A middle school instructional unit for size and scale contextualized in nanotechnology
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Cesar Delgado
Cesar Delgado is an assistant professor in the STEM Education program of the Department of Curriculum and Instruction in the College of Education at the University of Texas at Austin. His research interests involve students’ ideas about temporal and spatial magnitude and how they represent these ideas, modeling, learning progressions, and equity in education. He received his PhD in Science Education, MS in Chemistry, and MA in Learning Technologies from the University of Michigan.
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Shawn Y. Stevens
Shawn Stevens is an assistant research scientist in the School of Education at the University of Michigan. Her current research efforts include developing and empirically testing a learning progression for the structure, properties, and behavior of matter and developing interdisciplinary high school curriculum materials focusing on electromagnetic interactions. She co-authored a book to support secondary teachers’ development of pedagogical content knowledge for nanoscale science and engineering. She was a member of the design team for physical science that identified and defined the core ideas of physical science for the
Framework for K-12 Science Education. She received her AB in chemistry from the University of Chicago and her PhD in chemistry from the University of Michigan.Namsoo Shin is an associate research scientist in the School of Education at the University of Michigan. She is interested in the research and development of individualized, customized learning environments to support the learning of
all students. She is currently a principal investigator of the NSF project, “Developing an Empirically Tested Learning Progression for the Transformation of Matter to Inform Curriculum, Instruction and Assessment Design.”Joseph Krajcik is the director of the CREATE for STEM Institute and a professor in Science Education at Michigan State University. His research focuses on working with science teachers to reform science teaching practices to promote students’ engagement in and learning of science. He served as lead writer for the team developing Physical Science Standards for the NGSS and the lead writer for the Physical Science Design team for the Framework for K-12 Science Education. He served as president of the National Association for Research in Science Teaching from which he received the Distinguished Contributions to Science Education through Research Award.
Abstract
Size and scale is a “big idea” in nanoscale science and engineering and is poorly understood by secondary students. This paper describes the design process, implementation, and evaluation of a 12-h instructional unit for size and scale, in a summer science camp for middle school students from a low SES public school district. Instructional activities were designed following a construct-centered design approach and included the use of microscopes, custom-made computer simulations, and 2-D and 3-D scale models. The unit followed a project-based instructional approach and was contextualized with the driving question, “How can nanotechnology keep me from getting sick?” Pre- and post-intervention interviews revealed that students significantly increased their qualitative and quantitative knowledge of the size of objects including atom, viruses, and cells, with an effect size of 0.8 for an overall metric. The campers closed the gap with private middle school students and on some measures surpassed high school students from the same district. The principle of “broad spectrum” curriculum and instruction – activities that target specific advanced understandings but simultaneously scaffold or support the learning of more fundamental, prerequisite ideas – was inductively generated from an analysis of the learning activities.
About the authors
Cesar Delgado is an assistant professor in the STEM Education program of the Department of Curriculum and Instruction in the College of Education at the University of Texas at Austin. His research interests involve students’ ideas about temporal and spatial magnitude and how they represent these ideas, modeling, learning progressions, and equity in education. He received his PhD in Science Education, MS in Chemistry, and MA in Learning Technologies from the University of Michigan.
Shawn Stevens is an assistant research scientist in the School of Education at the University of Michigan. Her current research efforts include developing and empirically testing a learning progression for the structure, properties, and behavior of matter and developing interdisciplinary high school curriculum materials focusing on electromagnetic interactions. She co-authored a book to support secondary teachers’ development of pedagogical content knowledge for nanoscale science and engineering. She was a member of the design team for physical science that identified and defined the core ideas of physical science for the Framework for K-12 Science Education. She received her AB in chemistry from the University of Chicago and her PhD in chemistry from the University of Michigan.
Namsoo Shin is an associate research scientist in the School of Education at the University of Michigan. She is interested in the research and development of individualized, customized learning environments to support the learning of all students. She is currently a principal investigator of the NSF project, “Developing an Empirically Tested Learning Progression for the Transformation of Matter to Inform Curriculum, Instruction and Assessment Design.”
Joseph Krajcik is the director of the CREATE for STEM Institute and a professor in Science Education at Michigan State University. His research focuses on working with science teachers to reform science teaching practices to promote students’ engagement in and learning of science. He served as lead writer for the team developing Physical Science Standards for the NGSS and the lead writer for the Physical Science Design team for the Framework for K-12 Science Education. He served as president of the National Association for Research in Science Teaching from which he received the Distinguished Contributions to Science Education through Research Award.
