I remember being in math class as a student and pretty much everyday was the same. Notes, practice, and then finish up the assignment at home. The only time the patterned changed was if there was a test.
What I have found is that the math culture has changed and students are much more willing to ask the teacher, "why are we learning this" or "when am I ever going to learn this." I remember thinking the same thing, but never saying it out loud.
We all have a natural desire for variety, so I have found that activities and especially games break the monotony of notes and provides a great way of providing learning through peers. I enjoy the conversations that students have with one another while they are laughing and having a blast with the mathematics.
My favorite is Stats Soccer, which I used for my AP Statistics students. They were so competitive that some of them knew the statistics vocabulary better than I did. I have the activity on teacher pays teachers, but the one I want to go over is Greedy Pig. I heard about this game at a AVID conference and I enjoyed it so much, I turned it into an expected value learning activity.
The activity may seem complicated, but I have had upper elementary students all the way to seniors in high school play the activity. All ages enjoy it, because they can all make the simple choice to either stay in or get out of the round. I like them to play the game a few times because they can start seeing a pattern of how long they should stay in. I like to prime them with a few ideas we have gone over in class, to see if they can make the connection. After they answer the final question, we go over the exact answer using algebra or if we have talked about the geometric mean, I show them how to solve it that way. What makes this activity rich, is the problem solving that is needed with a game they have never played before. Everyone is on a level playing field and I have seen the mathematically gifted lose to struggling math student because of strategy. Mathematics goes beyond solving equations and computing difficult arithmetic. It is all about assessing what the problem is and finding the mathematical model that describes it.
Sunday, February 21, 2021
Tuesday, August 8, 2017
Mathematical Modeling
I am currently teaching a week long summer class on mathematical modeling at Waterhouse Guild in El Segundo, with age ranges from 9-14 including a variety of mathematical abilities. This concept was inspired by a former colleague and friend of mine, Nancy Butler Wolf, Ph.D. She wrote the book Modeling with Mathematics and begins by sharing a story about teaching factors and how all the students understood how to factor, but when the context was changed to a real life problem they could not answer the question correctly. In the same way, some of the students in my class understand slope and y-intercept and are comfortable with graphing, but when I presented the modeling activity, their understanding of these concepts did not give them an advantage over the rest of the students.
I started off with a simple block pattern with three figures on the board and I asked them to show that pattern using the blocks in front of them, and then to use those same blocks to create the next two figures. I have students in groups of 3 or 4 so there is mathematical dialogue, which in my opinion is the best part of the activity -- students conversing about mathematics, what could be better? I then asked them to describe in a sentence what was happening and a 9 year old said, "It {the pattern} is increasing by two." Then an older student said, "It is increasing by adding two blocks on the bottom."
I do not want to bore you with the rest of the modeling activity, but a pattern of wood blocks were able to open the eyes of elementary students to physical modeling, seeing a pattern, coming up with a model, and then projecting what the 50th figure would look like. Even though the algebra students I have know how to write equations and substitute, they had never before modeled mathematics, so they were just as engaged and challenged as the students with no algebra background.
I started off with a simple block pattern with three figures on the board and I asked them to show that pattern using the blocks in front of them, and then to use those same blocks to create the next two figures. I have students in groups of 3 or 4 so there is mathematical dialogue, which in my opinion is the best part of the activity -- students conversing about mathematics, what could be better? I then asked them to describe in a sentence what was happening and a 9 year old said, "It {the pattern} is increasing by two." Then an older student said, "It is increasing by adding two blocks on the bottom."
I do not want to bore you with the rest of the modeling activity, but a pattern of wood blocks were able to open the eyes of elementary students to physical modeling, seeing a pattern, coming up with a model, and then projecting what the 50th figure would look like. Even though the algebra students I have know how to write equations and substitute, they had never before modeled mathematics, so they were just as engaged and challenged as the students with no algebra background.
Monday, August 7, 2017
State the Reason You Want A Tutor
After tutoring for over 17 years, I have realized that not all parents and students same goals. I am going to summarize the different goals in three distinct levels, and with each level there is a greater depth in tutoring.
The first level is wanting the tutor to just help students finish their homework, which requires the tutor to just sit and watch the student work, offering advice only when the student gets stuck. If you are at this level, I only recommend a professional if there is no support from the math teacher or after school tutoring programs. Most schools and teachers have free after school programs that help students or there are student tutors that are excellent and cost effective for this level of tutoring. However, certain students need the one-on-one and feel more comfortable just having someone sitting next to them in case they run into trouble.
The second level is wanting the tutor to help students to raise their grades through homework assistance and studying for quizzes and tests. This requires a lot more skill from the tutor because they have to know what is being tested and be able to create their own problems either beforehand or on the spot. In this case, most peer tutoring ends up in social hour, so the tutoring sessions end up taking 2-3 hours, when a professional tutor could get it done in an hour. Keep in mind that the best option is always tutoring by the teacher, since the teacher knows exactly what is on the test and is free.
The third level is wanting to grow in their mathematical ability or filling in holes of mathematical knowledge. A teacher usually does not have time and group tutoring will also not help with this difficulty either. This is usually what parents desire in a tutoring session, but is impossible to accomplish with only once a week tutoring, unless done in the summer. Once a week tutoring is intended to keep a student on track with the current material. The tutor should meet with the student at least twice a week and it is necessary for the student to be on board as well, otherwise you are wasting your money, because a tutor cannot force learning down a student's throat.
