This blog begins with the importance of correcting all mistakes made on all assignments and ends with cutting-edge thoughts on "teaching to learn."
As we begin the 2019-2020 school year, it feels essential to send a brief message regarding the need for students to:
1. Correct all problems missed on any assignment: homework (HW), quiz, or test. And,
2. Correctly teach forthcoming assessment materials to an audience in advance of every exam. Such materials may be and/or include: study notes, pretests, announced and/or projected problem-types, etc.
Regarding Number 1: Correcting All Problems
The best thing to do for success in any math course is to stay current by working on HW and HW corrections. Any HW problem missed usually indicates the need to generate a number of similar problems to be worked and reworked until the student is confident that he/she knows how to work that problem-type.
But quiz and test corrections are also essential. While most students find it difficult to do quiz/test corrections when it is not toward the end of getting a new and higher score on that particular assessment, doing so will make all the difference. Since my exams are often comprehensive, to some degree, a student who can work all previous questions/problem types will typically see exam scores increase throughout the school year. The comprehensive element to my class and exams is what lays such a solid foundation for those students who actively engage in all of the above learning/learning strategies (which make correcting mistakes such a strong and pivotal role).
Regarding Number 2: Teaching to Learn
All students should work/rework every pretest and also successfully teach it to an audience as a significant exercise in taking themselves to the next level in their mathematical capabilities. Please make this a fun event and enjoy watching students grow as the year progresses.
On the principle of "teaching to learn," see this article on what some have called "The Protege Effect:"
Teaching the pretest to an audience in advance of the exam will require more of a time commitment, up front, but strong capabilities in math are well worth the time and the effort.
Finally, please remember that, even if you obtain outside tutoring assitance, it is still important to work on problems with Mr. Peters whenever there are difficulties; this will help him to track your improvement and will add still more to the quality of classroom instruction: knowing what concepts still present barriers to your success will help me address those things via review, bellwork, and overall lesson planning.
SPA Math Instructor