Discover Robotics & Programming - sample

Computer SCienCe CurriCulum

inStruCtor edition

3©2015 PCS Edventures, Inc. All rights reserved. Use of this material is restricted to PCS Licensees.

1. OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .• Document Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

• Pedagogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

• Programming in Arduino and Other Languages . . . . . . . . . . . . . . . . . .

2. JOURNALING AND REFLECTION . . . . . . . . . . . . . . . . . . . . . . . . .

• Journal Evaluation (classroom activities provided) . . . . . . . . . . . . . . . . .

3. THE BRAIN & CORTEX USERGUIDE . . . . . . . . . . . . . . . . . . . . . . .• The Brain Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

i. Powering, Recharging, and Buttons . . . . . . . . . . . . . . . . . . . .

ii. Lights and Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

iii. Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

• The Cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

i. Quick Start Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ii. Uploading to The Brain . . . . . . . . . . . . . . . . . . . . . . . . . .

iii. Writing Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

• About fishertechnik® . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4. COMPUTOR SCIENCE CURRICULUM . . . . . . . . . . . . . . . . . . . . . .• LeveL 1 - Students learn the basics of motor control through an introduction to

the language and reasoning used by computers to manage basic mechanical tasks.

• LeveL 2 - Students construct their first robot, and apply what they’ve learned about motor control to produce useful robotic behavior. Through activities with math and physics applications, and work with some more advanced coding, students expand their knowledge of programming while practicing math and science.

• LeveL 3 - This level introduces students to the use of subroutines, if- and for- loops, as well as the use of basic sensor inputs. These new skills are applied to challenges with new and interesting applications.

• LeveL 4 - In level 4, students will continue to expand their working knowledge of programming. They will create more sophisticated robots that interact with their environment in quite complex ways. Much of the logic used to create code in level 4 reinforces fundamental math concepts at a very intuitive level, setting the stage for explorations into discrete math and advanced programming applications.

5. APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B. Common Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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diSCover: robotiCS & programming

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6 ©2015 PCS Edventures, Inc. All rights reserved. Use of this material is restricted to PCS Licensees.

You may already be quite familiar with the following information. The purpose of this section is to explain the rationale for the design of this content.

engineering

With the advent of the Next Generation Science Standards, and the philosophical approach that underlies the Common Core, it has become clear that many educators could benefit from additional support regarding methods for instructing some of the processes now emphasized by these standards.

For more than 25 years, PCS has specialized in the kind of application-based, iterative discovery that characterizes an engineering design approach to problem-solving. With this curriculum, we have attempted to scaffold this process in a way that we hope will fit nicely into a more formalized classroom environment.

As an instructor, the critical piece of the engineering design approach is in the method of iteration. There are two typical erroneous ways that learners iterate on their solutions.

First, and often least effective, is some version of the classic “guess and check” approach, in which students invest little to no energy in planning their approach to a problem. Rather, they simply try something and then adjust, repeating this process until they either stumble upon a solution or lose interest in the problem. This is not always bad. Some students are more tactical in nature: very thoughtful about their plan following their first attempt(s) at solutions. When the stakes are low, there is no harm in this.

The second, sometimes problematic, approach to problem-solving (the one historically emphasized in any technical academic program/course) is purely analytical, wherein the first attempt is expected to be perfect, flawless if possible. While this method certainly has academic and educational merit, it fails to take into consideration practical, application-level issues (imperfect parts, environmental variation, etc.).

It is nested neatly between these two extremes—thoughtless fumbling and purely theoretical analytics—that the engineering practice lives. The activities in this curriculum were designed to encourage engineering design, but it is critical that oversight be diligent, such that students who fall toward one or the other extreme be provided with some guidance and redirection.

In the first case, simply mandating that they outline their plan prior to initiating any experimentation often solves the problem. In the second case, encouraging disengagement from analysis once a reasonable approximation is possible generally suffices to bring students closer to effective completion.

iterative diSCoverYENGINEERING PROCESS

TRIAL & ERROR

ACADEMIC ANALYSIS

MOST EFFICIENT

pedagogY

Overview


engagement

Effective instruction for innovative design and deep understanding of technical concepts is all about engagement. Often, it has been found, students are directed by an expert to follow a pre-established sequence of instructions (2, 28, 29), and this generally does very little to encourage students to develop and consider their own analytical process (21, 22, 23, 24) . If something is confusing, the resolution is obvious – ask the teacher.

