Standards Alignment

Extra lessons are nice, but Math teachers don't have 25 hours of spare classtime to spend on new materials, no matter how good it might be.

That's why Bootstrap is aligned to National and State Standards for Mathematics, covering most Functional and Algebraic standards from Grade 7 through Algebra 2. This alignment makes it possible to integrate Bootstrap into the classroom smoothly, using time you've already planned into your pacing guidelines or scope and sequence plans.

For states using the Common Core, Bootstrap is also a model implementation of Common Core Standards for Mathematical Practice, offering explicit pedgagogical recommendation across all eight practice standards.

Bootstrap also satisfies several of the CSTA (Computer Science Teacher's Association) standards across levels 1 (grades K-6), 2 (grades 6-9), and 3 (grades 9-12); Bootstrap1 (the algebra-oriented first course) covers standards in levels 1 and 2, while Bootstrap2 goes deeper into computer science and covers more standards in levels 2 and 3.

What's Covered in 25 Hours?

Alignment

MP.1: Make sense of problems and persevere in solving them Bootstrap students are confronted with challenging problems, and use a problem-solving methodology known as the Design Recipe to solve them. The recipe teaches critical thinking, asking students to write down what they know and think through each step on their way to a solution.
MP.2: Reason abstractly and quantitatively Students focus on mathematical models of program behavior, and use quantitative examples to prove these models correct.
MP.3: Construct viable arguments and critique the reasoning of others Teachers engage students in discussion about each step in the Design Recipe, asking them to explain how they move from one step to another. In addition, students are challenged to debug the code of others, not just by identifying programmatic flaws but by also identifying faulty reasoning.
MP.4: Model with mathematics When Bootstrap students want their characters to move, to stay onscreen or collide with one another, they must first model that behavior mathematically. And since the programming language is purely algebraic, these models become the programs themselves!
MP.5: Use appropriate tools strategically Even programmers know that a computer isn't the perfect tool for every situation. Bootstrap students draw graphical diagrams, write out written examples, and use the computer when the situation calls for it.
MP.6: Attend to precision Communicating precisely is key, whether you're a mathematician or a professional programmer. In Bootstrap, students consider datatypes, select clear function and variable names, and write comments for their code.
MP.7: Look for and make use of structure Bootstrap students look closely at worked-out examples before generalizing to a formula, as part of the Design Recipe. When working with the Circles of Evaluation, students consider the structure of arithmetic expressions as functions being composed on one another -- and this structure becomes the basis for their code.
MP.8: Look for and express regularity in repeated reasoning By practicing the Design Recipe repeatedly, students begin to discern the connection between multiple representations of functions. They notice patterns in the examples they write and contracts they derive.

Bootstrap Units

N-Q: Reason quantitatively and use units to solve problems. Units 1, 2, 3 and 5
6.NS.5-8: Apply and extend previous understandings of numbers to the system of rational numbers. Unit 1
7.EE.1-4: The student uses numerical and algebraic expressions and equations to solve real-life and mathematical problems. Units 3 and 6
8.F.1-3: Define, evaluate, and compare functions. Unit 4, 6 and 8
A-SSE.1-2: Interpret the structure of expressions Units 1, 2, 3, 7 and Supplemental Lessons
A-SSE.3-4: Write expressions in equivalent forms to solve problems Units 1, 2 and Supplemental Lessons
A-CED.1-4: Create equations that describe numbers or relationships Units 3, 4, 5, 6, 7, 8 and Supplemental Lessons
A-REI.1-2: Understand solving equations as a process of reasoning and explain the reasoning Units 1, 2 and Supplemental Lessons
A-REI.3-4: Solve equations and inequalities in one variable Unit 6
A-REI.10-12: Represent and solve equations and inequalities graphically Unit 6
8.G.6-8: Understand and apply the Pythagorean Theorem Unit 8
F-IF.1-3: Understand the concept of a function and use function notation Units 2-9 and Supplemental Lessons
F-IF.4-6: Interpret functions that arise in applications in terms of the context Units 3, 4, 6, 8 and Supplemental Lessons
F.IF.7-9: Analyze functions using different representations Units 3-9 and Supplemental Lessons
F-BF.1-2: Build a function that models a relationship between two quantities Units 3-9 and Supplemental Lessons
F-BF.3-4: Build new functions from existing functions Units 6, 7, 8 and Supplemental Lessons
F-LE.1-4: Construct and compare linear, quadratic, and exponential models and solve problems Unit 3
F-LE.5: Interpret expressions for functions in terms of the situation they model Unit 5 and Supplemental Lessons
F-TF.5: Model periodic phenomena with trigonometric functions Supplemental Lessons

