To the Moon and Beyond
By Jason Avent, Ellen Lukasik, Michael West
|
The classroom assessment technique for assessing skill in synthesis and creative thinking that I would use for my project lesson and calendar is the “Categorizing Grid.” Although students will have completed the “Memory Matrix” earlier in the unit, this assessment addresses students' ability to make further connections between algebraic concepts and the properties of special functions. Given the categories of parent functions (linear, quadratic, square root, inverse, exponential, and logarithmic) students will evaluate and analyze equations, graphs, tables, and verbal descriptions of functional relationships between variables. Higher level examples may require algebraic manipulation for the forms to become apparent. To further connect this activity to the project, some examples will describe relationships relating to speed, acceleration, supply depletion, and growth. Students will use these functions to describe and explain their design, flight plan, or special mission to the moon. To assess skill in synthesis and creative thinking, Algebra II students can create a concept map, detailing their knowledge of functions and relationships that exist among them. This summative assessment would give students a chance to visualize connections and tie together the forms of functions with specific properties. I could even show them mine upon completion for comparison! To relate this activity to my project, the concept maps can be extended to include the required applications to moon exploration and space travel. Students can thus use the map as a tool to communicate their project's direction and functional relevance. I appreciated the assessment of skill in problem solving of documented problem solutions. This has been one of few formative assessments that I have read that would be applicable to a long unit introducing and exploring parent functions. Over the course of five or six weeks, students examine algebraic forms, graphs, translations, representations, and ways to solve, recognize, and interpret problems. Using this classroom assessment technique, students could be given problems that require various approaches or methods of solving. Areas of focus calling for additional instruction could be revisited, while those of demonstrated mastery could be confidently set aside. This type of assignment also incorporates the ability to communicate mathematical processes, an all too often overlooked aspect of math courses that is stressed and detailed in the Principles and Standards of the National Council of Teachers of Mathematics. My favorite CAT for assessing skill in application and performance is ¡°Application Cards.¡± In fact, a critical part of my project is having students identify or define applications between various forms of functions and their project. During the fifth six weeks of Algebra II, students learn about linear (y = x), quadratic (y = x©÷), square root (y=¡îx), inverse (y = 1/x), exponential (y=ax), and logarithmic (y=logax) functions. They have to make connections between real world occurrences or phenomena that are expressed as forms of these functions to justify and create their flight plan and purpose as they travel to the moon. Using this assessment early in the introduction of functional forms provides students with a clear understanding of what they are to do, while demonstrating their ability to recognize functional forms in practice. It has the added benefit of bringing math ¡°off of the page¡± and into the real world, creating meaning and context for lesson objectives. Choosing an assessment for students' awareness of their attitudes and values has been the most difficult by far. In fact, I do not recall my math teachers ever including these types of assessments in the classroom! Course-Related Self-Confidence Surveys could be used particularly near the end of the unit of functions to evaluate student perception of strengths and weaknesses in recognizing parent functions, solving and graphing equations, and interpreting translations. If general consensus shows that students lack faith in ability to understand or perform particular tasks, additional instruction could be given. Students that underestimate their skills could be allowed the opportunity to see their true ability. Most probable, individuals that express more personal or unique concerns could be given resources to respond to their needs, fill gaps in understanding, and boost their confidence in addressing admitted difficulties. Although you can't find it in the TEKS, maintaining communication with students and expressing an interest in them individually is an important aspect of teaching a diverse student body. Surveys such as these will in some degree let students know that you are engaged in them enough to ask the questions and read their responses. To assess course-related learning and study skills, strategies, and behaviors, I would use Productive Study-Time Logs. I have had teachers use watered down versions of these in math classes before, and I think they can be quite useful. Students spend widely varying amounts of time studying and completing homework assignments. Although a long study time may be justified, it is also likely that some students may lack skills to interpret problems or solve them efficiently. Since my project exists over a unit introducing and emphasizing various functional forms and their properties, indications that students have either mastered concepts or lack clear understanding would allow me to adjust classroom activities to respond to students' needs. Thus, I become a more effective teacher, managing resources and tailoring instruction as needed.
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