It has been shown to be more effective if students create their own solutions to challenges. It is ideal if students practice seeking varied resources to develop those solutions. The ultimate is when students generate novel and innovative solutions to problems (1, 25, 30).

With our hands-on, activity based curriculum, we aim to encourage students to engage in low-stakes problem solving on various scales: setting up structures (building, assembly), planning for challenges (sketching out designs, gathering information, etc.), and analyzing results for future applications.

FeedbaCk

Learning is a constructive, iterative process. Learners actively build understanding by assembling bits of information into working models and concepts. A learner can then fortify his or her understanding by attempting to apply it to a new scenario (1, 25). Truth is subjective; something that withstands many of these iterations. When our process is rigorous, our truth is more universal.

Since the process of construction, testing, analysis, and reconstruction can take some time, it is ideal if no step along the way is bogged down by the need for excessive feedback. Traditionally, classroom feedback comes from the instructor. With many students and one instructor, this means that any individual learner’s process can be repeatedly slowed by the feedback bottleneck. Otherwise learners can find themselves in a sort of limbo, charting territory without feedback, often only to discover that they have been moving in a non-productive direction for some time.

Instructor feedback can be interpreted with hidden or counter-productive messages by students who receive abstracted information (grades, percentages, points, etc.). From these abstract concepts, students actively judge themselves and their peers in order to establish an intellectual hierarchy. Such habits reduce motivation among both high and low achieving students, and can severely hinder the development of effective collaboration skills (30, 31, 32, 5, 9, 10, 25).

Again, it has been shown through extensive studies and test groups that it is better to provide students with immediate, continuous feedback, coming directly from their personal experience. This is a primary goal of hands-on, activity based learning. Students, during the development of a project, are repeatedly observing the results directly the results of their work, and they can adjust their process according to that “natural” learning. In doing so, motivation tends to shift from extrinsic to intrinsic, as students focus on the task at hand rather than on others’ perception of their skill/value (14-20, 23, 25).

The design-build component of most PCS activities supports this repeated (nearly continuous) feedback loop. The act of connecting two elements together, all by itself, requires that a learner test the way their mind visualizes each element, and also demands hat they configure and reconfigure their methodology until they find something that works. Use of these manipulatives teaches the process of procedural organization and efficiency, as well as reinforcing basic physics, math, construction, and logic principles again and again. Thus, students are provided with constant learning on many levels.

Historically, students who proceed through a rote set of instructions have difficulty applying their methods in a new context. The design process offers resolution of this problem. Through hands-on projects, concepts can be accessed via visual, tactile, and even auditory experiences (in addition to pure, and abstract, cognitive connections). In this way, learners can more readily make neural connections (create lasting understanding) that are available for future learning and application toward novel challenges.

pedagogY (Cont.)

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The Cortex uses a graphical user interface to create code in the Arduino language. Whenever you install the Cortex onto your device, a library of functions and coding elements is installed as well. If your students show a serious interest in more advanced coding practice, the Cortex makes the language used to instruct the bot visible for inspection or for cutting and pasting into the free, open source Arduino software.

Arduino was originally built for custom electronics, developed specifically for hobbyists and hackers to create new and exciting devices. All of the basic Arduino-based components are extremely affordable. Students expressing an interest in these electronics can, and should, be encouraged to explore the platform further, using the coding they’re learning here as a jumping off point.

Finally, Arduino itself is a platform on top of the coding language of “C.” C is one of the most common and powerful computer programming languages in use today. For students who really want to take this to the next level, encourage them to explore and work with C. Fortunately, C is also free to the public.

programming in arduino and other languageS

Overview


2

FIRST BUILD! MOTOR TESTING STATION (LEVEL1)

JournalingP.A.R.

3

MOTOR PROGRAMMING & EXPERIMENTATION

(LEVEL 1)

JournalingP.A.R.

4

BUILD RiQ THE ROBOT

(LEVEL 2)

JournalingP.A.R.

