9P.1.3.4 Models
Use significant figures and an understanding of accuracy and precision in scientific measurements to determine and express the uncertainty of a result.
Overview
MN Standard in Lay Terms
Since many things in the physical world are too small, too big, happen too fast, or happen too slowly for people to understand, models are used to demonstrate or explain a science concept. By building mathematical models, people are able to predict what will happen in specific situations. However, since models are only a representation of the real thing, they have their limitations. Mathematical models are only as good as the technique of measurement and the instruments being used. In order to show the precision of the measurement and technique, significant figures are used. If significant figures are ignored, the results of a calculation give a false impression of its reliability. Scientists use significant figures to show the level of precision their calculations represents.
Big Idea
People try to explain the world around them with models. Physical models can give a visual representation of an actual occurrence. A mathematical model gives the ability to predict occurrences. However, all models are limited to their function. Mathematical models are limited by the ability to make accurate and precise measurements. Many measurements are limited by the ability of the instrument being used and the technique of the person doing the measuring. The limitations of the instrument must be accounted for when stating results. Otherwise, the results will falsely represent the precision of the data, giving the results a false amount of reliability, that can mislead people interpreting the results. Significant figures shows the precision of the instruments and calculations being used. The goal of science is to find the truth of the world around us, and misleading results can hinder that process.
MN Standard Benchmarks
9P.1.3.4.1 Use significant figures and an understanding of accuracy and precision in scientific measurements to determine and express the uncertainty of a result.
The Essentials
Stephen Wolfram, creator of Mathematica, talks about his quest to make all knowledge computational -- able to be searched, processed and manipulated -- in this video. His new search engine, Wolfram Alpha, has "no lesser goal than to model and explain the physics underlying the universe."
1) NSES Standards p 174 and 175:
"Students also need to learn how to analyze evidence and data. The evidence they analyze may be from their investigations, other students' investigations, or databases. Data manipulation and analysis strategies need to be modeled by teachers of science and practiced by students. Determining the range of the data, the mean and mode values of the data, plotting the data, developing mathematical functions from the data, and looking for anomalous data are all examples of analyses students can perform. Teachers of science can ask questions, such as ''What explanation did you expect to develop from the data?" "Were there any surprises in the data?" "How confident do you feel about the accuracy of the data?" Students should answer questions such as these during full and partial inquiries.
Public discussions of the explanations proposed by students is a form of peer review of investigations, and peer review is an important aspect of science. Talking with peers about science experiences helps students develop meaning and understanding. Their conversations clarify the concepts and processes of science, helping students make sense of the content of science. Teachers of science should engage students in conversations that focus on questions, such as "How do we know?" "How certain are you of those results?" "Is there a better way to do the investigation?" "If you had to explain this to someone who knew nothing about the project, how would you do it?" "Is there an alternative scientific explanation for the one we proposed?" "Should we do the investigation over?" "Do we need more evidence?" "What are our sources of experimental error?" "How do you account for an explanation that is different from ours?"
Questions like these make it possible for students to analyze data, develop a richer knowledge base, reason using science concepts, make connections between evidence and explanations, and recognize alternative explanations. Ideas should be examined and discussed in class so that other students can benefit from the feedback. Teachers of science can use the ideas of students in their class, ideas from other classes, and ideas from texts, databases, or other sources-but scientific ideas and methods should be discussed in the fashion just described."
Guide to the Content Standard
Fundamental abilities and concepts that underlie this standard include
ABILITIES NECESSARY TO DO SCIENTIFIC INQUIRY
IDENTIFY QUESTIONS AND CONCEPTS THAT GUIDE SCIENTIFIC INVESTIGATIONS. Students should formulate a testable hypothesis and demonstrate the logical connections between the scientific concepts guiding a hypothesis and the design of an experiment. They should demonstrate appropriate procedures, a knowledge base, and conceptual understanding of scientific investigations.
DESIGN AND CONDUCT SCIENTIFIC INVESTIGATIONS. Designing and conducting a scientific investigation requires introduction to the major concepts in the area being investigated, proper equipment, safety precautions, assistance with methodological problems, recommendations for use of technologies, clarification of ideas that guide the inquiry, and scientific knowledge obtained from sources other than the actual investigation. The investigation may also require student clarification of the question, method, controls, and variables; student organization and display of data; student revision of methods and explanations; and a public presentation of the results with a critical response from peers. Regardless of the scientific investigation performed, students must use evidence, apply logic, and construct an argument for their proposed explanations.
