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: - After the student completes his/her homework he/she will check the answers in the back of the book. If he/she has answers that are incorrect, he/she will go back and try to fix his/her mistakes. The student can do this as many times as he/she wishes. Checking answers and fixing incorrect problems.
- After the student has done the best he/she can do at that time, he/she will mark answers either as correct, or not correct yet and will write the number of correct answers out of the number of problems on the top of the page.
- When the student comes to class he/she will pick up and fill out a homework slip. The student will pass this slip in to me and I will store their current homework grade (correct/total).
- The student has one week to receive extra help, ask questions, correct the homework, and resubmit his/her work for a new grade of up to 100%.
- The student will email me the updated number of correct problems.
- On any evening the student may be revising old assignments and working on new homework.
This is great for retaining information! It is called interleaving (see study tips below).
- To ensure honesty:
- I will randomly select a students homework to collect and check to see that the number of correct problems is the number written on the homework slip. The calculator can randomly select a numbers, so I will use this tool.
- I may call on a student who claimed success on a problem to assist in completing a similar problem.
- I will spot check the re-submitted homework. That is, I may ask for a students resubmitted homework to check for an honest self report.
- This class is for the student to learn, so this method makes the student responsible for his/her learning.
- The student decides whether he/she needs more assistance and is motivated to come in for that extra help.
- It rewards the student for perseverance.
- The method encourages a growth mindset.
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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. - In the Classroom
- Warm Ups: questions are over content from previous classes.
- Brain Dumps: I ask the students to write down everything they remember about a certain topic and then they check their notes/share with a peer and see what they know and what they are missing.
- Quick Quizzes: a low stress assessment (the student can retake the quiz as many times as they wish before the chapter test) that forces the student to retrieve content and receive feedback
- The last 5 minutes of class I ask retrieval questions with the students materials packed away
- During notes I ask retrieval questions, tying in previously learned content.
- Outside of the Classroom
- Flashcards
- **it is so important that students actually retrieve the information and do not cheat themselves by saying "oh, I know this" and flipping the card over without actually retrieving the answer.
- Practice problems without the procedure or examples in front of them.
- Flashcards
- Parent and Student
- Ask your student what they learned in class today, last class, last week, last month. Get your student to retrieve that content and bring it into short term memory. Allow the student to check if they are right and add to their answer. (The feedback is just as crucial as the retrieval.)
- Ask your student to explain a concept for you.
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! - Inside the Classroom
- Warm Ups: Some questions may be from very old lessons allowing for that space in between.
- Homework: I include problems from previous sections.
- Outside the Classroom
- Reference Sheet: I talked with the students about creating a reference sheet where the student would have one page for each chapter. After a lesson the student would take this sheet out and try to remember as much content as they can and then fill in gaps and other content they forgot.
- Review notes from old lessons
- Start studying two weeks before a test. I provide a syllabus of the full chapter so the student knows, from the start, when the test will be.
- Parent and Student
- Remind your student to be reviewing old content
- Ask the student to explain old concepts to you
3. Elaboration 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. - Inside the Classroom
- I ask students to compare and contrast concepts
- We discuss how new concepts connect to old concepts as well as what skills you need from old concepts to do the new problems.
- Outside the Classroom
- The student would elaborate on a topic and check their notes to see if they are accurate.
- Parent and Student
- While your student is explaining a topic to you ask them why questions, ask for them to elaborate, compare and contrast this topic with something else they have told you about in math or in another subject.
4. Interleaving 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! - Inside the Classroom
- Homework: I include problems from previous sections
- Notes: I include a problem or two from earlier in the chapter
- Outside the Classroom
- The student can review the ideas in different orders
- Mix up those flashcards!
- The student can review the ideas in different orders
- Parent and Student: This strategy is very similar to spaced practice and goes hand in hand with it.
- Remind your student to be reviewing old content
- Ask the student to explain old concepts to you
- Remind your student to be reviewing old content
5. Concrete Examples For an abstract concept have a concrete example and multiple examples. - Inside the Classroom
- I provide examples for all abstract concepts. Calculus can be very abstract and it is crucial to have something concrete for the student to hold on to and connect.
- Outside the Classroom
- Collect the examples given in class
- Create your own examples
- Ask why the example applies to the concept
- Parent and Student
- Ask your student what examples he/she has for a given concept
- Ask you student why an example applies to the concept and have her/him elaborate
6. Dual Coding Tie visuals to concepts and find different ways to represent information. - Inside the Classroom
- Visuals are amazing and one of the many reasons I stand by Guided Notes, because I can add visuals to student notes.
- I have used the strategy of "drawing notes" with tutoring, but never in a classroom and I may introduce this strategy during a warm up or at the end of class. I am interested to see what the students come up with!
- Outside the Classroom
- Look at notes and find visuals
- Compare the visuals to the words
- Explain what the visuals mean with your own words
- Draw visuals to go along with what you are learning
- Parent and Student
- Ask your student how a visual applies to the concept they are learning
- Draw with your student!
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. Coming soon: 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! |
## Math PhobiaSome 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. ## Archives## Categories |