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## Appendix C Curriculum Projects—Detailed Analyses

### Building Math

The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001

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An analysis of teacher testimony, samples of student work, direct observations, and videotape data supported the underlying premise of the curriculum. More specifically, the study of mathematics can be enriched with contextual units of instruction that employ hands- on learning activities that require students to apply a variety of math concepts and skills while following an engineering design process to solve problems. The collection and analysis of their data during engineering design activities helped math students develop and demonstrate algebraic thinking skills. C-3

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Initiative Building Math Title Amazon Mission During Design Challenge 1: Malaria Meltdown, students will: Broad Goals x Calculate and interpret the slope of a line. x Graph a compound inequality. x Conduct two controlled experiments. x Collect experimental data in a table. x Produce and analyze a line graph that relates two variables. x Distinguish between independent and dependent variables. x Determine when it’s appropriate to use a line graph to represent data. x List combinations of up to five layers of two different kinds of materials. x Draw a three-dimensional object and its net. x Find the surface area of a three-dimensional object. x Apply the engineering design process to solve a problem. During Design Challenge 2: Mercury Rising, students will: x Calculate the surface area of a sphere using a formula. x Solve a multistep problem. x Convert measurement units (within the same system). x Use proportional reasoning. x Write a compound inequity statement. x Graph and analyze the relationship between two variables. x Design and conduct a controlled experiment. x Apply the engineering design process to solve problems. During Design Challenge 3: Outbreak, students will: x Identify and extend exponential patterns. x Generalize and represent a pattern using symbols. x Graph simulation data and describe trends. x Calculate compound probabilities. x Use a computer model. x Apply the engineering design process to solve a problem. Math Science Technology Salient x making line graphs x climate zones x shabono Concepts x heuristics (rules of x tropical x model & Skills x subtropical x prototype thumb) x independent x temperature x cold variables C-4

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x dependent x polar x rate of heat variables x X-axis transfer is based x Y-axis on differences in x scale temperature x controlled x scaling axes x proportional experiment x extinct reasoning x endangered x exponential x indigenous patterns x virus x linear patterns x mercury x rounding up x malaria x rounding down x rain forest x interpreting line graphs x ratios x converting units x equivalent fractions x cross-multiply x recursive equations x Cartesian plane x calculate the slope of a line x graph a compound inequality x sphere The materials introduced the following ideas about the nature of Engineering engineering. x Engineers play a part in the design and construction of things like houses, roads, cars, televisions, and phones. x Engineering is “the application of math and science to practical ends, such as design or manufacturing.” x All engineers use the engineering design process to help them solve problems in an organized way. x The engineering design process includes defining the problem, conducting research, brainstorming ideas, choosing the best solution, building a model, testing and evaluating a prototype, communicate the design to others, and redesigning the solution. x The engineering design process “is meant to be a set of guidelines” for solving technical problems. x Engineers may not always follow all the steps in the design process in the same order every time. x Engineers communicate their designs to others to solicit C-5

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feedback and ways to improve the design. x Engineers often go back to an earlier step in the design process during the “redesign” process. x The solution to a problem might go through several cycles of the design process before it is ready for “real-world use.” x A full-scale working prototype may be constructed once the design has gone through several cycles of the design process. x Constraints are “limiting factors” that engineers need to consider during the design process. x Criteria are the specifications that need to be met for the solution to be successful. The unit starts with a team-building activity and a review of Prominent prerequisite math skills. Activities 1. Read and analyze a poem (The Law of the Wolves) and discuss how it relates to working in teams. 2. Review basic mathematics skills that will be utilized during the unit (e.g., make a line graph, find the slope of two points, calculate surface area). 3. Review basic math skills related to converting units of measure. 4. Compose and use heuristics or rules of thumb. Introducing the Engineering Design Process engages students in the following activities to develop a basic understanding of the nature of engineering. 1. Read background information about the Yanomami people (i.e., their way of life, the threats to their existence). 2. Discuss the questions: What is an engineer? What does an engineer do? 3. Put cards describing the basic steps of the engineering design process into a logical sequence. 4. Match a series of events related to making and testing sails for a boat race with the basic steps in the design process. Design Challenge 1: Malaria Meltdown engages students in the following activities to design a container for transporting medicine that has to be kept cool in a tropical climate. 1. Read a scenario that contains the problem to be solved, the criteria that needs to be met, and the material constraints. 2. Analyze a graph containing data (temperature over time) that depicts the performance of the current container for transporting the medicine. 3. Gather, graph, and interpret data regarding the rate of heat conduction for specific materials (corrugated cardboard, foam board, bubble wrap, aluminum foil). C-6