Acknowledgments
This research is funded by the National Center for Learning and Teaching in Nanoscale Science and Engineering, grant number 0426328, from the National Science Foundation. Any opinions expressed in this work are those of the authors and do not necessarily represent those of the funder. Our thanks to Harry B. Short for helping to collect and code data.
Unpacking.
Big idea: One-dimensional Size and Scale
Grade level: middle school (6th–8th grade)
| Critical concepts | Prerequisite knowledge | Alternative ideas and findings from previous studies [Citation] | Phenomena (link to a nano product) | Claim | Evidence | Task |
|---|---|---|---|---|---|---|
| 1. There are unseen worlds that are too small to be seen with the unaided eye. | Students should know some examples of submacroscopic objects, e.g., microbes (typically covered in elementary), bacteria (middle school), atom and molecules (high school). | 15% [20] and 40% [21] of students mentioned a small visible object when asked for the smallest thing which they could think of. | Bacteria and viruses can make us sick (link to nanotoilet). | Students can compare and contrast the eye and the optical microscope as instruments used to visualize objects. | Students identify the greater resolution of the microscope as an advantage, and the limited field of view as a disadvantage, relative to the eye. | Students observe grains of sand and salt, and a mm ruler under the microscope and with the naked eye, and record their observations. They compare and contrast advantages of each tool. |
| 2. The unseen world can have serious impact on the everyday world. | Students should have some knowledge of the causes of illness. | Out of sight, out of mind. | Nanotoilet: bacteria, mold, and particles too small to see can stick to a toilet causing odors and potential health problems. | Students can construct an explanation about how the size of bacteria influences how we can get them and get rid of them. | Students’ explanation includes the idea that surface features larger than bacteria can help them “hide”; and that ultrasmooth surfaces are thus easier to clean and keep clean. | Students model toilet surfaces that can and cannot harbor bacteria using sandpaper and salt and construct an explanation. |
| 3. There are large relative size differences between submacroscopic objects. | Students should have heard of some of these: red blood cell, DNA, virus, bacteria, atom, and molecule. Should know what “X times bigger” means, be able to divide two sizes. | Learners tend to overestimate the size of small objects and underestimate the size of large objects [4, 27, 28]. Students may believe cells and atoms are similar in size [22, 23]. | Even a simple cell is thousands of times larger in diameter than an atom; nanoscale objects are too small to be seen with an optical microscope. | Students can estimate the relative size differences between selected small macro and microscopic objects. | 1) Students calculate that a human hair is ∼3×>cheek cell, and cheek cell ∼10×>a bacterium. | 1) Students observe and record a human hair, a cheek cell, and a bacterium (Staph A) at 100× on optical microscope and calculate relative size differences between all 3 pairs. |
| 2) Students determine the relative size of two objects, given the relative sizes of both in reference to a third object. | 2) Students use the relative size of A compared to B, and of B compared to C, to calculate the relative size of A compared to C, using the Size and Scale visualization. | |||||
| 4. The unseen world can be divided into micro-, nano-, and sub-nanoworlds, which are characterized by different objects, units, and instruments. | Students know of SI prefixes including kilo-, centi-, and milli-. | All objects too small to see are about the same size. | Optical and electron microscopes; micrometers and nanometers; viruses as nanoscale objects; bacteria and cells as microscale objects. | 1) Students can define micrometer and nanometer in terms of the millimeter and/or meter. | Student defines micrometer as 1/1000 mm or 1 millionth of m. Student defines nanometer as 1 millionth of mm or 10-9 m. | 1) Define micrometer and nanometer. |
| Students know of the optical microscope. | 43% of students of all ages accurately ordered mm, μm, and nm by size [5, 21]. Middle school students may not be able to define the millimeter as 1/1000 of a meter or name smaller units [9]. | 2) Students can discuss the limits of the optical microscope. | 2) Students can identify objects that cannot be resolved by optical microscope from the Size and Scale visualization. | 2) Using the Size and Scale visualization, identify the objects too small to see under the optical microscope. | ||
