Archi-Math for Teachers

Value and Expectations

Archimath Blog

Archimath series focuses on building a truly solid foundation of mathematical knowledge and skill, with deep explorations into algebra, geometry, and general logic and problem solving. In addition to the core content, these textbooks place a strong emphasis on communicating mathematics clearly, doing computations efficiently, and using common sense to check if answers and results make sense. The series has been written, translated, and edited by a group of talented mathematics educators with a focus on developing strong mathematical intuition and preparing students for high level mathematics.

 

This affordable textbook series is structured to provide a smooth experience for students and teachers alike. Each set consists of a textbook and a workbook, providing a full math curriculum for one semester. In the textbooks, each lesson fits onto a two-page spread, including the practice problems, making it easier to focus on the topic at hand. The workbooks provide space for students to try the solved examples from the reading on their own, plus additional worksheets to further student understanding. In both books, the exercises contain problems that are extremely similar to the solved examples, as well as variations that require critical thinking skills to transform difficult problems into more manageable ones.

 

These books cultivate a strong relationship between the students and the material; by using helpful color coding, symbols, and by providing appropriate scaffolding for students throughout.

They have been used with great success in :

  • Tehiyah Day School (El Cerrito, CA), a private non-denominational Jewish K-8 school (grades kindergarten through 8th grade)

Head of School: Deborah Massey

  • “Math Taught the Right Way”, a new weekly program in conjunction with the Berkeley Math Circle-Upper at UC Berkeley (grades 5-12) http://mathcircle.berkeley.edu

Director: Prof. Zvezdelina Stankova

                – Geffen Academy, a new middle/high school at UCLA, to commence in Fall 2017 (grades 6-12) http://geffenacademy.ucla.edu

Head of Math Department: Dr. Oleg Gleizer

 

You can check out our demos and choose between paperback and online  formats.

What we offer:

Textbooks with Solutions

Online Materials

Math Workbooks and Worksheets

Check Out Our Materials

Many students who expand their understanding using our program see growth in areas of algebra, geometry, and creative problem solving. It is the best preparation for middle and high school students to tackle college mathematics and beyond. Materials that should be in school, but are often not!

Continuity of the Curriculum

It is most important and advantageous for everyone that:   

The alternative has struck us as a very bad way to organize middle school math education. In- deed, when a person teaches the same grade year after year he/she:

  • gains no understanding of the “big picture” of pre-college math education;
  • shares no responsibility for the continuation of the program in the next grade (and a lot of time will be wasted in the beginning of each school year for the new teacher to test and get attuned to the new students);
  • has no incentive (or responsibility) for reaching the final goals of the program. Yes, I am acutely aware of the counterargument: “I do not want a bad math teacher to teach my kid for all of middle school. I would rather bite the bullet of a bad math teacher one year, so as to get the good math teacher the other year.”

In summary, many parents are (unwittingly) willing for their kids to endure on the average a mediocre middle school education. Can you imagine what kind of damage the “bad” teacher would do to the Temple of Mathematics during that, hope- fully, single year of “bad” math lessons?

Would the next, “good” teacher have the opportunity, or even the incentive, to rebuild the Temple AND cover the new material on top of that? Probably not.

 This kind of “averaging math teaching” is an- other major reason for the tremendous difficulties in U.S. middle school math education.

A teacher must be the asset of math education: equally important (if not more important) than the actual math curriculum! And so, the truth must be spoken: a bad math teacher must be let go, to prevent more irreversible damage to our kids;

 

–         a good math teacher must be treasured and given opportunities to further develop.

 

 

Our Program

 

 

is systematic, excellently organized, and easy to use;

is comprised of 50-minute lessons, each taking only 2 pages in the textbook;

has separate worksheets for class work and for homework;

has an introduction chapter that smoothly leads into the material each year, review lessons and tests of various lengths and difficulty for each chapter, and an extensive review chapter that summarizes and further tests the covered material at the end of each year;

is ambitious, and gratifying to both teachers and students and has been successfully implemented in several schools in the California Bay Area.