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4. Gather, graph, interpret, and present data regarding the rate of heat conduction for combinations of multiple materials. 5. Utilize research findings and material costs to develop a dimensioned sketch for a potential medicine-carrier design. 6. Select the best design from those developed by the members of the team through discussion and consensus. 7. Sketch a three-dimension representation of the selected design that includes dimensions and labels the materials used. 8. Sketch a “net” (a.k.a., development) of the selected design (a drawing that illustrates what a three-dimensions object would look like if it were spread out in the form of a two-dimensional layout). 9. Calculate the area of the materials needed to construct the selected design and use the results to determine the cost of making the final product. 10. Build a prototype for the selected design. 11. Use pieces of scrap to test the heat transfer rate of the materials used to make the container. 12. Test the ability of the container to protect a fragile object (an egg) by dropping the container to the floor from a height of one meter. 13. Determine the cost of making the actual container (a scaled-up version). 14. Present the final design to the class (e.g., how it performed in relation to the design constraints and criteria, the advantages of the design, the disadvantages of the design, the cost and profit potential of the design). 15. Reflect on the design and describe how it might be improved through redesign. 16. Conduct a self-assessment of the contributions made by each member of the team. 17. Reflect on how well the team worked together on the project (e.g., what went well, what did not work well, what can be improved). Design Challenge 2: Mercury Rising engages students in the following activities to design a water filtration device that removes mercury from river water. 1. Read a scenario that contains the problem to be solved, the criteria that needs to be met, and the material constraints. 2. Calculate the surface area of spheres with different diameters. 3. Determine the most cost-effective package of spheres to achieve a desire amount of total surface area. 4. Convert the units of measurement for minimum flow rate from 540 liters per day to the number of seconds need to filter 250 milliliters. C-7

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5. Convert the units of measurement for maximum flow rate from one liter per minute into the number of seconds need to filter 250 milliliters. 6. Gather, graph, and interpret data for the amount of time required for 250 milliliters of water to pass through different diameter holes. 7. Conduct a controlled experiment to gather, graph, and interpret data regarding another factor that could affect the amount of time required for 250 milliliters of water to pass through a filter. 8. Sketch a potential design for a water filter that shows where water will enter, be filtered, and subsequently exit. Use the research results to define how large the exit opening needs to be. 9. Select the best design from those developed by the members of the team through discussion and consensus. 10. Develop a drawing for the selected design that shows dimensions, identifies the materials used, and describes the role that each material plays in the filtering process. 11. Build a model filter based on the selected design. 12. Test the amount of time it takes for 250 milliliters of water to pass through the filter. 13. Present the final design to the class (e.g., how it performed in relation to the design constraints and criteria, the advantages of the design, the disadvantages of the design, what materials would be used to make a real filter). 14. Reflect on the design and describe how it might be improved through redesign. 15. Conduct a self-assessment of the contributions made by each member of the team. 16. Reflect on how well the team worked together on the project (e.g., what went well, what did not work well, what can be improved). Design Challenge 3: Outbreak engages students in the following activities to design a virus intervention plan to contain the spread of the flu. 1. Read a scenario that contains the problem to be solved, the criteria that need to be met, and the material constraints. 2. Conduct a simulation to illustrate exponential rate at which a virus can spread and infect a population. 3. Calculate the rate at which a virus would spread if a doctor were able to treat one member of the population per day. 4. Determine the rate at which a virus would spread if every member of the population wore a filtration mask that reduced the risk of infection by 50 percent. C-8