5

RiQ PROGRAMMING

ACTIVITIES(LEVEL 2-4)

JournalingP.A.R.

* Journaling & P.A.R. (Peer- assisted reflection) are both optional, reccommended extensions

getting Started guide

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MEET THE BRAIN AND CORTEX!

1


The PCS Brain is an Arduino compatible robotic microcontroller that responds to the commands sent to it by the PCS Cortex Programming environment.

Use The Brain to program devices that walk, roll, and shake as you explore computer programming in its most exciting way - robotics! The Brain is designed be an open platform, both through it's Arduino heart, and through it's unique housing which was designed to connect to all major building systems such as fischertechnik®, K’NEX®, Erector® and others. The Brain even has the ability to add on R/C standard nuts and bolts so you can bolt it on to anything. The Brain is designed to be open-ended, extensible, and flexible and to encourage creativity - just like your own brain.

the brain and Cortex


ON/OFF SWITCHWhen you turn The Brain switch ON with a power source connected, you will be able to power DC and servo motors.

Note: You can power The Brain for programming using the USB cable, however the USB is not ade-quate voltage to drive motors.

RUN/STOPPressing this button will run a program stored in The Brain's temporary memory, or will interrupt a pro-gram that is running.

RESTARTThis button will reset The Brain. Use this button if your program is not operating properly and you want to reset the microcontroller.

LIGHTS ON THE BRAINThe lights that flash on The Brain represent different things. Look at the illustration above for details.

RUN/STOP Button

RESET Button

Bluetooth DONGLE Connector

DC MOTOR Ports (4)

SERVO MOTOR Ports (4)

SENSORPorts (8)

Ports 6 & 7 are only INPUT

USB Port

ON/OFF Switch

Power Connector

the brain

buttonS

The Brain and

Cortex


The Brain and

Cortex

Software Installation Instructions:

Windows and Macintosh UsersTo install Cortex, go to riq.edventureslab.com/cortex or insert the Go to:

http://www.edventures.com/cortex

Download and install the appropriate installation package.Android UsersUsing your Internet connected tablet device, goto the Google Play Store and search and install "PCS Cortex." Alternatively you can go to the following web address and download and install the APK.

http://www.edventures.com/cortex

iOS UsersNote: Tablet users only. Go to the Apple App Store and search for PCS Cortex and install.

Contact [email protected] for help!

IMPORTANT NOTES ON INSTALLATION AND USE1. A current version of Java Runtime is required to run the Cortex software. JRE 6.0+2. You must have an active Internet connection to compile Cortex programs on a tablet.

Motor Commands

Profile

Library of Programs

Build the Program

Integrating virtual tablet sensors and the UI canvas

Arduino code display

Save Program

Complete and send program to The Brain

Run/Stop the program

Connection Status

ProcedureCommands

Sensor Commands

Logic Commands

MiscCommands

Shows which sensors are active and their output value

v 5 . 0

Cortex

This section will introduce you to the basics of programming with the Cortex programming environment.

QuiCk Start guide

introduCing Cortex


User Friendlyfischertechnik® elements are naturally friendly and approachable by students and staff alike. The simple approach to connections and the variety of pieces enables builders to quickly grasp the basics of building with this amazing system. fischertechnik® manufactures kits and models for students as young as five years old.

Precise and RealisticUtilizing an ingenious groove, slide, and interlocking pin system, fischertechnik® creations are more flexible, realistic, and robust in all modeling and simulation environments. This system is not a toy, rather a professional modeling system that enables students to experiment, design, produce, and create amazing machines with real world results.

DurableEngineered to scientific precision and manufactured using high strength nylon, plastic and steel, fischertechnik® components are designed to last not for years, but for decades and beyond. Many original kits purchased in the 60s are as good as new and continue to serve reliably year after year in high use settings. Purchasing fischertechnik® systems is an investment in quality that will serve your students for years to come.

StrongThe unique design of fischertechnik® results in far stronger physical connections when modeling and building. Students who have experienced frustration with watching their hours of work fall apart due to the limitations of a building system will appreciate the amazing strength and solidity of fischertechnik®. The multitude of options for mechanization and power are also extensive with access to an advanced power motor system that enable serious engineering endeavors.

