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Lessons that inspire critical reasoning and problem solving in mathematics What’s the difference, really? Linear and Exponential Relationships 1. Given a linear function, interpret and analyze the relationship between the independent and dependent variables. 2. Solve for x given f(x) or solve for f(x) given x. Analyze how changing the parameters transforms the 1. graph Represent of f(x)=mx +and b. solve equations and inequalities graphically 3. 2. Write, use, and solve linear equations and using graphical and symbolic methods with Understand the concept of ainequalities function and use function notation one or two variables. Represent solutions on a coordinate graph or number line. 3. Interpret functions that graphically arise in applications in terms of aofcontext 4. Solve systems of two linear equations and algebraically, and solve systems two linear graphically. 4.inequalities Analyze functions using different representations 5. Given a quadratic or exponential function, identify or determine a corresponding table or graph. 5. Build a function that models a relationship between two quantities 6. Given a table or graph that represents a quadratic or exponential function, extend the pattern to 6.make Build new functions from existing functions predictions. 7. 7. Compare the characteristics of and distinguish linear, quadratic, and exponential functions Construct and compare linear, among quadratic, and exponential models that are expressed in a table of values, a sequence, a context, algebraically, and/or graphically, and and solve interpret the domain and range of each as it applies to a given context. Interpret for functions in analyze termsthe ofrelationship the situation 8. 8.Given a quadraticexpressions or exponential function, interpret and betweenthey the independent model and dependent variables, and evaluate the function for specific values of the domain. 9. Given a quadratic equation of the form x²+ bx + c = 0 with integral roots, determine and interpret the roots, the vertex of the parabola that is the graph of y = x² + bx +c, and an equation of its axis of symmetry graphically and algebraically. What’s the difference, really? http://www.ted.com/talks/dan_meyer_math_curricul um_makeover.html What’s the difference, really? Use of multimedia 1.1. Lack initiative 2.2. Lack of perseverance Encourage student intuition 3. Lack of retention 3. Ask the shortest question you can 4. Aversion to word problems Let the students 5.4. Eagerness for formulabuild the problem 5. Be less helpful Exercise New Habits Get comfortable with discomfort Focus on the destination and allow many paths Ask questions about the inside, let the students address the outside Let’s play a game Exercise New Habits Designing “juicy” math problems Work backwards from goals or outcomes Come up with the basic question Encourage perseverance, trials and creativity Support students in providing explanations Review methods as a class (formulate) Give opportunities for practice Evaluate comprehension (not specific skills) Most teachers waste their time by asking questions which are intended to discover what a pupil does not know, whereas the true art of questioning has for its purpose to discover what the pupil knows or is capable of knowing. - Albert Einstein Marty Wilder ([email protected])