| 5. Students know of several small submacroscopic objects, including atom, bacterium, and cell, and have an idea of their sizes relative to each other and to a small submacroscopic object like a pinhead or the thickness of a hair, in both qualitative and quantitative terms. | Students should have heard of some of “germs”; they should know that some objects are too small to see. They should be able to order and group everyday objects by size; what “X times bigger” means; be able to divide two sizes; be able to measure everyday objects in inches, mm, cm. | All objects too small to see are about the same size. Students may not understand “what X times bigger” means [49]. 7% of 7- to 90-year olds correctly ordered atom, water molecule, bacterium, and cell [20]. Gifted high school seniors were accurate within an order of magnitude 20% of the time estimating micro- and nanoscale objects in terms of human body lengths [4]. Learners of all ages struggle to come up with objects of given sizes; accuracy of estimation of size of given objects is very low at the micro- and nanoscale [24, 25]. | Nanotoilet: “Smoothness on a nanometer scale helps prevent debris from sticking. With nothing to cling to, particles, molds, and bacteria can be washed away with every flush” | Students can estimate the relative size differences between small macro through atomic-scale objects. | Students measure reasonable values for relative size for various object in terms of another object; and calculate their absolute sizes when given the size of the reference object. | 1) Students determine the location of assorted objects from atom to hair, represented at 1,000,000:1 scale. |
| Surface features are ∼30 nm on the nanotoilet – smaller than bacteria, larger than small viruses. | Students can locate objects to scale given their absolute size and a scale factor. | 2) Given models of submacroscopic objects and a 1-nm unit, students calculate reasonable absolute sizes for the objects. |
Lesson description and alignment with learning goals.
| Title | Description | Learning goal addresseda |
| S&S 1: What I cannot see CAN hurt me | Introduce project, view video clip and read simplified news account of MRSA. Students tasked to advise school. Know/Need to Know list generated. | 1, 2, 5A |
| Students learn about dangerous bacteria that can be transferred from surfaces. Students swab various surfaces onto Petri dishes with growth medium to determine what surfaces had bacteria. | ||
| Introduce driving question, nanotech toilet. | ||
| They investigate the role of surface roughness in keeping a surface bacteria-free using sandpaper of different grades to represent magnified surfaces, and grains of salt to represent bacteria; view micrographs of various surfaces including teeth with bacteria on rougher areas. Instruction on “side views.” | ||
| Student groups create posters and present their explanation of the role of roughness to the class. | ||
| S&S 2: How small is small? | Brainstorm on smallest visible objects. Microscope online tutorial and practice. Students observe sand, dust, hair under microscope with mm ruler overlaid, at different magnifications. They sketch, then estimate the size (in mm). Students try to estimate diameter of a hair by viewing projected slides with 1 and 10 hairs lined up. | 1, 2, 5D, 5E |
| They use a tracing of the projected slide with 1 hair and the mm to determine the diameter, repeatedly tracing hair across the mm to get ∼1/10 mm. | ||
| Students observe their Petri dishes and determine what surfaces had bacteria. | ||
| S&S 3: Measuring the size of skin cells and Staphylococcus aureus | To evaluate nanotoilet claim (on brochure), students must determine the diameter of bacterium. Students prepare slides of their own cheek cells and a hair, observe relative scale of cell vs. hair (∼3× smaller), and calculate diameter of cheek cells (∼1/30 mm). Micrometers are introduced as 1000 μm=1 mm, diameter of hair and S. aureus calculated (∼100 μm, ∼30μm). | 1, 2, 3, 4, 5A, 5C, 5E |
| Hair, skin cell, and S. aureus bacterium (prepared slide) are successively projected and traced at 2000× magnification onto large sheets of butcher paper. Students trace skin cell across hair to determine diameter of cell, then bacterium across skin cell and/or hair to determine diameter of bacterium. Students evaluate the nanotoilet’s claim. | ||
| S&S 4: Virus – Small Size, Big Threat | Students view clip from “Outbreak,” learn about viruses that can also be transferred from surfaces. They use Size and Scale computer visualization [41] that automatically iterates the smaller object across the larger one to determine the diameter of a virus and evaluate the nanotoilet’s claim. Nanometers are introduced here as 1000 nm=1 μm. They use this simulation to determine absolute size of objects from hair to atom. | 1, 2, 3, 4, 5A, 5C, 5E |
| S&S 5: It is all Relative | A second simulation [42] provides the relative scale of various objects down to atom relative to pinhead. Students analyze the nanotech toilet’s tech specs, compare to what they know about bacteria and viruses to evaluate the claims from the manufacturer. | 1, 2, 3, 5B, 5D |
| S&S 6: A Million to One | Students interact with a 1,000,000:1 scale model where the thickness of hair is the length of a football field and students the size of bacteria. They use 3-D models of DNA, proteins, and viruses; 2-D model of a bacterium; and 1-D models of cells to visualize the micro-and nano worlds at once. They measure the absolute size of the smaller objects using a 1-mm thick wire that represents a nanometer, the medium objects with a small object, and so on. Student groups prepared a TV advertisement for the nanotech toilet, using scientific data to bolster their claims, to be presented at final day with parents in attendance. | 1, 2, 3, 4, 5A-E |
