieved 11/12.

• [5] National Governors Association Center for Best Practices, Council of Chief State School Officers. Common Core State Standards (Mathematics). 2010, National Governors Association Center for Best Practices, Council of Chief State School Officers, Washington D.C.

• [6] Running on Empty, http://www.acm.org/runningonempty, retrieved 11/12.• [7] Stephenson, C. , Wilson, C. , Reforming K-12 computer science education…

what will your story be?. ACM Inroads 3, 2, 43-46, 2012.