USE TECHNOLOGY AND MATHEMATICS TO IMPROVE INVESTIGATIONS AND COMMUNICATIONS. A variety of technologies, such as hand tools, measuring instruments, and calculators, should be an integral component of scientific investigations. The use of computers for the collection, analysis, and display of data is also a part of this standard. Mathematics plays an essential role in all aspects of an inquiry. For example, measurement is used for posing questions, formulas are used for developing explanations, and charts and graphs are used for communicating results.
FORMULATE AND REVISE SCIENTIFIC EXPLANATIONS AND MODELS USING LOGIC AND EVIDENCE. Student inquiries should culminate in formulating an explanation or model. Models should be physical, conceptual, and mathematical. In the process of answering the questions, the students should engage in discussions and arguments that result in the revision of their explanations. These discussions should be based on scientific knowledge, the use of logic, and evidence from their investigation.
RECOGNIZE AND ANALYZE ALTERNATIVE EXPLANATIONS AND MODELS. This aspect of the standard emphasizes the critical abilities of analyzing an argument by reviewing current scientific understanding, weighing the evidence, and examining the logic so as to decide which explanations and models are best. In other words, although there may be several plausible explanations, they do not all have equal weight. Students should be able to use scientific criteria to find the preferred explanations.
COMMUNICATE AND DEFEND A SCIENTIFIC ARGUMENT. Students in school science programs should develop the abilities associated with accurate and effective communication. These include writing and following procedures, expressing concepts, reviewing information, summarizing data, using language appropriately, developing diagrams and charts, explaining statistical analysis, speaking clearly and logically, constructing a reasoned argument, and responding appropriately to critical comments.
2) AAAS Benchmarks of Science Literacy and Atlas from Benchmarks Online - Project 2061
The Nature of Mathematics (2)
Mathematics, Science, and Technology (2B):
2B/H1 - Mathematical modeling aids in technological design by simulating how a proposed system might behave.
The Mathematical World (9)
Numbers (9A):
9A/H1 - Comparison of numbers of very different size can be made approximately by expressing them as nearest powers of ten.
9A/H3 - When calculations are made with measurements, a small error in the measurements may lead to a large error in the results.
9A/H4 - The effects of uncertainties in measurements on a computed result can be estimated.
Symbolic Relationships (9B):
9B/H3 - Any mathematical model, graphic or algebraic, is limited in how well it can represent how the world works. The usefulness of a mathematical model for predicting may be limited by uncertainties in measurements, by neglect of some important influences, or by requiring too much computation.
Uncertainty (9D):
9D/H2 - When people estimate a statistic, they may also be able to say how far off the estimate might be due to chance.
9D/H3 - The middle of a data distribution might be misleading when the data are not distributed symmetrically, when there are extreme high or low values, or when the distribution is not reasonably smooth.
9D/H4 - The way data are displayed can make a big difference in how they are interpreted.
9D/H5 - Both percentages and actual counts have to be taken into account in comparing different groups; using either category by itself could be misleading.
9D/H6a - Considering whether and how two variables are correlated requires inspecting their distributions, such as in two-way tables or scatterplots.
9D/H6bc - correlation between two variables doesn't mean that one causes the other; perhaps some other variable causes them both or the correlation might be attributable to chance alone. A true correlation means that differences in one variable imply differences in the other when all other things are equal.
9D/H7a - The larger a well-chosen sample of a population is, the better it estimates population summary statistics.
9D/H7bc - For a well-chosen sample, the size of the sample is much more important than the size of the population. To avoid intentional or unintentional bias, samples are usually selected by some random system.
9D/H8 - A physical or mathematical model can be used to estimate the probability of real-world events.
Common Core Standards
Math standards
(8.1.1.5) Express approximations of very large and very small numbers using scientific notation; understand how calculators display numbers in scientific notation. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation, using the correct number of significant digits when physical measurements are involved.
For example: (4.2×104)×(8.25×103) =3.465×108 , but if these numbers represent physical measurements, the answer should be expressed as 3.5×108 because the first factor, 4.2×104 , only has two significant digits.
(9.2.1.4) Obtain information and draw conclusions from graphs of functions and other relations.
Students can plot data of current and voltage to determine the resistance of a circuit.