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5. Use the results to graph the rate at which people become infected if there is no treatment, if there is one doctor, and if everyone wears a mask. 6. Calculate the chance of infection based on different combinations of interventions (e.g., the use of air filtration masks and antiviral hand gel, the use of antiviral hand gel and vaccinations). 7. Develop intervention plans that will reduce the rate of infection to less than 25 percent during a 30-day window of time. 8. Discuss the advantages and disadvantages associated with each team member’s intervention plan. 9. Identify the best intervention plan by determining what the individual plans have in common, identifying the best parts of the individual plans, and combining the best parts into one design. 10. Test the final intervention plan using a computer simulation model (an applet). 11. Use the results of the computer simulations to redesign the intervention plan and make it as cost effective as possible. 12. Present the refined intervention plan to the class (e.g., how it performed in relation to the design constraints and criteria, the advantages of the plan, the disadvantages of the plan, how would it be different if more money were available, how would it work with a larger population). 13. Reflect on the design and describe how it might be improved through redesign. 14. Conduct a self-assessment of the contributions made by each member of the team. 15. Reflect on how well the team worked together on the project (e.g., what went well, what did not work well, what can be improved). C-9

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Initiative Building Math Title Everest Trek During Design Challenge 1, Geared Up, students will: Broad Goals x Interpret a line graph. x Locate and represent the range of acceptable values on a graph to meet a design criterion. x Extrapolate data based on trends. x Conduct two controlled experiments. x Collect experimental data in a table. x Produce and analyze graphs that relate two variables. x Determine when it’s appropriate to use a line graph or a scatter plot to represent data. x Apply the engineering design process to solve a problem. During Design Challenge 2, Crevasse Crisis, students will: x Use proportional reasoning to determine dimensions for a scale model. x Use physical and math models. x Conduct two controlled experiments. x Collect experimental data in a table. x Produce and analyze graphs that relate two variables. x Compare rates of change (linear versus non-linear relationships). x Distinguish between independent and dependent variables. x Apply the engineering design process to solve a problem. During Design Challenge 3, Sliding Down, students will: x Conduct a controlled experiment. x Measure angles using a protractor. x Compare and discuss appropriate measures of central tendency (mean, median, mode). x Apply the distance-time-speed formula. x Produce and analyze a graph that relates two variables. x Locate and represent the range of acceptable values on a graph to meet a design criteria [criterion]. x Distinguish between independent and dependent variables. x Apply the engineering design process to solve a problem. Math Science Technology Salient x making line graphs x icefall x insulator Concepts x equal intervals x controlled x thermometer & Skills experiment C-10

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x cross-multiplying x x materials for temperature x heuristics (rules of x clothing (wool, hypothermia x fleece, nylon) thumb) compression x layering materials x data extrapolation x tension x prototype x based on trends strength x complete data x model x modulus of x beams (e.g., T- tables elasticity x application for line x beam, I-beam, tensile strength x graphs versus square channel) ultimate tensile x bridge scatter plots strength x identifying x ladder bridge x altitude x zip-line variables x density of air x independent x altitude sickness variables x gravity x dependent x acclimatize variables x altitude sickness x X-axis x insulator x Y-axis x proportional reasoning x scale x non-linear patterns x linear patterns x measuring angles with a protractor x interpreting line graphs x ratios x measures of central tendency (mean, median, mode x Cartesian plane x calculate the slope of a line x calculating speed x centimeters The materials introduced the following ideas about the nature of Engineering engineering. x Engineers play a part in the design and construction of things like houses, roads, cars, televisions, and phones. x Engineering is “the application of math and science to practical ends, such as design or manufacturing.” x All engineers use the engineering design process to help them solve problems in an organized way. C-11

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x Hands-on science inquiry projects. Pedagogical x Teachers guide children's explorations to deepen their Elements understanding of the physical science of building structures. x Teachers encourage the students to focus their observations and clarify their questions. x Open explorations that get the students to play with various building materials. x Focused explorations that give students more guidance in the context of solving a problem or meeting a challenge. x Teachers are trained to monitor student activities and asked questions about their work. x Teachers encourage students to discuss, express, represent, and reflect in order develop theories and understandings from their active work. x Teachers encourage students to learn from each other through “walkabouts” and “science talks.” The materials were field-tested across the nation in 2001 and Maturity 2002. The books were copyrighted in 2004 The video’s copyright is 2003. A team of early childhood educators at the Educational Diffusion Development Center, Inc., developed the Young Scientist & Impact Series. This project was nationally field tested from 2001- 2002. C-352

