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Archimath Books

These textbooks emphasize the logical structures that seem to lack in the U.S. curriculum. Even starting in the 6A-B series, one can see the build up in knowledge - latter sections require results from previous ones and clearly state so - and the cohesiveness of the algebra and geometry, where the two subjects support each other. When used correctly, the books can explain most results in one lesson, using previous lessons. This structure helps students think mathematically. A true mathematician always asks "Why is this true?" when given a result. It is great to see this type of thinking exposed and instilled in students at such a young age.In the U.S. math is commonly taught by memorizing algorithms without justifications: "It worksbecause I told you so." And everyone knows that this does not sit well with a rebellious teenager. The essence and beauty of math is whether or not an answer to a question can be found. I was taught to question the results when I started 6 th grade axiomatic geometry, using the translated French textbooks in Vietnam. And I am ecstatic to see that the present Bulgarian series provides students the same support and opportunity to question and develop their understanding of mathematics.
Harry Mai-Luu
BMC/MTRW assistant and instructor
I grew up in the U.S. with textbooks ... ... that were rote and unmotivated, with no applications for algebra students, no geometry or number theory for 6 th graders, and no guidelines in writing mathematics. The curricula that are popular in the Bay Area at the time of writing have sought to resolve this issue by making the entirety of student education exploratory, without practice or summarization of what is expected - and in both paradigms, the textbook authors take dozens of pages to get to the point. The current adapted Archimedes curriculum, by contrast, gives examples for students to explore and then guides them to correct conclusions. Algorithms are offered only after clarifying their logic and students are taught to work clearly and thoroughly through both numerical exercises and problems requiring more complex reasoning - and all this while calmly weaning reliance from calculators. It picks up where books like Singapore Math leave off, and offers students of all backgrounds and abilities entry into the deeper understanding they require to master future material. Because the topics are covered so thoroughly and a workbook is included with extra problems, there is absolutely no need for teachers to create extra worksheets, which means that the teacher can focus on planning lessons and evaluating student work. The Bulgarian Math textbook is more relaxing for both student and teacher to work from.
Elysée Wilson-Egolf
BA in Mathematics, UC Berkeley
Urban School of San Francisco
When I taught a problem-solving class at MTRW in 2018, I was once again reminded of how ... fragmented and incomplete mathematics curriculum is in a typical American middle school. Even motivated and bright students do not have adequate mathematical language; they lose confidence when trying to solve a problem that is not given in a familiar format; they find themselves at a loss when presented with an atypical word problem, even when they have all the knowledge to solve it.I grew up in the former Soviet Union. As a child, I remember the thrill of getting a new mathбtextbook at the beginning of each school year and looking through it in anticipation of learningбnew and exciting mathematics. Every Sunday morning during my school years I took a bus across town to attend a math circle class. When my three children were growing up in the U.S., I wanted them to discover the beauty of mathematics. In their elementary school years, I supplemented their standard school curriculum with the Singapore Math textbooks available in the U.S., with several editions of Russian math textbooks, and with the Math Circle Elementary material. Like learning a new language, becoming proficient in math takes time and practice. The earlier one starts, the easier it is and the greater proficiency one achieves. In a typical Eastern European mathematics program, middle school children are taught different areas ofmathematics, starting in 6 th grade and continuing through middle and high school. Such an approach supports giving children a solid mathematical foundation. My children attended different public and private middle schools in the U.S. None of their math textbooks covered math subjects broadly and geometry was often absent from middle school math. I wish the Bulgarian middle school textbooks had been available at the time. This program covers many areas of mathematics continuously over the course of 3 years, including algebra, geometry, logic, reasoning, statistics, and problem solving. There is no one-year “crash” course in geometry or any other math discipline. The Program supports math knowledge acquisition and retention at a steady pace throughout all middle school years. The exercises in textbooks are split into several levels to help with differentiation. Math contest problems, interspersed throughout the book, can be assigned to advanced students. Supplemental materials, offered as independent work, can add a “math circle” element and challenge even the most advanced students. The Bulgarian program teaches children not just to look for the right formulas to plug in the numbers, or for the right template or a recipe to use; it helps teach students how to approach and solve a problem as a mathematician: “Let’s pause to understand the problem, let‘s take a piece of paper and a pencil, and let’s think” I am excited to finally have an excellent middle school math program, and I love teaching it.
Elena Blanter
She received her Master’s degree in mathematics from Saint Petersburg University in Russia. Elena’s many years of experience in industry span mathematical risk modeling, statistical analysis, and development of financial analytical software. Elena is a co-founder of the Berkeley Math Circle Elementary Level (for grades 1-4) and has been teaching there since its inception in 2009. She is also a co-founder of the Stanford Math Circle Elementary Level at Stanford University, launched in 2011. Elena is thrilled to have the opportunity to bring her experience and passion to the Math Taught the Right Way Program (MTRW) at UC Berkeley.
These texts are such an improvement from ... ... the typical textbooks used in the American math education system. Rather than merely presenting formulas, these materials focus on their derivation and various applications. The result is remarkable, studying math becomes an engaging exploration for the students, rather than the tedious memorization and monotonous plug and chug students may be used to in the American math curriculum. The books contain beautiful explanations and plenty of examples, easing students into challenging problems. And although the books cover a wide range of mathematical subfields (geometry, algebra, etc.) the students are able to see how concepts from different subfields are integrated, as they are in the real world, outside the classroom. In my personal experience, growing up, I attended a Math Circle, which exposed me to creative, thought-provoking problem-solving approaches, as well as the connections between mathematical subfields, so I knew that the math classes I was taking in middle and high school were not a fair representation of how enjoyable studying math could be. These are the first math books I have come across that bridge the gap and incorporate the depth, clarity, and excitement of a Math Circle, while also tailored to the American math standards. These materials are the perfect tool for students and math teachers alike to truly experience and share the beauty and joy of studying mathematics.
Ellen Kulinsky
BA in Mathematics,UC Berkeley
“The Bulgarian curriculum is more rigorous than others I have used as it introduces Algebra in early grades. Variables are integrated into daily lessons so that students become as familiar with manipulating equations with x and y as they do with real numbers. This will pave the way for an easy transition to Algebra and set them up for success in higher grades.“
Laurie Gold
Pilot teacher
The quotes on this page are from more pilot teachers, parents, and educators. You will come across them in the Introduction chapter, in their original context. Thus, we strongly encourage you to carefully read the introduction first, before continuing with the actual math material. ”This book has been a tremendous resource for my students, and I wish I had it when I was in school. The lessons are laid out in a very clear manner. The math is approachable or challenging to meet the needs of a child at any level. There are many math books that claim to reach every person. This book successfully does so, and it is one of the best.“
Natalya St. Clair,
Pilot teacher
co-author, ”The Art of Mental Calculation“
“This Middle and High School Math Program is deeply aligned with the Common Core Mathematics Standards”.
Dr. Phil Daro
One of the Three Principal Writers
of the Common Core Mathematics Standards
”I feel that the Bulgarian texts are much more thorough than the American textbooks I am using for 7 th grade. The truth is that had there been this year also a translated 7 th grade Bulgarian textbook I could use, I would have definitely used it for all of my classes. It is much easier to teach from and saves me work.“
George Khasin
Pilot Teacher