 

The Value of a Teacher

 

 As with any textbooks, the present textbooks are just that: a basis for learning. They will come alive in the classroom only through the teacher. Let us not deceive ourselves: there is no universal panacea for the middle school math problems in the U.S. And although the present textbooks have been hailed by pilot parents as:

  • the best textbooks they have ever seen;
  • the most suitable for their children;
  • a resource to easily follow and learn from at home if a child is absent from school or did not understand something in class …

…still, a mediocre teacher will do a mediocre job even with the best textbook in hand. The fact that many middle school math positions are filled by non-specialists in math is alarming and is one of the major reasons for the current general downfall of U.S. middle school math. A non-specialist does not have an “eagle view” of the full middle and high school math curriculum. Although locally, he/she might be able to teach some of the material well, a lot of damage is done by a teacher’s limited knowledge and lack of understanding of what is important in the long run, even if hard to teach. The situation is similar to dropping by parachute the whole math class into the middle of a jungle, giving each student a flashlight, and waiting out- side the jungle to see who will come out alive. A better chance of “survival” will be ensured if the students are given a map of the area, taught how to read and use it, and equipped with the necessary tools, knowledge, and skills to efficiently cope with the difficulties that will inevitably occur on the way out of the jungle. And the teacher has to be there, with the students, every step of the way,… not just waiting for them outside of the “danger zone.” I personally never thought of school math in this “jungle vision” until my own children experienced several different U.S. math programs and the image of the “jungle” resembled more and more powerfully the reality of pre-college math education.

More often than not, non-specialist math teachers in middle and elementary school, for a variety of reasons, decide to change the order, depth, and emphasis of the math program they are teaching from. Not knowing the “big picture” of how mathematics will develop over high school and then college years (and perhaps, not caring about this big picture, since it is not part of their day-to-day job duties), their actions unintentionally destroy the logical structure and goals of the program, whether it is a good program or not. (See earlier discussion of this situation in Section 5: The Temple of Mathematics.) Fortunately, the new math program:

 Is straightforward to follow: every lesson is on 2 pages only! (Most importantly!)

 Ensures accountability from the teachers.

The program is so crystal clear that anyone can track where the students are and what they have covered at any time during the school year. By “anyone” we mean parents, administrators, and random visitors alike. It is essential, though, that a copy of the textbook resides at every student’s home: there is nothing to hide in the program, while there is so much to learn from reading the textbook at home!

When each lesson in the textbook is on 2 pages only, with 6-to-10 exercises, and when the concepts are practiced in the next lessons and incorporated in new situations for better understanding, it is very hard to justify staying on one particular lesson for a week or so (and killing everyone’s enthusiasm in the process. Due to the natural transparency of the material, it is impossible to hide behind phrases like “too much,” “too hard,” or “not well organized” “to be covered all in one year”. And the program does depend on the steady and full completion of the material in every middle school year, in order for the next year to be successful.

A Good Choice for a Teacher for this curriculum would take into account:

The Mathematical Level A teacher with a solid math background who can see several steps beyond middle school, e.g., the high school curriculum, and can recognize:

  • the math concepts,
  • types of solutions, and
  • features of analytical thinking that are indispensable and must be taught and reinforced in middle school, despite how hard it might be to teach them to a young audience unaware of them.

 The Pedagogical Level A teacher who can quickly adapt to new situations and turn them into an educational advantage for the students. A teacher who is constantly attuned to the weaknesses and strengths in students’ background and skills, and who emphasizes accordingly features of the curriculum in a balanced way to match and improve the classroom situation. A teacher who can communicate mathematics to young students.

The Level of Dedication A teacher who is dedicated to the well-being of the students and who will sacrifice his/her own desire to “shine on the career ladder” to providing a robust math education to his/ her young charges. A teacher who believes in and is ready to undertake and follow closely the new curriculum; who is ready to face the mathematical and cultural difficulties that will inevitably arise in introducing such a program. A teacher who will persevere.

 

The approach and methodology

 If it were up to us, up through 11th grade high school students would study a good balance of Algebra and Geometry topics, mixed with some Number Theory, Combinatorics, Probability, and Statistics. And only in 12th grade, with a solid preparation and math maturity under their belts, would they venture into advanced concepts such as limits, continuity, and derivatives, which comprise about half of Calculus BC. Thus, during their senior year, they would study thoroughly and deeply:

  • sophisticated definitions like the e-d definition of limit,
  • and powerful statements like the Intermediate and Mean Value Theorems, and the occasionally “dangerous” L’Hôpital’s Rule,
  • along with their proofs and relevant problem-solving techniques. A rigorous treatment of this material would take time and sustained effort from both teachers and students, and a whole year may be barely enough.

But this would be “the right prequel to college math courses” and “the right way to learn Calculus.”

Our students would thus march into college with fortified math knowledge and skills, and a clearer understanding of how mathematics works, better prepared for success in their college freshman math courses.

Archi-Math for Students

Archi-math for Students

Archimath Blog

Many students who expand their understanding using Archimath see growth in areas of algebra, geometry, and creative problem solving. It is the best preparation for middle and high school students to tackle college mathematics and beyond. Materials that should be in school, but are often not!