GROOVE

PIN

METRIC SYSTEM RULER: use this to measure the manipulatives

30 millimeter (mm) block is called a “Building Block 30”

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 (mm)

User Friendly

Precise and Realistic

Durable

Strong

about FiSCherteChnik®

The fischertechnik® manipulatives included with RiQ are high-end, quality products from Germany, ideal for engineering-related builds. Here are a few benefits of the fischertechnik® system.


In this level, you will continue to experiment with the basics of programming with The Brain robotic controller using the Cortex programming environment. You will build a basic robot out of fischertechnik® building elements and program it to complete different projects and challenges.

Programming Useful Behaviors

level two


Program a robot to execute a simple set of commands.

Start by building your robot—his name is RiQ.

You will use RiQ to complete multiple projects and challenges in subsequent activities. Follow the building plan. When it is complete, the RiQ will look like this:

Project 1Build Your Robot

2level

Project 1: Build Your Robot Extension Reflect

Project 2: Identity CommandsChallenge1: Circle Bot

Teaching Approach More Extensions Reflect

Challenge 2: The Big Enchilada Reflect Teaching Approach

Personal Project: Make Your Bot Draw Reflect

Key Concepts

level twoSChedule

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Materials you will need:

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Finished Model

Attaching LED - Option A

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Option A

Option A

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Once RiQ is built, write this program in Cortex that will move RiQ forward approx 60 cm (depending on your motors), then backward for the same distance.Measure and mark 60cm using the black electrical tape.

RiQ must travel on a 60 cm line segment (marked on the floor with tape) so it starts and ends at the same point.

You might notice that the motors are set at different power levels. Each motor is different, so you’ll need to adjust the power level for each to get RiQ to drive in a straight line.

This program is instructing RiQ to:

Motor A to SET PWR (set power) to 85%

Motor B to SET PWR to 100%

Motor A & B THIS WAY and ON FOR 3 seconds, then THAY WAY ON FOR 3 seconds

All programs are being interpreted by RiQ from the top of the program after the MAIN command through the END command at the bottom. Motors need to be identified in a command before they can follow directions.

Start programming


Student direCted

Students are given the challenge and free reign to develop solutions. Students present their solutions to one another at the end. (possibly very time intensive)

1. Prompt students: “You only get one chance at the circle. You may experiment all you like with the robot, but it may only drive a curved path once. The group whose circle is closest to the target (specified diameter D) wins.

When you have completed this challenge, you will present your problem solving process to the class. This presentation has the following requirements:

• You explain each idea (method of preparing the robot for success) that you considered, and why you decided it would or wouldn’t work.

• You explain any problems that you encountered, and solutions that your group came up with for those problems.

• Every group member should have a chance to participate in the presentation.

“If there are any materials that you need for experimentation, just ask.”

This option is best facilitated by a particular classroom culture. Specifically, it is ideal if students view failures as valuable and important. If this is the case, their presentations will be far more meaningful, the collaborations will be much less intense/competitive, and their experimentation will be more fruitful.

guided Student diSCoverY

Student groups work together to come up with possible problem-solving approaches. The instructor provides guidance in the form of prompts and suggestions. (time and instruction intensive)

1. Begin with the prompt: “What kind of a program might make the robot go in a circle?”

a. Initially ask individuals to think it over for a couple of minutes. (think)

b. Next, ask students to share ideas with members of their group. Have them specifically explain the rationale for each idea to one another. (pair)

c. After some specified time (approximately 5 minutes), have groups report back. (share)

d. Make a list of possible solutions and encourage debate/discussion about whether they might work.

They might produce a novel solution, but we’ve only seen this accomplished in the testing lab via different power levels on inside vs. outside wheels.

2. Next, (assuming they arrived at the same conclusion) prompt them with: “How could you figure out the required speed difference between the two motors without simply guessing and then repeatedly trying a circle?”

a. Repeat the same think-pair-share procedure.

teaChing approaChoptionS For teaCherS

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Drive through the Big Enchilada using the Accelerometer and it’s program included in Cortex.

To use the Accelerometer, you must use a tablet. Instructions for connecting the tablet to RiQ will be found on page 17.

Before being able to write this program, you must pull the Accelerometer onto the User Interface Canvas.