(9.2.2.1) Represent and solve problems in various contexts using linear and quadratic functions.
(9.2.2.3) Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions.
(9.3.1.3) Understand that quantities associated with physical measurements must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems.
For example: 60 miles/hour = 60 miles/hour × 5280 feet/mile × 1 hour/3600 seconds = 88 feet/second.
(9.3.1.5) Make reasonable estimates and judgments about the accuracy of values resulting from calculations involving measurements.
For example: Suppose the sides of a rectangle are measured to the nearest tenth of a centimeter at 2.6 cm and 9.8 cm. Because of measurement errors, the width could be as small as 2.55 cm or as large as 2.65 cm, with similar errors for the height. These errors affect calculations. For instance, the actual area of the rectangle could be smaller than 25 cm2 or larger than 26 cm2, even though 2.6 × 9.8 = 25.48.
(9.4.1.3) Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.
(9.4.2.3) Design simple experiments and explain the impact of sampling methods, bias and the phrasing of questions asked during data collection.
2010 Minnesota Academic Standards - English Language Arts K-12
Curriculum and Assessment Alignment Form
Grades 11-12 Literacy in Science and Technical Subjects
Minnesota Academic Standards: Language Arts
Anchor Standard | Benchmark |
1. Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text. | 1. Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account. |
2. Determine central ideas or themes of a text and analyze their development; summarize the key supporting details and ideas. | 2. Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms. |
3. Analyze how and why individuals, events, and ideas develop and interact over the course of a text. | 3. Follow precisely a complex multistep procedure when carrying out experiments, designing solutions, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text. |
4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone. | 4. Determine the meaning of symbols, equations, graphical representations, tabular representations, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11-12 texts and topics. |
5. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole. | 5. Analyze how the text structures information or ideas into categories or hierarchies, demonstrating understanding of the information or ideas. |
6. Assess how point of view or purpose shapes the content and style of a text. | 6. Analyze the author's purpose in describing phenomena, providing an explanation, describing a procedure, or discussing/reporting an experiment in a text, identifying important issues and questions that remain unresolved. |
7. Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words. | 7. Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem. |
8. Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence. | 8. Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying the data when possible and corroborating or challenging conclusions with other sources of information. |
9. Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take. | 9. Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible. |
10. Read and comprehend complex literary and informational texts independently and proficiently. | 10. By the end of grade 12, read and comprehend science/technical texts in the grades 11-12 text complexity band independently and proficiently. |
Misconceptions
- Students believe that errors in their labs are only "human error."
- Students believe that calculating a number several digits after a decimal is more precise than using significant figures.
Vignette
Three weeks into the school year, Mr. L wants his student to understand the importance of using physical models to help understand concepts. He doesn't want the learning of models to interfere with the learning of physics concepts, so he decides to give the students a task to develop a model that does not include the learning of a science concept. After reading an article in Science Scope (Moyer, R, & Everett, S. (2010). What makes a better box?. Science Scope, 77(2), 64-69), Mr. L designs an activity that reviews the process of engineering and also gets the students to use physical models to provide information for make a decision.
At the beginning of class Mr. L sets up a scenario for the days activity by say, "Businesses are always trying to find new ways to make products better and cheaper. However, one of the areas in the food production industry that has not changed much since the early 1900's is the packaging of cereal." He draws their attention to the screen that has a picture of a cereal box. "Because package and shipping is a large cost in manufacturing the cereal, a leading cereal company hires you to save them costs in packaging. You understand the best designing for a box can hold the most cereal (largest volume), with the least packaging material used to make the box (surface area)."
Mr. L steps to the side of the room where he has placed several boxes. "In your groups you are going to come up with a design that will hold the most cereal, but has the least amount of packaging material. There are several boxes that you can use to measure and calculate volume and surface area. Take into count the accuracy and precision of your measuring devices in your calculations by using significant figures." Mr. L steps over to another counter that has large sheets of poster board. "Once engineers come up with a design, they make a model, called a prototype, so that they can examine a single version of the product without a lot of cost. Your group will be given a 24 inch x 36 inch sheet of poster board. Your task will be to make a box with the greatest volume to surface area ratio (volume / surface) with the least amount of waste of paper. Before you actually build the prototype (model), you must show me your design." Mr. L pauses for a few seconds to let the students think about their task. "Any questions? Okay, get started."
