The question of how to grade homework efficiently and effectively is one that many teachers struggle to answer. It is brought up in meetings and textbooks consistently. I currently grade homework based on effort. If the student completes the homework with full effort then they receive full credit, whether or not all problems are correct. Questions may be brought into class and answered by me or the students peers. The main reason I grade homework based on effort is because I want homework to be practice. I do not expect every student to get every question correct the first time around. This method, in my opinion, works, but I was struggling with the challenge of devoting a significant amount of class time to homework questions. Some students needed to see the questions completed and others sat there bored. Also, the answers to the homework questions are in the back of the back and I request that students check their answers. Some students did and others did not, so some knew which questions to ask and others didn't. Another downfall is a student lacks the encouragement from me to revisit incorrect answers and correct them. So, I debated a few options: collect homework and give individual feedback, collect homework intermittently and give individual feedback, continue grading homework based on effort, but don't go over questions in class. I had a few options, but nothing struck the right chord with me. So I researched what other math teachers were doing and found a great resource on National Council of Teachers of Mathematics (NCTM).
The plan for homework is this:
I cannot contain my excitement for this information! I just want to tell every single person I cross paths with about these study habits, primarily retrieval practice.
Us teachers often have a review day and then tell our students to go home and study. Well...what does that mean? I think, and have found that many students do not know. I tutored Calculus 1 in college for 3 years and our focus at the Tutor Center was not the content, but rather the study skills. If we, as learners, know how to learn, then we can master any subject.
I came across these study habits while listening to my favorite podcast on my drive to UMF for my Graduate class. The podcast can be found at https://www.cultof
pedagogy.com/learning-strategies/. Jennifer Gonzalez interviewed Megan Smith and Yana Weinstein on their research about Learning Strategies. While listening, I compared my study habits with their strategies and realized that I naturally did all of them, but many students do not. Many students either don't know where to start or think they are studying when they really aren't. I often think of rereading notes or a textbook. The student thinks they are reviewing and studying, but this does not build new pathways in the brain or bring content into long term memory.
I will provide a brief introduction to each strategy and explain how I use it in the classroom, how your student can use it, and how you can use it with your student. Megan and Yana provide posters discussing each strategy that can be found at https://static1.squarespace.com/static/56acc1138a65e2a286012c54/t/57d03e669de4bbd3567d57a6/1473265254536/All-Color-Posters.pdf. I will be posting these in my room and discussing each strategy with the students.
1. Retrieval Practice
This strategy is the underlying practice in all of the other strategies and the one that I am obsessed with. The main idea is that the student puts away all of their materials and attempts to retrieve content from their memory. The student then checks their materials to see if they were right. This is often seen in flash cards and practice tests.
2. Spaced Practice
With this strategy the student spreads out their studying over a longer period of time compared to a few days or the night before. Yes, cramming can get a passing grade, but that information is only going into short term memory and will not be accessible in the next lessons or for future exams. We all know that math builds on itself!
This one is self explanatory in that the student would elaborate on the concept, asking why and connecting it to other concepts, comparing and contrasting these concepts.
Swap back and forth between concepts rather than doing the some problem over and over. When they discussed this on the podcast I thought of every single math teacher I had and of myself. Homework in math is often the same problem repeated a number of times. I will be changing this in my class!
5. Concrete Examples
For an abstract concept have a concrete example and multiple examples.
6. Dual Coding
Tie visuals to concepts and find different ways to represent information.
This week we really got going on some exciting content!
BC Calculus is cruising through their review of AB topics and have demonstrated mastery on a pretest of Chapter 3 topics including basic derivatives and particle motion. We have covered Chapter 4 and introduced a new BC Topic! We played around with parametric equations and how to take a derivative of such functions.
AB Calculus is underway with Limits. This is their first taste of an abstract concept. Limits have a procedure and set of steps to follow, but to answer questions correctly one must have a true understanding of the concept. It may have caused confusion for some at first, but I believe we are getting the hang of it.
Honors Algebra 2 has PSAT warm up questions to start every class, but the class got to experience a full PSAT test on Wednesday, where we took a break from our Algebra 1 review. We talked about some strategies when taking the PSAT and SAT. They took their first test on Friday over Algebra 1 review.
Honors Advanced Algebra with Trig also starts every class period with PSAT questions as Freshman will be taking the PSAT instead of the NWEA this year. It's always good to get some practice and experience in working with these types of questions. The class took a Quick Quiz this week. These Quick Quizzes are a way for the student to see if they are following along and keeping up with the content in a low stress situation. The Quick Quizzes can be retaken as many times as the student wishes before the Chapter Test. It also provides invaluable retrieval practice. Also, we are moving into new content as well, specifically complex numbers.
BC Calculus will be working on challenge activities to strengthen their understanding of Implicit Differentiation and Chain Rule as well as reviewing for an upcoming test over Chapter 3 and 4.
Both Blue and White day AB Calculus's will be reviewing and testing over Chapter 2.
Honors Algebra 2 will be moving on to new content next week. We will be discussing some of my favorite topics including piece-wise functions and transformations of parent graphs. These concepts are crucial for future courses, primarily Calculus!
Honors Advanced Algebra with Trig will be continuing to learn new material including completing the square and parent graphs!
Some students come into class with a math phobia. I understand that some of you may also dislike math and have an aversion to it. I ask that you please try to be positive when talking about mathematics. I work hard in building a class that students enjoy and find value in the content. I try to build curiosity into my class, so students are interested and buy in to what I am teaching. Ask your students what they learned in math! Encourage them to talk about and get excited about their ability to understand the concepts.