ED526b Learning and Assessment in Secondary Math
Unit 6 – Assignment 6.1
Tasks at this level will require the student to remember information or to recognize concepts. Students could be asked to describe the difference between rational numbers an irrational numbers. An assessment for this level of understanding could be to provide students with a list of numbers and have them place the number in the correct category. A second assessment could require the students to memorize the order of operations and then create a quiz to test their knowledge.
At the comprehension level of understanding students are able to work with facts and procedures. They can convert units of measure from one system to another. They should also be able to determine the classification of geometric figures. A task that could be used at this level might be to convert temperature readings from Celsius to Fahrenheit. An assessment for this level could be to provide students with graphic representations of data and have them answer questions based upon the information contained in the graph. Another assessment would require students to put a list of numbers in order from least to greatest.
At the application level students can use formulas and solve equations. They can apply their understanding to problems and calculate solutions. An example of a task at this level might be to have students plot two points on a coordinate plane and then use the slope formula to calculate the slope of the line containing the given points. An assessment for this level might be to have students find the areas of different geometric figures. Another assessment could involve the use of several quadratic equations where students would have to employ the quadratic formula to find the roots of the given equations.
At this level students can interpret results and make deductions. They can sort data and distinguish between various types of information. A task that could be used at the analysis level might be to provide students with sets of data and have them decide how to represent this information using a graph. As an assessment for this level students might be asked to determine the relationship between ordered pair s and to state if the data represents a first or second order relationship. A second assessment could be designed around a linear relationship where students would be given information and the goal would be to develop a verbal model, an algebraic model, and to ultimately calculate a solution to the problem.
The synthesis level of understanding is reached when students can take information and create new methods of working with the data. At this level students can recognize patterns and make predictions from their observations. A task at this level could be to have students discuss the concept of an asymptote or the value of an inverse function as the independent variable grows beyond all bounds. An assessment at this level could be to have students plan and create a method to study a physical system and to determine the mathematical relationship between the variables in the system. Student projects at this level could involve research of a topic and the creation of a presentation to demonstrate the topic. Another way to assess at this level is to provide student groups with a list of clues to solve a problem and to have the students work through the process of developing a plan to find the solution.
At the evaluation level students are able to make conclusions based upon given information. They can justify their explanations and are capable of appraising the validity of a solution. A task at this level would be to work through a mathematical proof. An assessment might be to have students explain and prove the Pythagorean Theorem. Another method of assessment at this level might be to have students solve a system of linear equations and then defend their solution by showing their work and explaining why the method provided the correct solution.