What results can we expect from students that are using Archimath’s textbooks

Our program prepares students:

to enter high school and college with confidence in their math skills and knowledge;

to be successful at any level of high school and first-year college math classes;

to develop maturity and a life-long relationship with mathematics that:

will distinguish them among their peers;

will serve them well in any profession and in any endeavor in which they chose to engage.

to effectively learn from a textbook that’s deep, systematic and doable

solution for parents who want the best math foundation for their kids

engaging math curriculum that students love, with reading and writing elements that develop critical thinking skills.

rigorous materials that teach in depth problem-solving skills, preparing students for exams and build the necessary foundation for math contest.

Stepping board for Ap exam, preparation for successful college math

courses ( in particular SAT exams)

 

How are we going to add more value to the students

 

  • Our steps to success

Reading Mathematics

Logic and Communication

Writing Mathematics

Multiple Solutions

Efficient Solutions

 

This textbook series creates the environment for a strong bond between the student and the material, in the difficulty and breath of math content; in the expectations of quality, depth, and rigor of student work; by building a robust Temple of Mathematics: always depending on previous knowledge and reinforcing it via new applications and without needless repetition; always looking ahead and linking current material to new things to discover by a gradual climb:

You can check out our demos and choose between paperback and online  formats.

 

What we offer:

 

Textbooks with Answer Key

 

Online Materials

 

 Math Workbooks and Worksheets

 

Check Out Our Materials

 

At any time throughout the school year the place and importance of the concepts, ideas, and techniques studied are clear within the “bigger picture” of Mathematics.

… There should be order, balance, and harmony in everything we do, teach, and learn. We cannot lower our standards when teaching mathematics to young minds. On the contrary, we must be especially careful because of the hierarchical structure of mathematics.

And thus, the present textbook series* has found the golden ratios*: mathematically sound and pedagogically sound;  the practical and the inspiring.

The textbook series promotes at all times

  • Simplicity and Elegance:

In anything we do, especially in mathematics.

  • Courage: Not being afraid to make mistakes and to learn from them.
  • Diversity of Ideas: Via multiple solutions to the same problem.

First and foremost:

  • Learning to Think Deeply:

Make connections with previously learned material.

These are not just catchy, “politically correct” phrases intended to sell more copies of this textbook. They truthfully describe this math program and help build a solid math structure, with adjoining “walls, windows, and doors,” through which to move from topic to topic and make connections between various concepts, formulas, and ideas.

More about what results can we expect from students that are using these textbooks?

The present program extends the mathematics taught in elementary school and completes it to a comprehensive K-12 math program that prepares students:

  • to enter high school and college with confidence in their math skills and knowledge;
  • to be successful at any level of high school and first-year college math classes;
  • to develop maturity and a life-long relationship with mathematics that:
  • will distinguish them among their peers; –
  • will serve them well in any profession and in any endeavor in which they chose to engage.
  • to effectively learn from a textbook that’s deep, systematic and doable
  • solution for parents who want the best math foundation for their kids
  • engaging math curriculum that students love, with reading and writing elements that develop critical thinking skills.
  • rigorous materials that teach in depth problem-solving skills, preparing students for exams and build the necessary foundation for math contest.
  • Stepping board for Ap exam, preparation for successful college math curses ( in particular SAT exams)
  • Problem-solving education that helps students excel in school and on tests while also encouraging them to pursue a deep, focused understanding of the content
  • Challenging problems presented in a way that encourages students to keep trying, teaching perseverance, proofs and world problems

Program that is deeply aligned with the Common Core Mathematics Standards and suitable as an in-depth supplement.

 The approach and methodology

If it were up to us, up through 11th grade high school students would study a good balance of Algebra and Geometry topics, mixed with some Number Theory, Combinatorics, Probability, and Statistics. And only in 12th grade, with a solid preparation and math maturity under their belts, would they venture into advanced concepts such as limits, continuity, and derivatives, which comprise about half of Calculus BC. Thus, during their senior year, they would study thoroughly and deeply:

  • sophisticated definitions like the e-d definition of limit,
  • and powerful statements like the Intermediate and Mean Value Theorems, and the occasionally “dangerous” L’Hôpital’s Rule,
  • along with their proofs and relevant problem-solving techniques. A rigorous treatment of this material would take time and sustained effort from both teachers and students, and a whole year may be barely enough.

But this would be “the right prequel to college math courses” and “the right way to learn Calculus.”

Our students would thus march into college with fortified math knowledge and skills, and a clearer understanding of how mathematics works, better prepared for success in their college freshman math courses.

Archi-Math for Parents

Archi-math for Parents

Archimath Blog

This affordable textbook series is structured to provide a smooth experience for students and teachers alike.

Each set consists of a textbook and a workbook, providing a full math curriculum for one semester. In the textbooks, each lesson fits onto a two-page spread, including the practice problems, making it easier to focus on the topic at hand.