Alignment

2-DA-07: Represent data using multiple encoding schemes. Bootstrap:Algebra - Units 3-8
Bootstrap:Reactive - Units 1-5
Bootstrap:Data Science - Units 1-9

Students encode data using multiple mathematical representations (Algebra), data structures (Reactive), and tabular or visual representations (Data Science).
2-DA-08: Collect data using computational tools and transform the data to make it more useful and reliable. Bootstrap:Data Science - Units 1-9
Bootstrap:Data Science introduces students to a number of data analysis methods, encouraging them to ask questions of large datasets and then sort, filter, and define functions over data to answer those questions.
2-DA-09: Refine computational models based on the data they have generated. Bootstrap:Reactive - Units 3-5
Bootstrap:Data Science - Units 2-9

Bootstrap:Reactive has students walk through an iterative design process for adding and refining elements in their programs based on what things will be changing within their programs. Bootstrap:Data Science has students refine data sets by sorting, filtering, and defining functions over data, as well as thinking critically about the need to remove outliers in their data.
2-AP-11: Create clearly named variables that represent different data types and perform operations on their values. Bootstrap:Algebra - Units 2-8
Bootstrap:Reactive - Units 1-5
Bootstrap:Data Science - Units 1-9

All Bootstrap courses cover functions and variables, including named values and inputs to built-in and user-defined functions.
2-AP-13: Decompose problems and subproblems into parts to facilitate the design, implementation, and review of programs Bootstrap:Algebra - Units 5-8
Bootstrap:Reactive - Units 3-5
Bootstrap:Data Science - Units 2-9

Bootstrap introduces students to programming problems that benefit from decomposition into multiple functions and/or data structures. The Design Recipe provides some structured guidance on when to introduce new functions when decomposing problems. Bootstrap:Algebra and Bootstrap:Reactive introduce the idea of top-down or bottom-up strategies for decomposition.
2-AP-14: Create procedures with parameters to organize code and make it easier to reuse. Bootstrap:Algebra - Units 3-8
Bootstrap:Reactive - Units 1-5
Bootstrap:Data Science - Units 2-9

Bootstrap:Algebra introduces the core idea of functions as abstractions over repeated computations. Bootstrap:Reactive moves into larger programs that get decomposed into subproblems, which are designed, implemented, and tested independently. Bootstrap:Data Science introduces the idea of writing functions over tabular data to answer meaningful questions about that data.
2-AP-17: Systematically test and refine programs using a range of test cases. Bootstrap:Algebra - Units 3-8
Bootstrap:Reactive - Units 1-5
Bootstrap:Data Science - Units 2-9

Design and execution of test cases is emphasized throughout all Bootstrap courses. Students are required to write multiple test cases (including expected answers for each) for each function; our software helps them track which tests are passing and which are failing.
2-AP-19: Document programs in order to make them easier to follow, test, and debug. Bootstrap:Algebra - Units 3-8
Bootstrap:Reactive - Units 1-5
Bootstrap:Data Science - Units 2-9

Bootstrap's Design Recipe emphasizes design, documentation, coding, and testing throughout every course. The process is explicit in Bootstrap's worksheets and exercises, and student-generated documentation is assessed along with the code it explains.
3A-DA-11: Create interactive data visualizations using software tools to help others better understand real-world phenomena. Bootstrap:Data Science - Units 1-9
Bootstrap:Data Science introduces students to pie charts, bar charts, histograms, scatterplots, and more as a way of answering questions about, and better understanding real-world datasets. The course culminates in students writing a research paper incorporating these data visualizations about a topic they care about.
3A-AP-16: Design and iteratively develop computational artifacts for practical intent, personal expression, or to address a societal issue by using events to initiate instructions. Bootstrap:Reactive - Units 3-5
Bootstrap:Reactive introduces the concept of reactors and event-driven programming, requiring students to write programs that respond to the passage of time, keypresses, and (optionally) mouse clicks and movement.
3A-AP-17: Decompose problems into smaller components through systematic analysis, using constructs such as procedures, modules, and/or objects. Bootstrap:Algebra - Units 5-8
Bootstrap:Reactive - Units 3-5
Bootstrap:Data Science - Units 2-9