Student begin by assigning roles for their group work. Mr. L has established the four roles in prior activities (manager/checker, recorder, calculator, and measurer). The groups get a box, measuring device, and begin to create a table to record their data. The measurer measures the boxes, recorder records the data, the calculator calculates the volume, surface area, and volume/surface area. The manager makes sure everyone is doing their job, and checks all work. After one box is completed, the students return the box and get a different shaped box to find its volume to surface area ratio. When student are done measuring boxes, the student groups use their data to design their own box. During this time the teacher goes from group to group asking questions to make sure the students know what they are doing.
When students have finished their cereal box design, they present their drawn designed to the teacher, who checks to make sure their dimensions fit the 24 inch x 36 inch poster board and that their calculations used significant figures. The students then build their prototype. When many of the groups are close to finishing the constructing their prototype, Mr. L stops the students to speak to them. "Many of you are almost done constructing your boxes. To verify your volume to surface area ratio, remeasure your box and calculated the actual volume to surface area ratio of your box." Students continue to work until the end of the period.
The next day, Mr. L has each group use large whiteboards to draw their box design and show their calculations for their volume to surface area ratio. He has the students put the whiteboards along the counters throughout the room, going for smallest ratio to largest ratio. After all the whiteboards are up, Mr. L has the students compare the large ratio boxes to the small ratio boxes. What are the similarities in the design of the large ratios? How are they different from the small ratio boxes? Once the students see that a square shaped box is a larger volume to surface area ratio than a rectangular box, Mr. L has each group come up with a list of advantages and disadvantages of the different box shapes. After ten to fifteen minutes, Mr. L has the groups share their ideas of advantages and disadvantages on the SMART board screen. "You can see from our list that making a box a certain way can have some advantages and some disadvantages. So now it comes back to our original task we started yesterday. You were hired by a company to design a box that is cheaper to manufacture. You want to sell your box. Your group is going to design a short 30 second presentation to convince the company your box shape is the best. You will present these to our class tomorrow."
Resources
Suggested Labs and Activities
Vernier Investigations:
Vernier technology is a source of data collection that allows students to accurately predict and analysis data. The links below are the complete labs as posted by Vernier Software and Technology.
Advanced Physics with Vernier: Vernier
Error Analysis (9P.1.3.4.1) - Determine the value of the acceleration of a freely falling object and compare your value with the accepted value for this quantity. Learn how to describe and account for variation in a set of measurements. Learn how to describe a range of experimental values.
Instructional suggestions/options
Robot Basketball (9P.1.3.4.1)
This lesson demonstrates the difference between precision and accuracy. Students design a device that can shoot a basketball free-throw shot accurately every time.
Spring Scale Design (9P.1.3.4.1 )
Lesson focuses on the engineering behind building a spring scale and its use as a measuring device. Students work in teams to design, build, and test their own spring scale that can measure the weight of an apple using everyday items. They compare their designs with those of other student teams and reflect on the experience.
Temperature Tactics (9P.1.3.4.1 )
Lesson focuses on how thermometers have been impacted by engineering over time, and also how materials engineering has developed temperature sensitive materials. Student teams design and build a temperature gauge out of everyday products and test a variety of materials for thermal properties. Students evaluate the effectiveness of their temperature gauge and those of other teams, and present their findings to the class.
Additional resources
School Programs for Engineering Projects (grades 9-12):
Engineering the Future: National Center of Technology Literacy (Boston Museum of Science)
The Infinity Project: Institute of Engineering Eduction
Gateway to Technology and Introduction to Engineering Design (Project Lead the Way)
Vocabulary/Glossary
Dennison, G., Glossary of Measurement and Error, Department of Physics, Utah State University
Precision - A measure of the reproducibility of a measurement. If an experiment has small random errors, it is said to have high precision.
Accuracy - A measure of the validity of a measurement. If an experiment has small systematic errors, it is said to have high accuracy.
Dimensions - The fundamental quantities used to express physical quantities independent of the system of units used. The basic dimensions are length (L), time (T), mass (M), and electric current (A).
Dimensional Analysis - The use of dimensions of physical quantities to verify calculations and formulas. For example, Newton's Second Law states that F = ma. Dimensional analysis shows that F has dimensions of MLT-2 represents the dimensions of force. Dimensional analysis is not capable of completely determining an unknown functional relationship, but it can limit the possibilities and, in some cases it can give the complete relationship to within a constant of proportionality.