aLearning Goals
1. There are unseen worlds that are too small to be seen with the unaided eye (“submacroscopic”).
2. The unseen world can have a serious impact on the everyday world.
3. There are large relative size differences between submacroscopic objects.
4. The unseen world can be divided into micro-, nano-, and sub-nano worlds, which are characterized by different objects, units, and instruments.
5. A. Know of several submacroscopic objects, including atom, bacterium, and cell.
B. Have an idea of their sizes relative to each other in qualitative terms.
C. Have an idea of their sizes relative to each other in quantitative terms.
D. Have an idea of their sizes relative to a small submacroscopic object like a pinhead or the thickness of a hair, in qualitative terms.
E. Have an idea of their sizes relative to a small submacroscopic object like a pinhead or the thickness of a hair, in quantitative terms.
Interview protocol.
Size and Scale interview protocol
Some additional questions were asked. These were not included as they were not analyzed in this paper.
Coding rubric.
Coding rubric for accuracy of content knowledge about the size of objects.
I. Smallest object respondent knows of
| Object | Size | Code | Reference |
|---|---|---|---|
| Macroscopic (e.g., grain of salt) or other (e.g., computer virus) | >100 μm | 0 | Respondents of all ages may be unable to think of objects too small to see [20, 21] |
| Cell/microorganism/germ/organelle | 1–100 μm | 1 | Over half of the second through fourth graders mentioned ants, bugs, and germs as the smallest objects of which they knew [20]; the NGSS include microbes in the fifth grade and bacteria in middle school [1] |
| Atom/small molecule (in 1+D, e.g., DNA) | 0.1–10 nm | 2 | Among respondents age 7–90, 45% of the respondents ordered the atom smallest [20]; NGSS introduces the atom in middle school [1] |
| Sub-atomic (e.g., electron) | <<0.1 nm | 3 | NGSS introduces protons, neutrons, and electrons in high school [1] |
II. Unit to express the size of that object, and/or smallest unit known
| Unit | Code | Reference |
|---|---|---|
| Do not know/do not exist/non-length (e.g., milligram) | 0 | NGSS includes measurements of an object’s motion in grade 3 [1] |
| Macroscopic-sized unit (e.g., inch, mm) | 1 | 18% of 7th–9th grade girls were able to define the millimeter as 1/1000 of a meter [9] |
| Submacroscopic (e.g., 1/1000 of inch, nanometer)a | 2 | Few 7th–9th grade girls had knowledge of units smaller than millimeter [9] |
aAccept descriptions of micrometer symbol.
III. Ordering 10 cards by size of the object depicted
| Code | Ordering | Distinction and reference |
|---|---|---|
| 0 | Macroscopic objects ordered incorrectly or interspersed with submacroscopic objects | Lack of distinction between smallest object and smallest visible object ([21], p. 571) |
| 1a | Atom ordered as larger than cell | Distinguishing cell and atom [21–23] |
| 2a | Cell larger than atom, but molecule, mitochondrion, or virus smaller than atom | Distinguishing atom and molecule [20, 21] |
| 3a | Atom smallest, but cell not ranked larger than molecule, virus, mitochondrion | Distinguishing cell and molecule [20, 22] |
| 4a | Atom and cell correctly ordered, but molecule/virus/mitochondrion out of order; or correct order without rationale | Distinguishing molecule, virus, mitochondrion (none found – emerged from the data) |
| 5a | All objects in the correct order AND student gives rationale for ranking. | Distinction between all of the objects (None found – emerged from the data) |
aLevels 1–5 include the macroscopic objects in correct order.
