Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
READING GRAPHS AND INTERPRETING SLOPE: A MATH/SCIENCE TARGETED CONNECTION Dr. Cheryl Malm, Northwest Missouri State University Dr. Patricia Lucido, SySTEMic Innovations RESEARCH FOCUS: To examine mathematics and science concepts to identify supporting ideas, processes, and skills that allow the design of parallel curricula or “targeted connections”. INTEGRATED CURRICULA DESIGN Single courses of study, usually taught by a single mathematicstrained or science-trained teacher, i.e. mathematics courses that incorporate science applications or science courses that utilize appropriate mathematical models. A continuum model that characterizes the relationship between the mathematics and science in integrated curricula. Math Independent Math Lesson Focused with Supporting Science Balanced lessons Science Focused with Supporting Math Independent Science Lesson CORRELATED LESSONS Correlated lessons extend the definition of integration, striving to achieve “balanced” integration in which the mathematics and science content is of equal importance (Berlin & White, 1994; Lonning & Defranco, 1997). Parallel mathematics and science lessons are developed by a team of teachers, each a content specialist in their own discipline, to allow the concepts from both disciplines to be almost equally taught (Vasques-Mireles & West, 2007). A strength is the team-teaching approach; conversations occur around the language and the parallel relationships that are being taught. The challenges range from lack of planning time and difficulties in coordinating team taught lessons to lack of materials and difficulties identifying appropriate connections (Vasques-Mireles & West, 2007). TARGETED CONNECTIONS Targeted connections expand the definition of correlated lessons to encompass correlated units of study. Rather than selecting a mathematics or science topic and then attempting to incorporate the pertinent topics from the other discipline , parallel programs would be designed in mathematics and science that would connect underlying, supporting conceptual understandings as well as appropriate skills and applications. Content designed to be taught simultaneously in a math course and a science course would each develop the connected conceptual understanding within the context of the separate discipline. TARGETED CONNECTIONS Correlated lessons would be utilized within the units to take advantage of the naturally occurring connections in processes, skills, and applications Math • Lesson • Lesson • Lesson • Lesson • Lesson Targeted Connection • Lesson Science • Lesson • Lesson • Lesson • Lesson • Lesson READING AND INTERPRETING GRAPHS/VELOCITY AND ACCELERATION Mathematics Unit Graphing Motion Follow a Graph/Tell a Story Explore Slope in relation to speed Explore non-linear motion situations Application Science Unit Explore motion with Balloon Cars Gather motion data Graph data on speed and acceleration Application NCTM STANDARDS: 9-12 REPRESENTATIONS Representation Instructional programs from prekindergarten through grade 12 should enable all students to— create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among mathematical representations to solve problems; use representations to model and interpret physical, social, and mathematical phenomena. COMMON CORE STANDARDS Represent and solve equations and inequalities graphically 10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). 11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. NRC – FRAMEWORK FOR K-12 SCIENCE Insert science standards here to make the connection?????? – see next slide SCIENTIFIC AND ENGINEERING PRACTICES Asking questions and defining problems Planning and carrying out investigations Analyzing and interpreting data Using mathematics and computational thinking Constructing explanations / designing solutions Engaging in argument from evidence Obtaining, evaluating and communicating information NRC – FRAMEWORK FOR K-12 SCIENCE Crosscutting Concepts Cause and effect: Mechanism and explanation Systems and system models Energy and matter: Flows, cycles and conservation Disciplinary Core Ideas Motion and stability: Forces and interactions Energy Engineering, Technology and the Application of Science Engineering design NRC – FRAMEWORK CORE IDEA PS3:ENERGY PS3.A: Definitions of Energy What is energy? Kinetic & Stored (potential) PS3.B: Conservation of Energy /Energy Transfer What is meant by conservation of energy? How is energy transferred between objects or systems? PS3.C: Relationship Between Energy and Forces How are forces related to energy? NATIONAL SCIENCE EDUCATION STANDARDS: MOTIONS AND FORCES Objects change their motion only when a net force is applied. Laws of motion are used to calculate precisely the effects of forces on the motion of objects. The magnitude of the change in motion can be calculated using the relationship F = ma, which is independent of the nature of the force. Whenever one