The Accelerometer will work if the program is correctly written, the Accelerometer is on the UI Canvas, you have Compiled and are running the program from Cortex.

What do you notice when driving through the Big Enchilada?

Is it easier or more difficult than programming? Are you as accurate? Record this in your Journal.

Extension

• COMPLETELY OPEN: Suggest that all three options below are available and ask the class which they think will be most effective/efficient. Respond to all student ideas with skepticism to encourage discussion regarding their approach to the problem. Ideally, some groups would attempt to approach it in each way. This way, they could debrief at the end. This is tricky. Often, groups observe others who appear to be doing better and quickly abandon their plan. You may also choose to either assign specific groups to each of the following approaches, or require all of them to use one or another method.

• FULL PROGRAMMING METHOD: Students apply the methods they discovered and/or applied in the previous challenge to prepare their code so that the course is navigated on the first try (without any trial runs). Point out in this case that they’ll need to determine times for each straight section as well as power ratios for each turn (and times for each turn). Once they’ve completed their first trial, they’ll go through and do some pointed debugging.

• PROGRAMMING AND TESTING HYBRID: Allow students to run trials on specific portions of the course (you can choose the limitations), but require that they still try to make it through the entire course on the first full try.

• FULL TESTING METHOD: Students write a full test code using their educated guesses about what will work (developed through the previous challenge). They will then systematically debug the inevitable errors.

teaChing approaChmore optionS For teaCherS

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Place a dry-erase marker in the pen holder on RiQ, robot and program it to draw something recognizable— a shape, letter, name, etc. (may not be a circle or a straight line).

This is Level 2 so it should show some level of difficulty. Then, clear your canvas to move to the next project.

Make a record of your project in the project section of your journal. This includes:

1. Goals

a. What were you trying to accomplish?

2. Procedure

a. How did you go about trying to achieve your goals?

3. Conclusions

a. What went well?

b. What useful techniques, skills, and ideas did you discover?

i. Focus on things that you might use in the future for other problems/challenges.

4. Evidence/Reasoning

a. Why do you think that these techniques, skills, and ideas are useful? What did you do or observe that shows they might be important?

Personal Project Turn RiQ into an Artist

2level

Reflect

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Robot — A machine capable of carrying out a complex series of actions automatically, especially one programmable by a computer. A robot uses a mechanical system which is controlled by an electrical system. That electrical system can be programmed to autonomously perform a task.

Debug — A systematic process of finding and correcting errors in a sequential instruction set. In coding/programming, debugging involves finding code errors in order to get the desired output

Pivot Point — The center point of any rotational system. A central point on which something balances or turns.

Line Segment — A part of a line that is bounded by two end points.

Circle — A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).

Diameter — A straight line passing from side to side through the center of a body or figure, esp. a circle or sphere.

Circumference — The distance around the outside of a circle.

Speed — The ratio of distance to time for a moving object. To calculate speed use this formula: Speed = Distance / Time

Accelerometer — A device that senses any change in orientation (e.g. tipping). Whenever you rotate a cell phone, tablet, etc, and the screen rotates, it is because the accelerometer has recognized that the device changed orientation. This device is used by the tablets when you control the bot by tipping the tablet.

Variables — Changeable values which are stored until they are changed by users or programs. Experiments are performed by changing variables

Uncontrolled Variables — Some variables cannot be controlled in experiments. Some examples can be temperature, humidity, noise, or any other conditions that you cannot control.

Systematic — Done or performed methodically, according to a fixed program.

Pi — The relationship between a circle’s diameter and its circumference is an irrational number—a number that never stops or repeats itself. To make pi manageable, it is usually abbreviated to 3.14

Absolute Error — The difference between the value measured, and the value expected.

Percent Error — The absolute error divided by the expected value.

BEEP — Play a short beep.

WAIT — Delay for a given time

Concepts & Key Terms 2levelLe

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The following standards are addressed, to varying degrees, by at least one activity in the sequence. In some cases, specific standards are repeatedly, and in various contexts, present in the majority of the four-level sequence. In particular, the curriculum stresses engineering design and technical thinking.

next generation SCienCe

mS-etS1 (a, b, and C) engineering deSign

1. Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.

2. Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

3. Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each that can be combined into a new solution to better meet the criteria for success.

international SoCietY For teChnologY in eduCation

CreativitY and innovation Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.

4. Apply existing knowledge to generate new ideas, products, or processes5. Create original works as a means of personal or group expression

CritiCal thinking, problem Solving, and deCiSion making Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

A. Identify and define authentic problems and significant questions for investigationB. Plan and manage activities to develop a solution or complete a projectC. Collect and analyze data to identify solutions and/or make informed decisionsD. Use multiple processes and diverse perspectives to explore alternative solutions

CommuniCation and Collaboration with a digital portFolio Students can use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

A. Interact, collaborate, and publish with peers, experts, or others employing a variety of digital environments and media

B. Communicate information and ideas effectively to multiple audiences using a variety of media and formats

C. Develop cultural understanding and global awareness by engaging with learners of other cultures

D. Contribute to project teams to produce original works or solve problems

reSearCh and inFormation FluenCY Students apply digital tools to gather, evaluate, and use information.

A. Plan strategies to guide inquiryB. Locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of

sources and mediaC. Evaluate and select information sources and digital tools based on the appropriateness to

specific tasksD. Process data and report results

appendix aStandardS alignment A

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gradeS 6-8 language artS

ELA-LITERACY.WHST.6-8.1.BSupport claim(s) with logical reasoning and relevant, accurate data and evidence that demonstrate an understanding of the topic or text, using credible sources.

ELA-LITERACY.WHST.6-8.1.EProvide a concluding statement or section that follows from and supports the argument presented.

ELA-LITERACY.WHST.6-8.2.DUse precise language and domain-specific vocabulary to inform about or explain the topic.

ELA-LITERACY.WHST.6-8.2.FProvide a concluding statement or section that follows from and supports the information or explanation presented.

ELA-LITERACY.RST.6-8.3Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical task

ELA-LITERACY.WHST.6-8.6Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas clearly and efficiently.

ELA-LITERACY.WHST.6-8.10Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

grade 6 math

MATH.CONTENT.6.SP.A.2Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

MATH.CONTENT.6.SP.A.3Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

MATH.CONTENT.6.EE.A.2.CEvaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

appendix bCommon Core

Ap

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grade 7 math

MATH.CONTENT.7.G.A.2Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions.

MATH.CONTENT.7.G.B.4Know the formulas for the area and circumference of a circle and use them to solve problems.

MATH.CONTENT.7.G.B.6Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

grade 8 math

MATH.CONTENT.8.G.A.4Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

MATH.CONTENT.8.SP.A.1Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

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Responsive Teaching and Learning

Maskiewicz, A., & Winters, V. (2012). "Understanding the Co-Construction of Inquiry Practices: A Case Study of a Responsive Teaching Environment." Journal of Research in Science Teaching, 49(4), 429-464.

Sikorski, T., & Hammer, D. (2010). "A Critique of how Three Learning Progressions Conceptualize Sophistication and Progress. Learning in the Disciplines: Proceedings of the 9th International Conference of the Learning Sciences (ICLS 2010) - Volume 1, Full Papers. International Society of the Learning Sciences: Chicago IL.

Formative Assessment Methodology

Coffey, J., Hammer, D., Levin, D. M., Grant, T. (2011) "The Missing Disciplinary Substance of Formative Assessment." Journal of Research in Science Teaching, 1109-1136.

Vokos, Stamatis, et. al. “Using Facet Clusters to Map Learner Modes of Reasoning.” Seattle Pacific University. 2006.

Diagnosing and Responding to Misconceptions

Eleanor Close, et. al. “Exploring Relationships: Teacher Characteristics and Student Learning in Physical Science.” Seattle Pacific University. December 2006.

Goldberg, et. al. “The CPU (constructing Physics Understanding) Project.” San Diego State University. 2011

Computer Science Motivations

Hartford, Tim. "The Benefits of Trial and Error." Online video clip. TEDGlobal 2011. July 2011. http://www.ted.com/talks/tim_harford

Lockard, C. Brett and Wolf, Michael. “Occupational employment projections to 2020.” Bureau of Labor Statistics. 2010.