IV. Grouping 10 cards by size of the object depicted
| Grouping | Code |
| Number of groups | 1–10 |
V. Size relative to pinhead and absolute size for atom, cell, human, Earth
| Object | Relative: Range for code 1 (else 0) | Absolute: Range for code 1 (else 0) |
|---|---|---|
| Atom | 500,000–100 million | 0.01 nm–2 nm |
| Red blood cell | 10–2000 | 0.5–100 μm |
| Human | 150–20,000 | 0.15 m–20 m (7 inches to 60 feet)a |
| Earth | 109–150×10 | 1000–150,000 km |
For students who rank cell<atom<pinhead, substitute cell or atom to get another series of two submacroscopic objects ranked smaller than pinhead. Acceptable ranges: virus 1000–200,000; mitochondrion 50–10,000; molecule: cannot determine due to range of sizes of molecules.
aCode both in SI only and best estimate in ANY unit.
References
[1] NGSS Lead States. Next Generation Science Standards: For States, by States. The National Academies Press: Washington, DC, 2013.Suche in Google Scholar
[2] National Research Council. A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas. National Academies Press: Washington, DC, 2013.Suche in Google Scholar
[3] Stevens SY, Sutherland L, Krajcik JS. The Big Ideas of Nanoscale Science and Engineering: A Guidebook for Secondary Teachers. NSTA Press: Arlington, VA, 2009.Suche in Google Scholar
[4] Tretter T, Jones G, Minogue J. Accuracy of scale conceptions in science: Mental maneuverings across many orders of spatial magnitude. J. Res. Sci. Teach. 2006, 43, 1061–1085.Suche in Google Scholar
[5] Batt C, Waldron A, Broadwater N. Numbers, scale and symbols: the public understanding of nanotechnology. J. Nanopart. Res. 2008, 10, 1141–1148.Suche in Google Scholar
[6] Jones MG, Taylor AR, Falvo MR. Extreme Science: From Nano to Galactic. NSTA Press: Arlington, VA, 2009.Suche in Google Scholar
[7] Tretter T. Godzilla versus scaling laws of physics. Phys. Teach. 2005, 43, 530–532.Suche in Google Scholar
[8] Tretter T. Conceptualizing nanoscale. Sci. Teach. 2006, 73, 50–53.Suche in Google Scholar
[9] Jones G, Taylor A, Minogue J, Broadwell B, Wiebe E, Carter G. Understanding scale: powers of ten. J. Sci. Educ. Technol. 2007, 16, 191–202.Suche in Google Scholar
[10] Eames C, Eames R. Powers of Ten [Motion picture]. IBM: United States, 1977.Suche in Google Scholar
[11] Schank P, Wise A, Stanford T, Rosenquist A. Can High School Students Learn Nanoscience? An Evaluation of the Viability and Impact of the Nanosense Curriculum (Technical report). SRI International: Menlo Park, CA, 2009.Suche in Google Scholar
[12] Pellegrino JW, Krajcik JS, Stevens SY, Swarat S, Shin N, Delgado C. Using construct-centered design to align curriculum, instruction, and assessment development in emerging science. In Proceedings From ICLS ’08: International Perspectives in the Learning Sciences: Creating a Learning World, Vol. 3, Kanselaar V, Jonker V, Kirschner PA, Prins F, eds., International Society of the Learning Sciences: Utrecht, The Netherlands, 2008, pp. 314–321.Suche in Google Scholar
[13] Shin N, Stevens SY, Krajcik JS. Tracking student learning over time using construct-centred design. In Using Analytical Frameworks for Classroom Research: Collecting Data and Analysing Narrative, Rodrigues S, ed., Routledge: London, 2010, pp. 38–58.Suche in Google Scholar
[14] Delgado C, Morton K. Learning progressions, learning trajectories, and equity. In The Future of Learning: Proceedings of the10th International Conference of the Learning Sciences, Vol. 1, van Aalst J, Thompson K, Jacobson MJ, Reimann P, eds., International Society of the Learning Sciences: Sydney, 2012, pp. 204–211.Suche in Google Scholar
[15] Krajcik J, McNeill K, Reiser B. Learning-goals-driven design model: developing curriculum materials that align with national standards and incorporate project-based pedagogy. Sci. Educ. 2008, 92, 1–32.Suche in Google Scholar
[16] Mislevy RJ, Steinberg LS, Almond RG, Haertel GD, Penuel WR. Leverage Points for Improving Educational Assessment (PADI Technical Report). SRI International: Menlo Park, CA, 2003.Suche in Google Scholar
