Appendix C
Curriculum Projects—Detailed Analyses

Building Math

Institution

Museum of Science

Science Park

Boston, MA 02114

Tel: (617) 589-0230

Fax: (617) 589-4448

E-mail: eie@mos.org

Web site: http://www.mos.org/eie/index.php

Leaders

Peter Y. Wong, National Center for Technological Literacy

Barbara M. Brizuela, Tufts University

Funding

GE Foundation

Grade Level

6-8

Espoused Mission

“…to involve math students in collecting and analyzing their own data in hands-on investigations integrated with engineering design activities.”

Organizing Topics

The curriculum features the following three units of instruction:

  • Everest Trek is a sixth-grade unit presented in the context of scaling the world's tallest peak. It engages students in designing a well-insulated coat, a ladder bridge to span a crevasse, and an emergency zip-line transportation system.

  • Stranded! is a seventh-grade unit presented in the context of being marooned on a deserted South Pacific island. It engages students in designing a shelter, a water collection device, and a strategy for loading and unloading a canoe.

  • Amazon Mission is an eighth-grade unit that is presented in the context of helping indigenous people in Brazil. It engages students in designing an insulated carrier that will keep medicine cool, a water filtration system, and a strategy for tempering the spread of an influenza virus.

Format

The Building Math program comprises three spiral-bound books. Each book represents a unit of instruction for a given grade level that features three distinct design challenges. Every design



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Building Math Museum of Science Institution Science Park Boston, MA 02114 Tel: (617) 589-0230 Fax: (617) 589-4448 E-mail: eie@mos.org Web site: http://www.mos.org/eie/index.php Peter Y. Wong, National Center for Technological Literacy Leaders Barbara M. Brizuela, Tufts University GE Foundation Funding 6-8 Grade Level “…to involve math students in collecting and analyzing their own Espoused data in hands-on investigations integrated with engineering design Mission activities.” The curriculum features the following three units of instruction: Organizing x Everest Trek is a sixth-grade unit presented in the context of Topics scaling the world's tallest peak. It engages students in designing a well-insulated coat, a ladder bridge to span a crevasse, and an emergency zip-line transportation system. x Stranded! is a seventh-grade unit presented in the context of being marooned on a deserted South Pacific island. It engages students in designing a shelter, a water collection device, and a strategy for loading and unloading a canoe. x Amazon Mission is an eighth-grade unit that is presented in the context of helping indigenous people in Brazil. It engages students in designing an insulated carrier that will keep medicine cool, a water filtration system, and a strategy for tempering the spread of an influenza virus. The Building Math program comprises three spiral-bound books. Format Each book represents a unit of instruction for a given grade level that features three distinct design challenges. Every design C-1

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challenge features a series of lessons that follow an eight-step engineering design process that is outlined at the beginning of each unit. The books have reproducible handouts, rubrics, and self- assessment checklists for students. The following pedagogical elements can be found in each unit. Pedagogical x All the units and their design problems are framed in authentic Elements sounding contexts that middle school students should find interesting and challenging. x Every unit begins with a series of exercises that can be used to assess or address prerequisite knowledge and skills. x Each unit also begins with a team-building activity that asks small groups of students to complete a task that cannot be achieved without benefit of cooperation. x Each design challenge includes a series of lessons (or tasks) that use an engineering design process to construct knowledge in small and sequential increments. x The lessons (or tasks) feature objectives, implementation procedures, guiding questions, possible answers, and support materials for students. x The instruction is very Socratic in nature (i.e., posing questions, addressing questions). x Most of the learning activities involve inquiry. More specifically, developing solutions to the problems posed involves making observations, taking measurements, gathering data, interpreting data, generalizing patterns, applying patterns to the solution, building and testing models, and reflecting on the quality of the solutions as well as the learning process. x Each unit includes a very detailed and comprehensive rubric for facilitating student assessment. The GE Foundation funded the project for three years. The Maturity materials underwent two years of pilot testing and refinement during that period of time. The final units are currently available through Walch Publishing. Stranded and Everest Trek bear a 2006 copyright and Amazon Mission shows a 2007 copyright. The series was pilot tested with hundreds of students in ten Diffusion Massachusetts schools over the course of two years. This process & Impact produced positive testimony from pilot-site teachers. For example, Joseph McMullin at the Mystic Valley Regional Charter School in Malden, Mass., was quoted as stating: "In addition to relating math concepts to the physical world, my students improved their communication, graphing, critical thinking, and problem solving skills. Students especially enjoyed designing their own test." C-2

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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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The open explorations serve as introductory activities that are Activities designed to help students become familiar with the various building materials and to discover how they work together to make structures. The following learning activities fall under the open explorations: 1. Discussing prior experiences with building blocks and other construction materials. 2. Explaining the rules for building structures (e.g., how to take building blocks off shelves, how to take structures apart, how to put building blocks away). 3. Engaging in “block play” to learn how to use the building materials. 4. Acknowledging the structures built during block play, talking to children about their structures, and introducing new vocabulary during discussions (e.g., upstairs, downstairs, walls, roof, foundation). 5. Sharing building experiences through questions (e.g., Do you remember when you rebuilt it here at the bottom? How did you change it?). 6. Introducing new building materials (e.g., new blocks) and new props (e.g., toy horses that need a home). 7. Engaging in additional block play and acknowledging the children’s structures. 8. Conducting a “walkabout” where children study and talk about each other’s structures. 9. Conducting a “science talk” where children share their thought about making structures in response to questions (e.g., Tell us about your building? Which parts of it wiggled or fell down? How did you keep it up?). The “open explorations” are followed by “focused explorations.” During this phase of the curriculum students are given more guidance and the building activities are designed to address a challenge or problem. 10. Discussing prior experiences with building something that is tall. 11. Introducing children to the challenge of building a tall tower. 12. Discussing the safety issues associated with making something tall (e.g., wearing hard hats). 13. Observing and acknowledging children’s work while building tall towers (ask questions about stability and balance). 14. Conducting a “walkabout” where children study and talk about each other’s towers. 15. Conducting a “science talk” where children share their C-354

