Math is an important activity in today’s world because it opens doors and provides skills needed for life and further academic work. Math will be used by the student both in the tasks of daily life and of the workplace, in ways which are not necessarily predictable or anticipated. Every student should develop his or her mathematical powers and become willing to approach problems mathematically. We work to instill a positive attitude and self-confidence in students by providing a variety of activities directed towards different learning styles.

Mathematics is not merely a static body of knowledge, formulae, and factual information. Mathematical knowledge develops from and enhances a variety of activites and experiences in problem solving. Mathematical activities include:

• counting,
• measuring,
• finding patterns,
• estimating,
• experimenting and making conjectures,
• evaluating results and outcomes,
• finding appropriate mathematical models for situations,
• choosing appropriate methods of notation and mathematical manipulation,
• communicating mathematically,
• making connections,
• exploring ideas and asking questions,
• reasoning deductively to explain or justify conclusions,
• developing new ways of looking at things, and
• finding new methods of approach.

We want students to be able to “do math”, to be able to attack a variety of problems, to enjoy math, to work on others with math problems, and to be able to learn new materials. We want them to have a broad background to serve as a foundation for whatever math they might need in their adult life – both in careers and life skills. More specifically, we want to prepare them for the next step in their mathematical career, from elementary grades to college work. The outcomes are developed by the Department, in the context of student needs, with reference to the NCTN and State Standards.

Curriculum Notes

The Sant Bani School math curriculum is developed with the belief that children are natural learners and enjoy discovery. At the younger grades (grades K-7) much learning is done through hands-on processes and discovery. Practice is also important. Students learn best if they can become active participants in what they are learning. Each student has a unique background of mathematical concepts, number sense and spatial sense, along with a unique learning style. Teachers provide materials and problems through which the students can build upon and develop their foundation of knowledge and understanding. Students are taught to use their judgment to evaluate and check procedures. Experience with concrete materials precedes visualization and pictorial methods of work, and these precede the more abstract pencil-and-paper operations and mental math. The more concrete experiences the students have to refer to, the greater their ability to understand and use the concepts involved. Listening to the students as they ask questions or explain their ideas and work is essential.

In Eighth Grade, students start the Interactive Mathematics Program. Three more years of IMP are required, with options such as Calculus and mini-math courses being offered in order to take four or more math courses in high school. Throughout the grades, problem solving (seeing different ways to solve problems, learning how to extend problems and seeing inter-relationships among problems) is stressed. An integrated approach is important at all levels so that students develop a connection to math within topics of math as well as to topics outside of math. Connecting math to the student’s world is important. Students learn how to communicate verbally and on paper about their learning processes. Students often learn within the context of cooperative groups. Homework is an important component of math classes. Daily homework boosts mathematics achievement. Parents are expected to support regular homework assignments.

__Department Head: Jonathan Powell

__How Can I Help My Child?

Parents can help their children develop into independent learners and thinkers as well as develop their thinking and reasoning by asking questions such as:

• Does this remind you of other problems you’ve worked?
• What have you come up with so far? (Write down whatever you have tried on your homework, even if it is not correct so your teacher can see where you need help).
• Where do you think you should start?
• What is the problem asking you to do?
• Would drawing a picture help?
• Can you break down the question into parts?
• Can you work out a simpler problem?
• What do you know so far?
• Can you find examples in your notes or previous assignments?
• Can you show me what you did in class today?
• How can I help you?
• How did you find your answer?
• Why does that work?
• Is there another way?
• How do you know it solves the problem?
• Have you ever solved a problem like this before?
• Do you see a pattern?
• Can you convince us that your answer makes sense?
• Is it true for all cases?

Remember that wait time is important when asking questions. Wait at least ten seconds to allow children to think.

Links for Math Programs Used

IMP

Connected Mathematics

Investigations:

• Scott Foresman
• TERC
• Center for STEM Education at Northeastern University
• The ARC Center (information about the three NSF-funded elementary programs)
• Portland Public Schools Family Mathematics Resource
• Everett Public Schools Online Math Resource
• National Library of Virtual Manipulatives

Game 24 (Basic Facts practice for Grades 1-5)

Australian Math

Student Comments

IMP

__"The concepts we learned were thorough enough so that we will most likely not forget any of them."

“Having two teachers was nice because we could hear things from two different people and maybe one of them would make something more clear for one concept and then the other would make a different concept clear for you with different points of view and ways of saying things.”

“I think my confidence has grown exceedingly high and I am glad for that. … I felt like it was a great help to work with others. It was good to know that you can always look to people if you do not understand something from the book. I also enjoyed helping others too because it also boosted my confidence within myself knowing that I understood the work.”

“I would say that this year was different because it was more related to real life, for example, things were tied into something that we might actually use it for. I definitely think my group skills have improved this year, because we are always with our group.”

“I really like that the year is split up into units about a lot of different mathematical ideas, instead of a lot of basics. I learned a lot about math this year. I also am working a lot better with other people than I did in the beginning of the year. That is one of the neat “side-effects” of this mathematics program; our people skills improve.”