[17] National Research Council. In Knowing What Students Know: The Science and Design of Educational Assessment, Pellegrino JW, Chudowsky N, Glaser R, eds., National Academies Press: Washington, DC, 2001.Suche in Google Scholar
[18] Wilson M. Constructing Measures: An Item Response Modeling Approach. Lawrence Erlbaum Associates: Mahwah, NJ, 2005.Suche in Google Scholar
[19] Stevens S, Delgado C, Krajcik J. Developing a hypothetical multi-dimensional learning progression for the nature of matter. J. Res. Sci. Teach. 2010, 47, 687–715.Suche in Google Scholar
[20] Castellini O, Walejko G, Holladay C, Theim T, Zenner G, Crone W. Nanotechnology and the public: effectively communicating nanoscale science and engineering concepts. J. Nanopart. Res. 2007, 9, 183–189.Suche in Google Scholar
[21] Waldron A, Spencer D, Batt C. The current state of public understanding of nanotechnology. J. Nanopart. Res. 2006, 8, 569–575.Suche in Google Scholar
[22] Flores F. Representation of the cell and its processes in high school students: an integrated view. Int. J. Sci. Educ. 2003, 25, 269–286.Suche in Google Scholar
[23] Harrison A, Treagust D. Secondary students’ mental models of atoms and molecules: Implications for teaching chemistry. Sci. Educ. 1996, 80, 509–534.Suche in Google Scholar
[24] Jones G, Taylor A, Broadwell B. Concepts of scale held by students with visual impairment. J. Res. Sci. Teach. 2009, 46, 506–519.Suche in Google Scholar
[25] Jones G, Tretter T, Taylor A, Oppewal T. Experienced and novice teachers’ concepts of spatial scale. Int. J. Sci. Educ. 2008, 30, 407–427.Suche in Google Scholar
[26] Delgado C. Units of length: a notational system for conceptual understanding of size and scale. In Learning in the Disciplines: Proceedings of the 9th International Conference of the Learning Sciences, Vol. 2, Gomez K, Lyons L, Radinsky J., eds. International Society of the Learning Sciences: Chicago, 2010, pp. 362–363.Suche in Google Scholar
[27] Hapkiewicz A. Naïve ideas in earth science. MSTA J. 1999, 44, 26–30.Suche in Google Scholar
[28] Phillips W. Earth science misconceptions. Sci. Teach. 1991, 58, 21–23.Suche in Google Scholar
[29] Brook A, Briggs H, Driver R. Aspects of Secondary Students’ Understanding of the Particulate Nature of Matter. University of Leeds And Children’s Learning in Science Project: Leeds, 1984.Suche in Google Scholar
[30] Griffiths A, Preston, K. Grade-12 students’ misconceptions relating to fundamental characteristics of atoms and molecules. J. Res. Sci. Teach. 1992, 29, 611–628.Suche in Google Scholar
[31] Wiedtke, W. Measurement. In Mathematics for the Young Child, Payne JN, ed., National Council of Teachers of Mathematics: Reston, VA, 1990, pp. 229–249.Suche in Google Scholar
[32] Joram E, Subrahmanyam K, Gelman R. Measurement estimation: Learning to map the route from number to quantity and back. Rev. Educ. Res. 1998, 68, 413–449.Suche in Google Scholar
[33] Lehrer R. Developing understanding of measurement. In A Research Companion to Principles and Standards for School Mathematics, Kilpatrick J, Martin WG, Schrifter D, eds., National Council of Teachers of Mathematics: Reston, VA, 2003, pp. 179–192.Suche in Google Scholar
[34] Piaget J, Inhelder B. The Child’s Conception of Space, Langdon FJ, Lunzer JL, Trans., Routledge & Kegan Paul Ltd.: London, 1971.Suche in Google Scholar
[35] Resnick LB. From protoquantities to operators: building mathematical competence on a foundation of everyday knowledge. In Analysis of Arithmetic for Mathematics Teaching, Leinhardt G, Putnam R, Hattrup RA, eds., Lawrence Erlbaum Associates: Hillsdale, NJ, 1992.Suche in Google Scholar
[36] Magaña A, Brophy S, Bryan L. An integrated knowledge framework to characterize and scaffold size and scale cognition (FS2C). Int. J. Sci. Educ. 2012, 34, 2181–2203.Suche in Google Scholar
[37] Tretter T, Jones G, Andre T, Negishi A, Minogue J. Conceptual boundaries and distances: Students’ and experts’ concepts of the scale of scientific phenomena. J. Res. Sci. Teach. 2006, 43, 282–319.Suche in Google Scholar
[38] Krajcik, JS, Blumenfeld, PC. Project-based learning. In The Cambridge Handbook of the Learning Sciences, Sawyer RK, ed., Cambridge University Press: New York, 2006, pp. 317–333.Suche in Google Scholar
