Singapore Math

Singapore Math is an English term that designates the approach used by the national math curriculum of the country of Singapore. During the 1980s, the government of Singapore developed its own curriculum that was based on three core areas: bar models for word problems, fewer concepts but greater depth, challenging advanced learners. Its intuitive bar model is based on a process that takes the learner from the concrete, to pictorial, to abstract representation of math problems. This new, national curriculum helped catapult Singapore to the heights of international math exams. At Lionheart Tutoring, we use the bar model and its applications to fractions in order to help students who struggle processing word problems. The bar model provides a visual tool that can be applied to all elementary word problems and even more advanced problems (such as those found on the SAT). Students learn how numbers in problems have relationships that can be easily represented to reveal their components. Equipped with this go-to model, students feel confident in approaching even the most challenging word problems.

Contemporary Math

According to Dr. Morris Klein, U.S. has seen repeated changes to its mathematics curriculum over the past century, with the most dramatic occurring in the last fifty years. These approaches to teaching math have fallen under several different names like New Math, but could be labeled “contemporary math,” so as to lose the connotations certain terms have in the education world. Contemporary math approaches tend to use a spiral, rather than mastery method of instruction that has the same concepts taught over and over again as a student goes from grade to grade. Unfortunately, many students fall into a rut because they do not have enough time for a particular subject, such as fractions, during one year and fall behind. We have worked with many contemporary math approaches, such as Everyday Math, Investigations, and the Chicago School of Mathematics/CPM model. In our work with students, we have found certain areas that students commonly need additional help to master. With clear, step-by-step instruction and copious amounts of practice, we have found students to overcome their temporary difficulty with renewed confidence.

Middle School

Middle school marks a major turning point in a student’s education, in which he or she will experience greater degrees of abstraction in mathematics. From percents, to proportions, to variables, students must develop the ability to represent and manipulate numbers in novel ways. We have found that many students benefit from our straightforward approach to pre-algebra and algebra that takes them step-by-step through each type of problem or concept. Many students find themselves overwhelmed when given too many approaches, so we have found core steps that they can use over and over again without confusion. We have familiarity with contemporary math programs, like CPM that uses tiles for algebra, and can help students go through curriculum-specific techniques that parents have not experienced before.

High School

Many of the math subjects that high school students study nowadays were held off until college in earlier times, so it is natural that many students struggle with understanding and excelling at these topics. Our objective in tutoring high school math is to make things understandable and then build up from a strong foundation. Many students find themselves stuck because they do not fundamentally understand what a particular concept represents, such as a radian in trigonometry. As a result, they struggle to memorize countless patterns of data rather than understand and use deduction from key concepts. Students in high school benefit from our custom approach to standard subjects, which takes them through each type of problem in a logical and clear manner. In particular, our critical points method for geometry helps students deal with the difficult areas of mathematical proofs that require a great deal of creativity using abstract concepts. We are sure to be patient and understanding as many students feel frustrated when they do not get it at first.

Meet Our Tutors

I love seeing how students discover they can thrive in subjects they always dreaded. It’s wonderful to see the growth in their self-confidence with each session.

Dan Chinburg


Inspired by what he saw in South Korea as a Fulbright Teaching Fellow, Dan Chinburg began tutoring students on the Main Line in 2009. He graduated with a M.S.Ed. in Reading/Writing/Literacy from the University of Pennsylvania with a K-12 reading specialist certification and has a B.A. in English & World Literature from Pitzer College. Since his return to the states, he has taught over 110 students through word-of-mouth. He loves working with struggling students and advanced students alike. Always striving to get the best results, he has tutored Singapore Math at a charter school and has explored many different approaches to higher mathematics. Over the years, he has designed his own grammar, writing, and standardized test program to meet the demands of his students. He particularly enjoys the challenge of giving crash-courses in subjects before last-minute finals for new students.

It’s always fun to see the shock that parents have when they hear their children speak Chinese for the first time. They can’t believe their kids can learn so quickly!

Yuanyuan (Elizabeth) Zhang

Chinese Director / Tutor

Fluent in English and a native-speaker of Mandarin Chinese, Yuanyuan brings an incredible breadth of language training and linguistic expertise to her Chinese and ESL sessions. She graduated with a M.S.Ed. in TESOL from the University of Pennsylvania and has a B.A. in Business English. While in China, she taught classes of Chinese students of all levels in English at the prestigious private tutoring firm in Shanghai. She has developed the Chinese program of Lionheart Tutoring through her self-designed learning programs for students in grades PreK-12. She brings an energetic approach to Chinese instruction while incorporating games, iPad apps, songs, poems, and multimedia with her students. Parents have been delighted to find her as many private schools have embraced Chinese as a foreign language across the Main Line. Always dear to her heart, she loves working and developing her toddler program for young Chinese learners who are training their ears for the novel tones of Chinese.