“I liked being in groups going over homework. That way I saw how other people might have done an assignment … So I did get more confident about my work on homework assignments. I really liked having two teachers available because if one of them was busy the other one was usually open to help so for me it helped me get more time with a teacher in class. This I know is important because in public school there is less time a teacher can help a student when there are so many of them.”

“This unit was different from others because we learned a lot on our calculators. … We learned much more advanced math than we have in the past.”

“We worked very hands on in this unit and with pictures, which really help me in math. I find that the more hands on things are, the easier things are to explain. I love being challenged. The teaching was also very good and helpful. I have changed because now I am confident in my math. I feel that I can work as a team and working in groups in math did help my team building. I want to say thank you for the fun classes and pushing me to become such an improved student.”

“This experience was different for me this year because we did the experiments to find out the problem, not just you supplying us with some (perfect) results. I guess I haven’t changed much because of just this class, but I believe that it made me more interested in some of math’s aspects and less interested in the others.”

“I’ve learned more… Overall, I thought this and other units were interesting and really, really confusing, and had good teachers.”

“This program covered a lot of parts of math in one year and normally I don’t cover as many points. The math I learned was at the right level because it was not too hard, but I did not know it. I think I have more confidence in the work I do and the answers I get. I also have more confidence in other people in my group. I learned a lot this year and I will try to put what I know to use.”

“I like the program because of some of the activities we did like the pioneers, but I didn’t like the huge text book we had to carry home every day. I feel like my confidence has boosted in math. I have learned a lot this year and have progressed significantly. I think that I do work better with others now because of this program.

Connected Math

“I liked the textbooks we used because they explained things more clearly than the books I had in public school. My two favorite activities we did this year were Elmart and Money Market. It was a fun activity that let us move around the room and it was cool to see how you could find something that was worth a certain amount of money and then you have to take the tax of it so the price was different which made it tricky. The other one was Money Market. I liked it because we got to choose our amount of each money and trade with other people money and compare our amounts.”

“Well, we really haven’t had any other book to compare it to, but the mathematical reasoning is very clear and easy to understand. There is that certain element of challenge, but there still is that simple straightforward question. I enjoyed ElMart (even though I was off) because it was sort of a real life situation. I kind of liked the Map of the United States because it was easy but still you had to be mathematical when you guessed the size, and some of the answers surprised me.”

“I really liked the textbook we used this year. … I think we should continue to use them. I really enjoyed a lot of activities we did this year. My favorites though, were ElMart, the Chocolate Bar fractions, and Ellen’s diner. I can really say the same thing about all of them: they were a lot of fun and not at all dull or boring.”

“I pretty much liked the textbook we used this year, because it is not big and heavy and also has interesting or straightforward problems in it. My favorite activities this year in math class were the proton/anti-proton addition grids and the positive/negative card game because they were fun.”

“I liked the textbooks because there was nothing not to like about them. I enjoyed the ElMart and money market activities. They were good arithmetic and involved lots of strategy.”

“I really liked having the textbooks that were small enough to fit in our binders instead of having one big textbook that we would have to lug around in our backpack. Probably my favorite activity was the protons/anti-protons because I didn’t know much about it and when I figured out how to do it, it was really easy and fun.”

“I thought the textbooks were good. We kept on track the whole year, and knew what we were doing. I liked that we could look back, and if we were stuck on a problem the glossary was there or former problems that explained how to do them. I liked the activities that you did outside the book also though. I liked all of the activities. My favorite was probably Money Market. We learned how to use our money different ways, and find some rules… You could strategize with yourself or others.”

“My favorite activity this year had to be ElMart. I enjoyed the different items that had been cut out of magazines with the real prices of the items. Following in a close second would be the addition (proton/anti-proton) grids on the computers. I had a lot of fun on it.”

“I liked the textbook we used this year because it showed you how to do things and then let you do them, and everything made sense, but at times it was repetitive. I though both the ElMart and the money market activities were fund and interesting because they were very hands on and interactive.”

“I thought that the textbook we used …was overall pretty good. I liked the way they illustrated what they wanted and that made it more interesting. The way they used real life situations I thought was very helpful giving us a reason why we should learn the technique. The activities that I enjoyed most this year and thought I learned the most from were ElMart, because it let us choose things that we were interested in to buy and gave us a motive for wanting to get as close to $1000 as possible. The games I enjoyed because they gave us a chance to use our skills that we had learned and want to use them, giving us a motive fore being better at them. The true/false quiz I liked because it gave us an opportunity to guess and see if we were lucky or not while still learning math.”

“I liked some of the stuff we did in the textbooks and I liked the size of the textbooks but I felt like sometimes the textbook combined weird things together and went into a little bit too much explanation. I enjoyed the Map of America because I got to argue and I got to do something that I am not very good at (I have spatial issues) but I had a lot of fun doing the activity because it related to something that I will use in my life.”

“I liked the textbook because they were easy to carry around. I also liked how the textbook taught us how to do things that we might need in real life, like figuring out how tall something is by its shadow and a meter stick’s shadow. I enjoyed a lot of the activities. I think any activities that we do are a fun way to learn how to do a particular thing. It is good not only to do problems during class, but if we have hands on things to do, it will make more of an impact on our memory therefore keeping it in our head.”__