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Young Scientist Series Initiative Title Building Structures with Young Children Pre-kindergarten through kindergarten Grade Level Building Structures with Young Children guides children's Broad Goals explorations to deepen their understanding of the physical science present in building block structures—including concepts such as gravity, stability, and balance. Children will do the following: x Learn to build with a variety of different materials. x Experience the ways forces such as gravity, compression, and tension affect a structure's stability. x Build an understanding about how the characteristics of materials affect a structure's stability. x Develop scientific dispositions including curiosity, eagerness to explore, an open mind, and delight in being a builder. Math Science Technology Salient x building Describing objects Science concepts Concepts x structures in terms of their taught to teachers & Skills x shape x tower include x gravity x size x walls x tension x quantity x foundation x compression x patterns x roof x balance x standard x materials x stability x stories (of a measurements x non-standard x observations building) measurements x directionality x order x position The curriculum is intended support the study of science. Engineering However, under the auspices of science, the materials focus on building structures for reasons that include strength, safety, durability, and stability. The teaching and learning process includes planning a structure, building the structure, observing the structure, collecting information about the structure, and using sketching to record their designs. The curriculum features “open” and “focused” explorations. Prominent C-353

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experiences while making towers (e.g., Tell us about your tower? Could it be taller without falling down? What would happen if you used the thinner side of each block?). 16. Examining and discussing pictures of tall buildings. 17. Conducting a “walkabout” around the school to uncover the features of tall structures. 18. Making representational drawings of their towers. 19. Using different strategies and objects to measure their towers (e.g., counting blocks, using string, photographing students next to their towers). The same pattern of activities is used to engage students in making structures that are essentially enclosures (e.g., discussing prior experiences, challenge children to make enclosures, observing and acknowledging children’s work, conducting walkabouts, conducting science talks). C-355

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engineer. How do these blocks fit together? What will happen if you use this block? Should the big block be on top or on the bottom? What would happen if you put the big block on top? Is your tower taller than you or shorter than you? How many stories did you build? Is that space big enough for your turtle? Addressing questions such as these can be construed as being more consistent with engineering than science because most of the emphasis is on solving problems in contrast to uncovering laws of nature. The context of the work is more attentive to the human- made world than the natural world. The approach is consistent with engineering in the sense that the children address a problem, gather information, implement and test ideas, document their ideas and work in the form of drawings, and communicate their work to others. Analysis Analysis appears to be highly dependent on the nature of the dialog between the teacher and the students. The materials clearly recommend using questions to guide students in noting the nature of the building materials, making observations about the structures they build, detecting the features of their structures relative to what they do or represent, connecting what they have seen with what they have built, and assessing the ability of their structures to fulfill their functions (e.g., making a doghouse that will not fall down). Constraints Constraints are subliminally imposed on the children by the nature of the materials that are available for them to use. Very simply, the size, shape, weight, and strength of the materials intrinsically influence what can be made. The characteristics and limitations of the materials would inevitably surface during the course of the children’s thinking, experimenting, building, and explaining. For example, they may discover something has to be built without the benefit of a piece of material that has a given size, shape, or strength because it is not available, there is not enough, or another child is using it. During the course of their building the children will also discover what the materials can and cannot do. These discoveries would have to be taken into accounted during subsequent building attempts. Given the nature of children and the scope of early childhood programs, the children would be given finite amounts of time to create their structures. Therefore, time is likely to be another constraint that may or may not be addressed in an overt manner. Modeling The concept of modeling is addressed in both indirect and direct ways. Indirectly, the curriculum clearly engages children in C-357

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making lots of models with simple modeling materials without addressing the concept. The process of imaging a way to stack blocks, actually stacking the blocks as conceived, observing what happens in terms of balance and stability, and reconfiguring the blocks based on success or failure suggests modeling is informing the design process. In many ways it is a four-year-old’s version of an aeronautical engineer gathering data from a model airplane in a wind tunnel. In a more targeted sense, the materials suggest both teachers and children use the word “model” during their interactions. Furthermore, the materials recommend engaging children in making models of their models. This step requires the children to study their models made of relatively large blocks to build a smaller (table-top) version from easy to work materials (e.g., cardboard, pieces of foam). However, this kind of modeling is being presented in the interest of having children produce multiple representations of their ideas as a way to deepen understanding. Regardless of the intent, making models, studying models, and talking about models constitutes a valid, although subliminal, treatment of the concept because the blocks, straws, and wires that the children work with are representing things that are, in reality, much bigger. Thus, implementing the curriculum as written would “get students to talk about how the things they play with relate to real things in the world” (AAAS, 1993, p. 268). These activities would intrinsically help children realize “a model of something is different from the real thing but can be used to learn something about the real thing” (AAAS, 1993, p. 268). However, it is important to note that these ideas reside between the lines of the curriculum and they are not represented in the lists of learning outcomes. Optimization Optimization is another concept that is embedded in the curriculum. The materials clearly guide children through multiple rounds of thinking, building, observing, and explaining. The use of iterations is presented in the context of scaffolding the teaching and learning process. However, during this process the children are also revising and improving their structure to meet a challenge or solve a problem. If the curriculum were implemented as written, teachers would implicitly guide and encourage children to optimize their structures (e.g., make it tall, make it stronger, make it more stable, make the opening bigger). There are some modest references to the concept of trade-offs in the recommendations for learning activities. More specifically, the C-358