Rowling, JK. "The Benefits of Failure." Online video clip. Harvard Commencement Ceremony. Filmed June 5, 2008, TED January 2010. http://www.ted.com/talks/jk_rowling_the_fringe_benefits_of_failure

Simms, David. "The Power of Positive Failure." Harvard Business Review. web. July 26, 2010

Sobel, Anne.(2014) "How Failure in the Classroom Is More Instructive Than Success." The Chronicle of Higher Education. December 8, 2014

Sullo, David. (2009) "The Motivated Student." Association for Supervision and Curriculum Development. May 2009.

Either equal or greater content acquisition in PBL when compared to traditional instruction

Belland, B. R., Glazewski, K. D., & Richardson, J. C. (2008). "A Scaffolding Framework to Support the Construction of Evidence-Based Arguments Among Middle School Students." Educational Technology Research and Development, 56, 401-422.

Ceren, Tekkaya, Ömer Geban, and Semra Sungar. "Improving Achievement through Problem-based Learning." Journal of Biological Education 40.4. web. http://www.newtechnetwork.org/sites/default/files/dr/scienceachievementturkey.pdf

Dods, R.F. (1997). "An Action Research Study of the Effectiveness of Problem-Based Learning in Promoting the Acquisition and Retention of Knowledge." Journal for the Education of the Gifted. 20(4), 423-437.

Gallagher, S. A., & Stepien, W. J. (1996). "Content Acquisition in Problem-Based Learning: Depth Versus Breadth in American Studies." Journal for the Education of the Gifted, 19(3), 257-275.

Gallagher, S., Stepien, W., & Rosenthal, H. (1992). "The Effects of Problem-Based Learning on Problem Solving." Gifted Child Quarterly, 36(4), 195 – 200.

Hmelo-Sliver, Cindy. "Problem-Based Learning: What and How Do Students Learn?"Educational Psychology Review 16.3. web. http://kanagawa.lti.cs.cmu.edu/olcts09/sites/default/files/Hmelo-Silver_2004.pdf

Stein, Bob. "Computers and Writing Conference Presentation." Purdue University. Union Club Hotel, West Lafayette, IN. 23 May 2003. Keynote Address.

appendix CbibliographY

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VanTassel-Baska, Joyce. (1998) "Curriculum, Instruction, and Assessment for the Gifted: A Problem-Based Learning Scenario." Gifted Child Today. January 2013 vol. 36 no. 1 71-75

Van Tassel-Baska, J., Bracken B.A., Stamabaugh, T., & Feng, A. (2007). "Findings from Project Clarion." Presentation to the United States Department of Education Expert Panel, Storrs, CT.

Van Tassel-Baska, Joyce. "What Works in Curriculum for the Gifted." Asia Pacific Conference on the Gifted. July 18, 2008. Keynote Address.

Verhoeven, B. H., et al. (1998). "An Analysis of Progress Test Results of PBL and Non-PBL Students." Medical Teacher, 20(4), 310–316.

More PBL Support

Blumenfeld, Phyllis C., et al. "Motivating Project-Based Learning: Sustaining the Doing, Supporting the Learning." Educational Psychologist. Volume 26, Issue 3-4, 1991 pages 369-398.

Application to Medical Training

Vernon, D T, Blake, R L. "Does Problem-Based Learning Work? A Meta-Analysis of Evaluative Research." Academic Medicine, July 1993

Direct vs. Student-centered instruction

Kuhn, Deanna. (2007) "Is Direct Instruction an Answer to the Right Question?" Educational Psychologist Volume 42, Issue 2, 2007

Pink, Daniel. Drive, the Surprising Truth About What Motivates Us. New York: Penguin Group, 2009. Print.

United States. National Research Council. Inquiry and the National Science Education Standards: A Guide for Teaching and Learning. Washington: GPO, 2000. Print.

Hidden Messages from Feedback

Abbott, S. (Ed.). (2014) "Hidden Curriculum." The glossary of education reform. web. http://edglossary.org/hidden-curriculum

Kay Sambell & Liz McDowell. (2006) "The Construction of the Hidden Curriculum: Messages and Meanings in the Assessment of Student Learning." Assessment & Evaluation in Higher Education. 2006.

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