[39] Wilson R. (2013, October 12). Eagles-Buccaneers game a go despite latest MRSA outbreak. CBSSports.com. Retrieved August 16, 2014, from http://www.cbssports.com/nfl/eye-on-football/24072908/eagles-buccaneers-game-a-go-despite-latest-mrsa-outbreak.Suche in Google Scholar
[40] Tang K, Delgado C, Moje E. An integrative framework for the analysis of multiple and multimodal representations for meaning-making in science education. Sci. Educ. 2014, 98, 305–326.Suche in Google Scholar
[41] Delgado C, Ravaioli U, Raschke M. Size and Scale (computer simulation). Ann Arbor, MI, 2008.Suche in Google Scholar
[42] Song M, Quintana C. WIIS: Multimodal simulation for exploring the world beyond visual sense. In ACM Conference on Human Factors in Computing Systems (CHI 2009) Extended Abstracts. Boston MA, 2009, pp. 4699–4704.Suche in Google Scholar
[43] Ambert A, Adler PA, Adler P, Detzner D. Understanding and evaluating qualitative research. J. Marriage Fam. 1995, 57, 879–893.Suche in Google Scholar
[44] Bell P, Osborne R, Tasker R. Finding out what children think. In Learning in Science: Implications of Children’s Science, Osborne R, Freyberg P, Eds., Heinemann Publishers: Auckland, 1985, pp. 151–165.Suche in Google Scholar
[45] Novak JD. Learning How to Learn. Cambridge University Press: New York, 1984.Suche in Google Scholar
[46] White RT, Gunstone RF. Probing Understanding. Falmer: London, 1992.Suche in Google Scholar
[47] Anderson G, Arsenault N. Fundamentals of Educational Research. Routledge: London, 2005.Suche in Google Scholar
[48] Lipsey MW, Puzio K, Yun C, Hebert MA, Stienka-Fry K, Cole MW, Busick MD. Translating the Statistical Representation of the Effects of Education Interventions Into More Readily Interpretable Forms. NCSER Publications: Washington, 2012.Suche in Google Scholar
[49] Vergnaud G. Multiplicative structures. In Number Concepts and Operation in the Middle Grades, Hiebert J, Behr M, eds., Erlbaum: Reston, VA, 1988, pp. 141–161.Suche in Google Scholar
[50] American Association for the Advancement of Science. Benchmarks for Science Literacy. Oxford University Press: New York, 1993.Suche in Google Scholar
[51] American Association for the Advancement of Science. Benchmarks online. Retrieved January 19, 2010, from http://www.project2061.org/publications/bsl/online/index.php.Suche in Google Scholar
©2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- In this issue
- Editorial
- Special issue on Pre-college nanoscale science, engineering, and technology learning
- Review
- Published research on pre-college students’ and teachers’ nanoscale science, engineering, and technology learning
- Nanotechnology education
- Instructional impact on high school physics students’ nanoscience conceptions
- A middle school instructional unit for size and scale contextualized in nanotechnology
- Science teachers’ perceptions of nanotechnology teaching and professional development: a survey study in Taiwan
- Integrating nanoscience and technology in the high school science classroom
- The making of nanotechnology: exposing high-school students to behind-the-scenes of nanotechnology by inviting them to a nanotechnology conference
- Precollege nanotechnology education: a different kind of thinking
Artikel in diesem Heft
- Frontmatter
- In this issue
- Editorial
- Special issue on Pre-college nanoscale science, engineering, and technology learning
- Review
- Published research on pre-college students’ and teachers’ nanoscale science, engineering, and technology learning
- Nanotechnology education
- Instructional impact on high school physics students’ nanoscience conceptions
- A middle school instructional unit for size and scale contextualized in nanotechnology
- Science teachers’ perceptions of nanotechnology teaching and professional development: a survey study in Taiwan
- Integrating nanoscience and technology in the high school science classroom
- The making of nanotechnology: exposing high-school students to behind-the-scenes of nanotechnology by inviting them to a nanotechnology conference
- Precollege nanotechnology education: a different kind of thinking