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materials encourage the teacher to prepare and ask questions about the advantages and disadvantages associated with different design options. For example, in the context of building a model house, teachers are encouraged to entertain ideas like making the roof from something light will require less support but it is not likely to be strong. If children chose to make a strong roof, they might also need to build in more support. Systems The materials do not address the concept of systems in an explicit manner. Nevertheless, by default, students are likely to uncover the fact that parts work together to do things that individual parts alone cannot do. Furthermore, they are liable to discover structures can fail if a part is installed wrong, missing, or removed. Despite the richness of the materials, the notion of deliberately looking at structures as systems is not among the recommendations for engaging students in inquiry or asking questions about their designs. Building Structures with Young Children espouses helping Science teachers guide children's explorations that deepen their understanding of the physical science of building structures. The materials were clearly developed with science in mind. The activities are constantly asking the students to explore, question, and investigate. Furthermore, they are in a sense, collecting data through the use of their senses and their observations, and experiences tell them how to build a better building. They are recording and representing their data (and ideas) by making drawings of what they have built. The curriculum purports to look at science “in a new way” without giving this methodology a name. Through this novel approach the curriculum strives to develop “important science inquiry skills such as questioning, investigating, discussing, and formulating ideas and theories.” It endeavors to build these skills through exploring, designing, and building structures. Given the amount of attention dedicated to exploring the human- made world, in contrast to the natural world, one could argue it fosters skills more in the context of doing engineering than doing science. The instruction targets concepts like gravity, stability, and balance while teaching children, “…how to make things strong, tall, or elegant.” The symbiotic blending of science and technology is, in part, the essence of engineering. The materials approach science in such a way that one could replace the word “science” with the word “engineering” with relative ease without compromising validity. Therefore, one could characterize this C-359

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new approach as “children’s engineering.” The curriculum does not teach math directly but it does apply and Mathematics reinforce a variety of foundational concepts and skills. For example, teachers are trained to use questions to engage children in dialogs about their structures. These questions are intended to lead children into describing their buildings using things like quantities, shapes, features, patterns, sizes, and more. The materials also recommend using questions to nurture the children’s understanding of the directionality, order, and position of objects. Measurement is another theme that can be found in the materials. The recommended activities employ both standard and non- standard forms of measurement for the length, height, or area of objects and structures. Standard units of measurement include things like “my tower is ten blocks high” and non-standard units of measurement could include things like “my tower is as tall as me” or “my tower is as tall as this string.” In these examples, measurement is being used to assess the extent to which the structure addresses the problem posed (build a tall tower). During the course of their activities children are asked to think Technology about, make, test, and talk about the parts of their structures. These parts include things like foundations, walls, roofs, supports, and more. The attention given to the basic anatomy of buildings enables children to apply, practice, and expand their technical vocabulary (a.k.a., domain knowledge). The activities also address building techniques that are technological in nature. This is especially evident in the process of having student examine buildings and study pictures of buildings to uncover the techniques that they can use to build their structures. These include things like overlapping blocks, making strong corners, and keeping walls from falling down. Their experiences with stacking blocks will be analogous to the techniques used to build real structures, especially masonry buildings. Consequently, the learning activities enrich the children’s knowledge of how things are done and subsequently, how to do things. The materials present rich sets of outcomes for science inquiry, Treatment of mathematical reasoning, social behavior, learning skills, and Standards language development. Although they read like standards, no attempt is made to reference national standards or correlate these outcomes with national standards. Despite the lack of attention given to standards, it is very easy to envision using the materials as C-360

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