Discrepancy - The difference between two measured values of the same quantity.
Uncertainty - The outer limits of confidence within which a given measurement "almost certainly" lies. It is important to specify what criteria are used to determine the confidence limits.
Absolute Uncertainty - The uncertainty of a quantity expressed in the same units as the quantity. For example, a measured length might be 1.0 +/- 0.1 m, that is a length of 1.0 m with an uncertainty of 0.1 m.
Relative (Fractional) Uncertainty - The ratio of the absolute uncertainty to the estimated value of a measured quantity. The example above has a relative uncertainty of 0.1 or 10%.
Systematic Errors - Errors which are characterized by their deterministic nature. Such errors are frequently constant. An improperly zeroed meter results in a typical systematic error.
Random (Statistical) Errors - Errors which are due to random or stochastic phenomenon which are characterized by the property that repeated occurrences of the phenomenon do not always lead to the same observed outcome. The uncertainty in the number of radioactive decays per unit time from a standard source is an intrinsically random error.
Procedural Errors- Errors resulting from mistakes on the part of the experimenter. Computational errors are included in this category. A common illegitimate error is to read the wrong scale of a meter stick.
Physical Model - a smaller or larger physical copy of an object.
Mathematical Model - a mathematical representation (equation) of a science concept.
Percent Error - The ratio, expressed as a percentage, of the difference between two values of an unknown to the average value of the quantity.
Propagation of Errors - A method of determining the error inherent in a derived quantity from the errors of the measured quantities used to determine the derived quantity.
Significant Figures - A notation convention for writing the value of measured quantities. In general, the measured quantity should have only as many significant figures as warranted by its absolute uncertainty.
Rounding - A method of truncating numbers, particularly useful in the context of significant figures. By standard convention, numbers to be rounded should be truncated for trailing numbers less than 5, rounded up for trailing numbers over 5, and rounded to the nearest even number for a trailing 5.
Units - An arbitrary set of measurement standards used to compare physical quantities. Common systems of units include the meter-kilogram-second (MKS or SI) system, the centimeter-gram-second (CGS) system, and the footpound-second (English) system.
Free Data Tool Plotting and Analysis Software
DataTool is a data analysis tool for plotting and fitting data from the laboratory, simulations, video analysis, or any other data set organized into columns. A click of a checkbox in DataTool allows the user to change the appearance of plots, see standard statistics for the data set or apply built-in linear, quadratic or cubic fits to the data set. DataTool also includes a number of standard mathematical functions that can be applied to the data set, allowing for further analysis and extending the range of potential fits to the data. Features of DataTool include:
changing the appearance of plots
getting standard statistics for the data set
showing the slope (tangent) and area under curve
automatic fits of data to pre-defined analytical expressions
Fit Builder: fitting data to user-defined analytical expressions
Data Builder: applying standard mathematical manipulations to the data set
Free Tracker Video Analysis Software for Modeling in Physics
Tracker is a free video analysis and modeling tool built on the Open Source Physics (OSP) Java framework. It is designed to be used in physics education.
Tracker video modeling is a powerful new way to combine videos with computer modeling. For more information see Particle Model Help or my AAPT Summer Meeting posters Video Modeling (2008) and Video Modeling with Tracker (2009).
Web Based Instructional Videos:
Bob Abel's Series on Significant Digits (9P.1.3.4.1)
Videos to learn how to implement the National Standards using Inquiry Techniques from the Annenburg Foundation:
1. Introduction
Classroom footage and new footage of scientists in the field explain and illustrate the concept of inquiry.
Assessment
Assessment of Students
1. How many significant digits are in the number 0.000000003?
a. 1
b. 2
c. 3
d. 6
e. 10
Answer A
2. A billion barrels (1 x 109) of oil would fill a cubic container of what length on each side?
a. 10 m
b. 500 m
c. 5 km
d. 50 km
e. 500 km
Answer B
3. 10 m2 is equal to which one of the following?
a. 10 cm2
b. 100 cm2.
c. 1000 cm2.
d. 1000 mm2.
e. 100,000 cm2.
Answer E
4. The length and width of a floor is measured. The length is measured to be 5.0 m with a cheap ruler while the width is measured to be 3.457 m using a calibrated laser measurement. What would be the best value for the area of the floor?
a. 17 m2
b. 17.2 m2
c. 17.285 m2
d. 17.2850 m2
e. 20 m2
Answer B
5) What is the product of 7.2 and 1.32 written with the correct number of significant figures in scientific notation?