Bootstrap introduces students to programming problems that benefit from decomposition into multiple functions and data structures. The Design Recipe provides some structured guidance on when to introduce new functions when decomposing problems.
3A-AP-18: Create artifacts by using procedures within a program, combinations of data and procedures, or independent but interrelated programs. Bootstrap:Algebra - Units 3-8
Bootstrap:Reactive - Units 3-5
Bootstrap:Data Science - Units 1-9

All Bootstrap courses culminate in a final project. For Bootstrap:Algebra and Reactive, the project is a video game or animation that makes use of multiple student-created functions to handle movement and interactivity. In Bootstrap:Data Science, students create a research paper and data science project as a result of analyzing, transforming, and interpreting data with functions.
3A-AP-23: Document design decisions using text, graphics, presentations, and/or demonstrations in the development of complex programs. Bootstrap:Data Science - Units 4-9
The final project for Bootstrap:Data Science is a research paper written by each student which incorporates text, code, and data visualizations to demonstrate their process of analyzing, transforming, and interpreting data to answer meaningful questions.
3B-NI-05: Use data analysis tools and techniques to identify patterns in data representing complex systems. Bootstrap:Data Science - Units 1-9
Bootstrap:Data Science introduces students to a number of data analysis methods, encouraging them to ask questions of large datasets and then sort, filter, and define functions over data to answer those questions.
3B-NI-07: Evaluate the ability of models and simulations to test and support the refinement of hypotheses. Bootstrap:Data Science - Units 2-9
Bootstrap:Data Science has students examine various issues affecting data collection and analysis, including collection bias, threats to validity, and outliers. Using linear regression methods, students can test and refine their hypotheses about relationships in their dataset.
3B-AP-14: Construct solutions to problems using student-created components, such as procedures, modules and/or objects. Bootstrap:Algebra - Units 5-8
Bootstrap:Reactive - Units 1-5
Bootstrap:Data Science - Units 2-9

Bootstrap:Algebra introduces the core idea of functions as abstractions over repeated computations, and has students document, test, and code multiple functions to create a video game. Bootstrap:Reactive moves into larger programs that get decomposed into sub-problems and helper functions, which are designed, implemented and tested independently. Bootstrap:Data Science introduces the idea of writing functions over tabular data to answer meaningful questions about that data.
3B-AP-21: Develop and use a series of test cases to verify that a program performs according to its design specifications. Bootstrap:Algebra - Units 3-8
Bootstrap:Reactive - Units 1-5
Bootstrap:Data Science - Units 2-9

Design and execution of test cases is emphasized throughout all Bootstrap courses. Students are required to write multiple test cases (including expected answers for each) for each function; our software helps them track which tests are passing and which are failing.
3B-AP-22: Modify an existing program to add additional functionality and discuss intended and unintended implications (e.g., breaking other functionality). Bootstrap:Reactive - Units 3-5
Bootstrap:Data Science - Units 2-9

Bootstrap:Reactive has students walk through an iterative design process for adding and refining elements in their programs based on what things will be changing within their programs. Bootstrap:Data Science has students refine data sets by sorting, filtering, and defining functions over data, as well as thinking critically about the need to remove outliers in their data.