So when making an appointment with a tutor, make sure you, your student, and your tutor understand what the goal of the tutoring sessions are, so you get exactly what you want.
The first level is wanting the tutor to just help students finish their homework, which requires the tutor to just sit and watch the student work, offering advice only when the student gets stuck. If you are at this level, I only recommend a professional if there is no support from the math teacher or after school tutoring programs. Most schools and teachers have free after school programs that help students or there are student tutors that are excellent and cost effective for this level of tutoring. However, certain students need the one-on-one and feel more comfortable just having someone sitting next to them in case they run into trouble.
The second level is wanting the tutor to help students to raise their grades through homework assistance and studying for quizzes and tests. This requires a lot more skill from the tutor because they have to know what is being tested and be able to create their own problems either beforehand or on the spot. In this case, most peer tutoring ends up in social hour, so the tutoring sessions end up taking 2-3 hours, when a professional tutor could get it done in an hour. Keep in mind that the best option is always tutoring by the teacher, since the teacher knows exactly what is on the test and is free.
The third level is wanting to grow in their mathematical ability or filling in holes of mathematical knowledge. A teacher usually does not have time and group tutoring will also not help with this difficulty either. This is usually what parents desire in a tutoring session, but is impossible to accomplish with only once a week tutoring, unless done in the summer. Once a week tutoring is intended to keep a student on track with the current material. The tutor should meet with the student at least twice a week and it is necessary for the student to be on board as well, otherwise you are wasting your money, because a tutor cannot force learning down a student's throat.
So when making an appointment with a tutor, make sure you, your student, and your tutor understand what the goal of the tutoring sessions are, so you get exactly what you want.
Friday, August 4, 2017
5 Reasons to Hire a Math Tutor in September
1. Grades. When starting with tutoring at the beginning of the semester, the student stays on top of the assignments and begins the semester off with a good grade. Mathematics is the subject that progressively gets more and more difficult. So as the semester gets more challenging, they are consistently finishing the assignments and are actively developing stronger skills that grow with the material, instead of the material surpassing their knowledge.
2. Self-confidence. When a student starts off well in a class, they tend to enjoy that class, which leads them to perform better in the class. Self-confidence is developed in mathematics based on success. It is never based off of false praise. Mathematics is one of the few subjects where there is a clear correct answer, so when a student consistently has the correct answer, it makes them feel successful and self-confidence is formed.
3. Discipline. There is something to be said about the story of The Tortoise and the Hare. Students like to cram right before a test or quiz, which will produce short term memory, but not learning that will last. Students that consistently put in the time will have a much better return at the end of the semester. I have had students from basic math skills classes to AP Statistics, and at the end of the year I can decipher the ones who put in the time each day.
4. Problem solving. When I was a young teacher, I went through all the teaching classes and knew all the key phrases you should say, but that was nothing compared to seeing truly gifted teachers. When I saw what great teaching should look like, I grew more as a teacher in one year than I had in all my years of education. There is nothing better than being mentored by a professional in all walks of life. When a student sees an expert solve a problem, they learn to emulate that expert and become a great problem solver.
5. Save money in December. I do not know how many times I have had parents calling me in November or even December asking for tutoring. I hate to say it, but it is too late. A quick cram session for the final might get them to pass the class (if the parent pays for 3 or 4 sessions for at least a week or two), but it does not give the student the confidence for the next semester or teach them discipline. Mathematics is a marathon not a sprint, and truly becoming a mathematically strong student does not happen in one month.
2. Self-confidence. When a student starts off well in a class, they tend to enjoy that class, which leads them to perform better in the class. Self-confidence is developed in mathematics based on success. It is never based off of false praise. Mathematics is one of the few subjects where there is a clear correct answer, so when a student consistently has the correct answer, it makes them feel successful and self-confidence is formed.
3. Discipline. There is something to be said about the story of The Tortoise and the Hare. Students like to cram right before a test or quiz, which will produce short term memory, but not learning that will last. Students that consistently put in the time will have a much better return at the end of the semester. I have had students from basic math skills classes to AP Statistics, and at the end of the year I can decipher the ones who put in the time each day.
4. Problem solving. When I was a young teacher, I went through all the teaching classes and knew all the key phrases you should say, but that was nothing compared to seeing truly gifted teachers. When I saw what great teaching should look like, I grew more as a teacher in one year than I had in all my years of education. There is nothing better than being mentored by a professional in all walks of life. When a student sees an expert solve a problem, they learn to emulate that expert and become a great problem solver.
5. Save money in December. I do not know how many times I have had parents calling me in November or even December asking for tutoring. I hate to say it, but it is too late. A quick cram session for the final might get them to pass the class (if the parent pays for 3 or 4 sessions for at least a week or two), but it does not give the student the confidence for the next semester or teach them discipline. Mathematics is a marathon not a sprint, and truly becoming a mathematically strong student does not happen in one month.
Tuesday, September 27, 2016
Why Tutoring Matters
"So what does correlate with success? One thing emerges very clearly from Bloom's work: All the superb performers he investigated had practiced intensively, had studied with devoted teachers, and had been supported enthusiastically by their families throughout their developing years."
excerpt from "The Making of an Expert"
by Harvard Business Review
Click here for the full article.
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