Early math: ws 62 new material day 3

These sets of worksheets are very repetitive. Each is constructed based on the material considered in the previous one, hopefully, giving students an opportunity to view the material from geometric, numerical, graphical, and algebraic perspectives. Many mathematical concepts take time to process. In a classroom, students take the worksheets to the board and help each other, and the teacher jumps in when needed. More topic practice can be found in the playlists. Link to ws # 62 https://docs.google.com/document/d/1j... Grading policy: A holistically taught math class and grading policy In a holistic approach, many of the term’s topics, especially the most challenging ones, are introduced early in the semester and then the skills and associated concepts are practiced and discussed throughout the entire duration of the course. Usually, within the first three weeks of the semester, 75% of the course content has been introduced. Students are given numerous tests to determine areas of weakness with many subsequent opportunities to learn from previous mistakes. Tests are lengthy and challenging. Patterns of performance tend to be established from the first test, but often hard working students initially in the median range of performance close the gap towards the higher range scores by the end of the semester. Midterm and final term grades are based on a student’s cumulative mastery of the material. Credit for each topic learned, whether that concept is mastered during the first week of the term or the last is given. It is very common to have a median of 10% on an initial assessment, even if a significant number of questions are a review from the previous level. These early test scores have almost no bearing on a student’s midterm or letter grade; however, once the high score and median score are announced to the class, students have a general sense of where they stand in the group as well as the opportunity to begin the process of correcting any mistakes made. Students no longer are allowed to proceed with gaps in understanding. The same topics are repetitively covered giving the instructor numerous opportunities to assess whether during class workshops or on tests the depth of that student’s mechanical as well as conceptual understanding is indeed happening. Final letter grades are based on achievable goal posts set by the instructor a month or so before grades are due. This gives students control over their final grades and encourages good effort. Early in the term, tests tend to be 40 questions in length, but towards the latter stages of the term that number often more than doubles. The opportunity to consider a variety of topics each day allows students to potentially see patterns of numerical behavior inherent in the study of functions. Recognizing patterns is the touchstone of one’s learning to think mathematically. Practicing how to express those patterns using symbolic notation is the artistic side of this discipline. In this teaching method, a student has a bit more flexibility in determining the rate at which he or she works through topics which gives that student more ownership of the learning process. While the more traditional methods of grading that are well established in the sequential style of instruction do not seem to fit this type of instruction, grades do still recognize solid academic progress by assigning letter grades in the B range, while the very best students are given well deserved A/A- scores. Test scores are still the major determinant of letter grades, but in-class efforts will also be considered. A nice video to ponder:    • Einstein Never Memorized  Here’s What He D...