A) 9.504
B) 9
C) 9.5
D) 10
E) 9.50
Answer C
6. The force acting on an object is equal to its acceleration multiplied by its mass. What are the dimensions of force?
A) [M1L1T2]
B) [M-1L1T-2]
C) [M1L1T-1]
D) [M1L1T-2]
E) [M-1L1T2]
Answer D
7. How many significant figures in the quantity 42.0340 L
A. 2
B. 4
C. 5
D. 6
Answer D
8. Give correct answer with appropriate number of significant figures 2.55 km x 6.7 km.
A. 17.085 km^2
B. 17.1 km^2
C. 17.09 km^2
D. 17 km^2
Answer D
9. Give correct answer with appropriate number of significant figures and correct units in the 28.113 cm + 44.56 cm + 1143 mm
A. 1869.73 mm
B. 186.97 cm
C. 187.0 cm
D. 186.9 cm
E. 186.9 mm
Answer C
10.How many significant figures in the measurement 1.000001 cm?
A. 2
B. 5
C. 6
D. 7
Answer D
11. What type of device could make a measurement of 1.000001 cm?
a. a ruler
b. a micrometer
c. a laser measurement device
d. a Vernier caliper
Answer C
Assessment of Teachers
Modeling Instruction in High School Physics, Chemistry, Physical Science, and Biology
Materials and readings for teacher discussion and use for professional development
The Modeling Method of High School Physics Instruction has been under development at Arizona State University since 1990 under the leadership of David Hestenes, Professor of Physics. The program cultivates physics teachers as school experts on effective use of guided inquiry in science teaching, thereby providing schools and school districts with a valuable resource for broader reform. Program goals are fully aligned with National Science Education Standards. The Modeling Method corrects many weaknesses of the traditional lecture-demonstration method, including fragmentation of knowledge, student passivity, and persistence of naive beliefs about the physical world. Unlike the traditional approach, in which students wade through an endless stream of seemingly unrelated topics, the Modeling Method organizes the course around a small number of scientific models, thus making the course coherent. In 2000 the program was extended to physical science and in 2005 to chemistry, by demand of committed teachers.
Differentiation
Strategies from The Inclusive Classroom: Teaching Mathematics and Science to English-Language Learners, (Jarrett, D. (1999). The inclusive classroom: teaching mathematics and science to english-language learners. Portland, Oregon: Northwest Regional Educational Laboratory.)
Thematic Instruction: Theme-based units can help ELL students connect prior knowledge to language and real-world applications.
Cooperative Learning: Students use language related to task, while conversing and tutoring one another.
Inquiry and Problem Solving: Inquiry and problem solving can be used prior to proficiency in English. Inquiry approaches in science can help student's language acquisition as well as their content knowledge.
Vocabulary Development: Students learn the meaning of words best during investigations and activities, instead of as a vocabulary list.
Modify Speech: Teachers can help ELL students by using an active voice, limiting new terms, using visual support, and paraphrasing or repeating difficult concepts. Slowing down speech, speaking clearly, and using a simple language structure will help ELL students with understanding.
Make ELL Students Feel Welcome: Encourage ELL students to express ideas, thought, and experiences. Focus on what student is say, not how they say it.
Website: Strategies for teaching science to ELL Students
Book: Teaching Science to English Language Learners
Article: PER research techniques for the multicultural classroom
Parents/Admin
Administrators
Ideas adapted from (Daniels, H, Hyde, A, Zemelman, S, & Heinmann, Initials. (2005). Best Practice: Today's standards for teaching and learning in America's schools. Portsmouth,NH:).
If observing a lesson on this standard, administrators might expect to see:
1. Students being challenged to think about the use of physical and mathematical models in physics.
2. Students testing their understanding of physical and mathematical models through investigations or solving real-life scenarios.
3. Students taking responsibility for their own learning.
4. Students working in collaborative groups, analyzing, synthesizing, and defending conclusions.
5. Students sharing explanations for the results of investigation and their understanding of concepts.
6. Students continuously assessing and being assessed on their understanding physical and mathematical models, including the precision of significant figures.
7. Students' concepts are being built on prior knowledge of the process of doing science (scientific method) and the physical and mathematical models used.