object exerts force on another, a force equal in magnitude and opposite in direction is exerted on the first object. NCTM STANDARDS: 9-12 ALGEBRA PRINCIPLES AND STANDARDS FOR SCHOOL MATHEMATICS: 9-12 REPRESENTATIONS A flight from SeaTac Airport near Seattle, Washington, to LAX Airport in Los Angeles has to circle LAX several times before being allowed to land. Plot a graph of the distance of the plane from Seattle against time from the moment of takeoff until landing. adapted from Hughes-Hallett et al. Calculus, 1994, p. 6 PRINCIPLES AND STANDARDS FOR SCHOOL MATHEMATICS: 9-12 REPRESENTATIONS Fig. 7.40. A representation that a student might produce of an airplane's distance from its take-off point against the time from takeoff to landing PRINCIPLES AND STANDARDS FOR SCHOOL MATHEMATICS: 9-12 REPRESENTATIONS Fig. 7.41. A more nearly accurate representation of the airplane's distance from its takeoff point against the time from takeoff to landing DATA STUDIO: MOTION DETECTOR DATA STUDIO: FOLLOW THE GRAPH GIZMOS Mathematics 9-12: Algebra: Graphing Linear PLANNING EXPERIMENTS 9 Steps to the Plan Starting with 4 questions from Cothron, Giese, Rezba’s Students and Research ENGAGE What do graphs look like with changes in distance? Physical feel for the graphs. “Walk the graph” activity, uses the GLX probes and a motion detector to investigate the graphs created with constant rates of change vs. variable rates of change. Mathematics 6-8: Algebra: Graphing: Applications Distance-Time Graphs Distance-Time and Speed-Time Graphs EXPLORE Explore distant/rate Gizmos: discussion will include using them in engage and/or explore sections Balloon or rubber band cars Measure distance and time stop watches and measuring tape EXPLAIN Show and discuss graphs made by students Tie Pasco motion detector, the Gizmos graphs, and balloon / rubber band cars together. e.g. speed time/ rate GIZMOS Science 6-8 Physical Science: Motion and Force: Fan Car Physics ELABORATE Science 6-8 physical science: Motion and force: Fan Cart Physics Nine question strategy – student design investigations, Use Fan Cart Gizmo 9 question with Fan Cart Physics Different graphs WHAT MATERIALS ARE AVAILABLE FOR EXPERIMENTING WITH FAN CARTS? What materials / conditions are available for conducting experiments on Fan Carts ? Cart Forces in terms of fans Load placed on the cart Q1 HOW CAN THE MATERIALS / CONDITIONS BE CHANGED? (INDEPENDENT VARIABLE) Cart -------- Fans number direction Load mass Track -------- Q2 HOW TO FAN CARTS ACT? Change position with time Accelerate over time Have speed or velocity HOW CAN THE RESPONSE TO THE CHANGE BE MEASURED? (DEPENDENT VARIABLE) Cart position Speed Cart or velocity (m/s) Acceleration (m/s2) Q4 WHAT EQUIPMENT OR MEASUREMENT TOOLS ARE NECESSARY? Means of detection or measurement – Measurement is completed in the simulation. Balloon cars meter sticks or tape and stop watches Q6 WHAT OTHER SUPPLIES ARE NEEDED? Gizmo - The camera feature is very useful. WHAT IS THE EXPERIMENTAL PLAN? Title Hypothesis Independent Variable Control Levels of the Independent Variable Number of Trials Dependent Variable Constants Q5 THE EFFECT OF MASS ON THE ACCELERATION OF A FAN CART Hypothesis: The greater the mass, the slower the acceleration of the Fan Cart Independent Variable: the load (mass) in the cart 0 load (control) 1 load unit 2 load units 2 load units 3 trials 3 trials 3 trials 3 trials Dependent Variable: acceleration (m/s2) Constants: cart, track, number of fans, fan direction GIZMOS Science 6-8 Physical Science: Motion and Force: Fan Car Physics WHAT KIND OF DATA ARE COLLECTED? Types of Data in terms of: Discrete – only whole integers Continuous – divisible into partial units Types of Data in terms of: Quantitative –measurements Qualitative – load: none, low, medium, high Q7 WHAT KIND OF DATA DISPLAY IS APPROPRIATE? Scatter plots Box and Whiskers Histograms Bar Graphs Pie Charts Frequency Distribution Line Graphs Q8 MEAN The sum of a set of values divided by the number of samples. Mean = X = X n X is sample mean n is the total number of samples DATA TABLE Mass units Acceleration Acceleration Acceleration Total Mean Trial 1 Trial 2 Trial 3 0 mass units .80 m/s2 .79 m/s2 .81 m/s2 2.40 m/s2 .80 m/s2 1 mass unit .39 m/s2 .40 m/s2 .41 m/s2 1.20 m/s2 .40 m/s2 2 mass units .26 m/s2 .28 m/s2 .27 m/s2 .81 m/s2 .27 m/s2 3 mass units .19 m/s2 .20 m/s2 .21 m/s2 .60 m/s2 .20 m/s2 WHAT KIND OF GRAPH IS APPROPRIATE? Line graph or bar graph? WHAT STATISTICAL DESCRIPTIONS ARE APPROPRIATE? Descriptive statistics Central Tendency Variation Inferential statistics t Test Chi-Square Q8 BOX AND WHISKERS PLOTS Lower extreme - line Lower Quartile 25% of values below this Median line in box - 50 % of values above / below line Upper Quartile 75% of values below this Upper Extreme - max value EVALUATE Find a way to make the Fan Cart Gizmo look like this graph. When you are successful, explain what you needed to do in terms of force, time, and direction