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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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The audience for this curriculum includes pre-school teachers, Salient kindergarten teachers, and teacher trainers. Over half of the Observations documentation is directed toward the teacher trainers that conduct workshop on how to implement the curriculum. The workshop materials include outcomes, objectives, timelines, handouts, activities, and reproducible masters. The balance of the documentation is directed toward the teachers that will implement the curriculum in their classrooms. It features teaching plans, recommendations, examples, questions, assessment tools, learning outcomes, and information about additional resources. The materials clearly espouse enriching the study of science. They Engineering do not deliberately target ideas about engineering, invention, or technology. However, in its treatment of science content and inquiry the curriculum inadvertently addresses basic engineering principles and ways of thinking that are appropriate for young children. Design The materials do not address the concept of engineering design directly. However, they do ask children to create solutions to problems. For example, They may be asked to build a house for a dog (possibly represented by a plastic toy). In this context, they would be encouraged to make sure their dog will fit in the house (a design specification) and their dog will not get hurt by a falling roof (another design specification). Other potential problems include building a tall tower, making a house for a turtle, and erecting a structure that will withstand the wind. During the course of solving these problems the students are encourage by their teachers to practice inquiry skills under the auspices of science. In simple vernacular these skills include doing things, noticing things, wondering about things, and questioning things. More specifically, the children are asked to engage in following activities: x Explore how things work (tinkering with building blocks). x Investigate ideas (staking blocks and seeing what happens). x Collect data (counting the number of blocks). x Record observations and experiences (drawing pictures). x Reflect on experiences (answering questions). x Communicate the results (sharing ideas and experiences). Even though these activities are presented in the context of scientific inquiry, they are also consistent with thinking like an C-356

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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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an integral part of an early childhood program that is designed to address standards. The learning activities outlined in Building Structures with Young Children are consistent with standards recommended by the American Association for the Advancement of Science (AAAS) in Benchmarks for Science Literacy (1993). For example, according to AAAS, by the end of second grade students should be able to “make something from paper, cardboard, wood, plastic, metal, or existing objects that can actually be used to perform a task.” Making a structure that provides shelter for a toy turtle could make a valid contribution toward the attainment of this standard. The questioning and debriefing strategies that are recommended throughout the materials are also consistent with developing students’ ability to “Describe and compare things in terms of number, shape, texture, size, weight, color, and motion.” Similarly, the role that sketching plays in the teaching and learning process can help children develop an ability to “Draw pictures that correctly portray at least some features of the thing being described.” Inversely, targeting the following standards about systems could have added additional ideas and new lines of inquiry that can enrich the dialog between teachers and students. x “Most things are made of parts” (p. 264). x “Something may not work if some of its parts are missing” (p. 264). x “When parts are put together, they can do things that they couldn't do by themselves.” The materials are well laid out and easy to follow. They ask Pedagogy teachers to address the study of structures from multiple perspectives. Attention is given to configuring the learning environment to encourage exploration, conducting neighborhood tours that involve examining and discussing real structures, using books to inspire and inform designs, incorporating guest speakers, helping students learn from one another, and debriefing students about their experiences. Attention is also given to establishing schedules and routines that support learning, facilitating core experiences, offering suggestions for making connections to families, surveying the children’s work during classroom “walkabouts,” conducting group discussions during “science talks”, using books and pictures to inform designs, and more. All of the learning activities include the same elements that are C-361

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organized into a logical sequence. The instruction is consistent with constructivist pedagogy in the sense that it asks teachers to activate prior experience, introduce new concepts, engage students in using existing knowledge in conjunction with new knowledge, employ tactile experience to support active learning, use questions for acknowledging ideas and guiding the development of new ones, and ask students to represent their ideas in multiple ways. The curriculum and instruction is extremely Socratic in nature. Posing questions is the primary tool used to implement the teaching and learning process. Emphasis is placed on thoughtfully observing students, formulating questions based on their work, using question to access their thought processes, posing questions to leverage experience and guide the incremental develop of understandings, and using questions to reflect upon and learning experiences. In short, questions are used to encourage student to discuss, express, represent, and reflect in the interest of helping them construct understanding from their active work. Building Structures with Young Children, clearly capitalizes on Implementation materials and supplies that early childhood teachers are likely to have in their classrooms (e.g., building blocks, craft supplies, toys representing people and animals). However, the implementation of the curriculum at the scale described in the materials could easily require more supplies and manipulatives than teachers have on hand. Therefore, implementation is likely to require additional expense for capital improvements (e.g., purchasing additional maple building blocks) and consumables (e.g., buying craft supplies). More than half of the documentation for the program focuses on facilitating teacher training. Tremendous attention is given to informing and developing teachers’ abilities to prepare the learning environment, to observe children building, to use carefully crafted questions to uncover thought processes and guide thinking, to engage children in composing multiple representation of their ideas, to engage children in looking back on their experiences, and to debrief children about their learning. Therefore, the greatest challenge associated with implementing this curriculum is allocating the time and resources needed for the professional development of teachers. C-362