What Parents Say

”As a teacher and teacher educator, I am familiar with several ... math programs that have been used throughout the past 20 years in California. The Bulgarian math program is exceptional in the way it supports students’ deep understanding of mathematical concepts, develops students’ ability to transfer skills to new and unfamiliar mathematical situations, and creates a mathematical language for students to express themselves mathematically, using numbers, drawings, and narratives. Teaching is sort of like farming. You never know how your crops are going to turn out, but I have noticed with my son that his work has improved, and I really like the way he is talking about math. I can see, and most importantly hear, the way my child interacts with the Bulgarian math program and I am impressed with the strong foundation it is giving him that will surely lead to lifelong competency and the ability to pursue more advanced mathematics.”
Jacqueline Regev
6th grade pilot parent
“You have done a masterful job of adapting this curriculum to the U.S. reality. The U.S. Education System needs this kind of prodding. The Common Core ideas are heading in the right direction but the instruments of change are too unwieldy and we cannot just stand by and wait to see what will happen. I hope that your efforts will be successful. Thanks for all of your hard work.”
Tom Rike
”Our daughter has ... learned to love math with the Bulgarian math curriculum. It stimulates not only her technical mathematical abilities but also challenges her to strategically and creatively solve problems. This program keeps her interested and excited.“
Eve Maidenber
6th grade pilot parent
”Thank you so much... ...for this feedback! Our daughter is struggling to catch up. I feel like she is learning more math now in one month than she did all last year. Thank you for your help!“
6th grade pilot parent
”I feel that the Bulgarian textbooks are much more thorough than the American textbooks I am using for 7 th grade. The truth is that had there also been a translated 7 th grade Bulgarian textbook I could use this year,I would have definitely used it for all of my classes. It is much easier to teach from and saves me work.“
Jacqueline Regev
6th grade pilot parent and educator

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