Alignment

Practice 1: Fostering an Inclusive Computing Culture By integrating Computing into standard math classes, Bootstrap allows schools to immediately create an inclusive computing environment. Everyone takes math, which means everyone computes. But in addition to the course settings the curriculum allows, Bootstrap also embeds teamwork, metacognition and group reflection into every step of the programming process - from co-designing a game to thinking about effective co-working strategies, Bootstrap's pedagogy fosters an inclusive culture.
Practice 2: Collaborating Around Computing Bootstrap students work on small teams, and must cultivate relationships with other students who possess diverse perspectives, skills and personalities. Students work on problems together, and are given strategies to evaluate and give feedback to one another at each step in the problem-solving process.
Practice 3: Recognizing and Defining Computational Problems Bootstrap uses real-world problems throughout the course, as students are constantly engaged in the creation of a meaningful computational artifact (a videogame of their own invention, modeling a physics simulation, or analyzing a rich dataset). Each part of this project requires that students identify problems that can be solved computationally, decompose those problems into sub-problems, and evaluate the limits of their solutions.
Practice 4: Developing and Using Abstractions Students develop and use abstractions throughout the course, starting with visual-spatial representations for arithmetic expressions and ending with complex, multi-function programs that define, use and re-use student-generated abstractions. Students define everything from Functions (Bootstrap:Algebra) to Data Structures (Bootstrap:Reactive), and Reactive Simulations (Bootstrap:Physics) to Big Data queries (Bootstrap:Data Science).
Practice 5: Creating Computational Artifacts Bootstrap's project-based approach is absed on the creation of computational artifacts. Students write programs to draw flags, make a rocket blast off, trap a butterfly, run a cash register, implement a videogame, answer real questions with data, and model an observed physical phenomenon. The creation of these artifacts is personal, customizable, and based on a rigorous methodology for iterative design and problem solving.
Practice 6: Testing and Refining Computational Artifacts Many introductory courses treat testing as a second-class citizen, either asking students to test by running a program and "seeing if it looks right" or by using programming tools that completely lack any framework for automated testing. By contrast, Bootstrap introduces testing early on in each course, and our languages and software enviroments offer rich support for writing tests and developing software based on test feedback.
Practice 7: Communicating About Computing Students in our Data Science module must choose a question that matters to them, select a relevant dataset, and answer that question - justifying their choice and answer at every step. Students in our Physics, Data Structures and Algebra courses explain their thinking as well, whether it's about the creation of a piecewise function to handle key events or a data structure to model an interactive program.
Hardware and Software Bootstrap:Reactive, Bootstrap:Data Science and Bootstrap:Physics introduce students to sophisticated programming paradigms, in which they must process user input as mediated by the software evironment. This mediation involves the flow of information from multiple sources (keyboards, mice, GPS systems, and internet-connected resources), and students must consider this flow when designing their programs.
Troubleshooting All Bootstrap modules embrace Example Driven Design, in which students write test cases for each abstraction they create. This bakes in troubleshooting by design: a student immediately has a mechanism to locate an error, and knows a pedagogical approach for debugging their thinking process.
Data Collection Students in Bootstrap:Data Science and Bootstrap:Physics collect data using an array of tools techniques: tapping into existing datasets (e.g. - Spreadsheets) as well as automated or manual sampling using an array of instruments. The choice of sampling mechanism is instruction, as it exposes students to the strengths and weaknesses of a particular approach. Movement-tracking via observation v. changes in a cell phone's GPS coordinates, for example, will influence the amount and quality of the data that is collected.
Visualization and Transformation Our Data Science module embraces authentic data science concepts in a lightweight fashion: students must identify, transform, clean and manipulate data sets as they explore a research question of their own design. This involves everything from visualizing to aggregation, and rearrangement to transformation.
Inference and Models Bootstrap:Algebra and Bootstrap:Reactive are all build around students' developing a model for a desired (or observed) behavior. Bootstrap:Algebra has students model the process of computation, and Bootstrap:Reactive gives students the ability to model the data behind it. Bootstrap:Physics goes one step farther, having students use these models to predict the behavior of a complex system. In these activities, the tradeoffs between model complexity and model quality become clear.
Algorithms Bootstrap students consider many algorithms throughout our material. They are confronted with multiple ways to reach a solution, asked to generalize a algorithms so they can be re-used for other problems, and given opportunities to discuss the tradeoffs between different approaches.
Variables Bootstrap introduces variables early on, with students confronting variables and functions almost immediately in Bootstrap:Algebra. These variables can be used to represent Numbers, Strings, Images, Booleans, data structures of infinite complexity, and even remote spreadsheets stored across the internet! Our pedagogy explicitly asks students to come up with meaningful identifiers for every variable they use, and Bootstrap:Reactive allows students to select their own Data Structures. (Note: in a slight deviation from the K12CS standards, Bootstrap uses the mathematical concept of variable. Namely, we do not discuss the notion of "machine storage", since that concept directly undermines the notion of variables in mathematics.)
Control Students in all of Bootstrap's modules confront program control, sequences of evaluation, and conditionals. Bootstrap:Reactive, Data Science and Physics add loops and event handlers, to create more complex behavior.
Modularity Bootstrap's focus on abstraction works hand in hand with the concept of modularity. Students decompose complex problems into smaller ones, and build abstractions (functions, data structures, etc) to solve them. The abstractions are used to organize code, and can be composed with one another or repurposed to solve more complex problems without having to duplicate code. Students assemble these abstractions to form complex, reactive programs - relying on the modularity of those abstractions to manage complexity.
Program Development Our pedagogy is based on a robust process for program development, known as the Design Recipe. This approach has been used for decades at the university level, and mirrors many best practices from industrial contexts. The Design Recipe is an iterative process that involves defining type specifications, communicating those specifications through writing, building example-driven test cases, implementation, and testing.