The workbooks provide space for students to try the solved examples from the reading on their own, plus additional worksheets to further student understanding. In both books, the exercises contain problems that are extremely similar to the solved examples, as well as variations that require critical thinking skills to transform difficult problems into more manageable ones.

 

These books cultivate a strong relationship between the students and the material; by using helpful color coding, symbols, and by providing appropriate scaffolding for students throughout.

 

Many students who expand their understanding using Archimath see growth in areas of algebra, geometry, and creative problem solving. It is the best preparation for middle and high school students to tackle college mathematics and beyond. Materials that should be in school, but are often not!

 

Our Program is:

 

is comprehensive and easy to understand, written in a straightforward and simple manner, encompassing materials that are often missed or superficially covered in school;

is suitable for motivated learners, ready to explore new material;

provides easy-to-use resources for students working with parents or tutors;

expands students’ understanding and growth in algebra, geometry, and creative problem solving, as well as probability and statistics;

is the best preparation for middle and high school students to tackle college mathematics and beyond.

 

Check Out Our Materials

 

More about what results can we expect from students that are using these textbooks?

The present program extends the mathematics taught in elementary school and completes it to a comprehensive K-12 math program that prepares students:

  • to enter high school and college with confidence in their math skills and knowledge;
  • to be successful at any level of high school and first-year college math classes;
  • to develop maturity and a life-long relationship with mathematics that:
  • will distinguish them among their peers; –
  • will serve them well in any profession and in any endeavor in which they chose to engage.
  • to effectively learn from a textbook that’s deep, systematic and doable
  • solution for parents who want the best math foundation for their kids
  • engaging math curriculum that students love, with reading and writing elements that develop critical thinking skills.
  • rigorous materials that teach in depth problem-solving skills, preparing students for exams and build the necessary foundation for math contest.
  • Stepping board for Ap exam, preparation for successful college math curses ( in particular SAT exams)
  • Problem-solving education that helps students excel in school and on tests while also encouraging them to pursue a deep, focused understanding of the content
  • Challenging problems presented in a way that encourages students to keep trying, teaching perseverance, proofs and world problems

Program that is deeply aligned with the Common Core Mathematics Standards and suitable as an in-depth supplement.

 

Can girls succeed in math?

 Upon coming to the U.S., I was shocked by this question. I was raised in a provincial town in Bulgaria and made it as a high school student to two IMOs, winning silver medals. There was another girl on the Bulgarian team for the 2 years I was there. It took the U.S. 25 years of participating at the IMOs before the first U.S. girl, Melanie Wood, qualified for the IMOs. I was privileged to train the U.S. national team when the Melanie competed at the IMOs, also earning two silver medals. Later, I participated in the training of the other two U.S. girls, who went on to win gold medals at the IMOs. To cut the long story short: anything is possible and gender does not matter as far as mathematical talent and success are concerned.

Gender apparently matters in the social and cultural aspects of education, and this severely handicaps many U.S. girls who might have otherwise become excellent mathematicians. Decades after competing at the IMOs, I learned that Bulgaria is the top country in the world in sending the largest number of girls, 21, to the IMOs. Germany and Russia are next, with 19 and 15 girls, respectively. USA has only 3 girls so far. Perhaps, it is time for the U.S. educational system to follow examples of other programs from around the world that have been hugely successful in raising generations of women who are highly educated in math and other STEM (Science, Technology, Engineering and Mathematics) disciplines, and who have been brought up to think of men and women as intellectually equal.

Why America is bad at math?

Research shows that the way math is taught in schools and how its conceptualized as a subject is severely impairing American student’s ability to learn and understand the material.

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Introduction to the Program

I have been asked over and over again by parents, students, and teachers alike: ”Can you give us good textbooks for our middle and high school math curriculum? What we have is not working and it hasn’t worked for years!“

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Learn more about our curriculum and its benefits

Every year, for the past 20 years, while working* with 500 students in grades 5-12 at the Berkeley Math Circle (BMC), I have been asked over and over again by parents, students, and teachers alike:

”Can you give us good textbooks for our middle and high school math curriculum? What we have is not working and it hasn’t worked for years!“

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Zvezda

Zvezdelina Stankova is a teaching professor of mathematics at UC Berkeley and the founder and director of the Berkeley Math Circle, a weekly math circle for elementary, middle and high school students. She found her passion for mathematics as an elementary school student growing up in Bulgaria.

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Value and Expectations

What is the added value? With Archimath

There should be order, balance, and harmony in everything we do, teach, and learn. We cannot lower our standards when teaching mathematics to young minds. On the contrary, we must be especially careful because of the hierarchical structure of mathematics. And thus, the present textbook series* has found the golden ratios

Continue reading