Online classes
We offer both individual and small group classes.
Individual classes are ideal for students seeking maximum growth or independent learners who occasionally need an instructor to explore material in depth.
Group classes are limited to just 2-4 students to ensure each student receives enough personal attention while still benefiting from peer interaction. If you are interested in this option, please organize a group with family and friends.
Most courses include either 12 or 20 lessons.
Contact Van Koroleva at hourglasslearning@protonmail.com for more information.
Curricula
While the content of each course is personalized to the students, the level of rigorousness is similar to that of the Math Circles books from American Mathematical Society and Arts of Problem Solving textbooks.
For grades 1-3, emphasis is placed in exploration of mathematics rather than formal introduction of mathematical concepts and formulas. Students are exposed to the beauty of mathematics through problems that they enjoy solving.
Grades 4 and 5 are transitional time when formal mathematical concepts are gradually introduced.
For grades 6-12, we offer separate courses in algebra, number theory, geometry, counting and probability, and calculus, as well as integrated courses and special topics that meet the need of each student.
True learning happens when students actively recall material and struggle to solve problems on their own. Therefore, an integral part of each course is homework when students are expected to write complete solutions. This helps them become articulate in logical reasoning which is useful beyond the study of mathematics.
Mini courses
MINI COURSE: SYMMETRY AND PATTERNS
Nature is full of beautiful patterns, from honeycombs to the wings of butterflies to snowflakes. In human cultures, we see intricate patterns from Roman mosaics to Islamic architecture, from household items such as carpets and quilts to mandalas, the spiritual symbols in various religions.
One thing that makes these patterns pleasing to the eye is the symmetries that they possess. One will perhaps appreciate these patterns a little bit more after looking deeper and seeing their structures through the lens of mathematics. That is the focus of this mini course.
The course starts with different types of symmetries and basic geometric transformations. Students will learn the language of symmetry and the techniques to identify and draw different types of symmetry. They will then be delighted to see that what they have just learned can help them understand beautiful and intriguing patterns found in both nature and in art. Starting with fractals, we will make snowflakes out of paper, calculate the number of Sierpinski triangles, and find out how Koch snowflakes change after each iteration. Next, we will draw images from multiple mirrors and find out how a kaleidoscope works. Finally, students will be introduced to tessellations where they will see amazing patterns formed by simple polygons and read a fascinating story about quasicrystal.
Students won’t just sit and admire beautiful pictures but they will get their hands wet by solving math problems in each topic that is covered. They will draw and color, use their computational skills as well as their imagination. It is a treat for both young mathematicians and young artists alike.
Course outline
1. Polygons.
2. Point symmetry.
3. Reflection symmetry.
4. Rotational symmetry.
5. Four basic geometric transformations.
6. Snowflakes. Fractals.
7. Mirrors. Kaleidoscopes.
8. Tessellations.
The recommended ages for this course are 8-11 years old. Depending on the students’ background and progress, the course can be completed between 5 and 8 sessions.
MINI COURSE: THE STORIES OF TIME
Course outline
1. Natural time cycles. Calendars.
How did people in the ancient time measure natural time cycles? In the first calendars, how many days were there in a year, in a month? To answer these questions, we will review accounts from ancient civilizations and middle age Europe that led to development of the Gregorian calendar, the most popular calendar in use today.
2. What day of the week is your birthday?
Why does a week have seven days? The periodicity of a seven-day week gives rise to many interesting math problems. By journaling your birthday over the years, for example, you will find out which year is a leap year.
3. Around the globe. 24 time zones.
When the night rolls in at one place on Earth, dawn arrives at another place. Let’s travel the globe through a map to learn about the 24 time zones. Problems in this unit include calculating arrival time for flights and adjusting clocks while traveling from one location to another.
4. Holidays.
The New Year takes place on a fixed day in the Gregorian calendar, but this is not the case with many other holidays. Thanksgiving day in the US takes place on the fourth Thursday of November. Determining when to celebrate Easter each year involves matching the phases of the Moon with the solar calendar. In this unit, we will learn about holidays in different cultures.
5. Seasons. Daylight saving times.
What gives rise to seasons? In countries with daylight saving times, the clock falls back one hour in the Fall. What does that mean? We will solve math problems that involve daylight saving times in both the Northern and Southern Hemispheres.
6. Evolution of the clocks. Getting ever more precise with time measurement.
After several thousand years struggling to create an accurate calendar, in the last few hundred years, we made long strides in measuring time. From the crude hour of a sundial to the nanosecond of an atomic clock, we are getting ever more precise with time measurement. In this unit we will work with problems involving the hourglass, the pendulum, the wrong hours shown by a digital clock after a power outage. Many problems in this unit require both logical reasoning and computational skills.
7. Beginning of time. Time in space
In this final lesson we will travel all the way back in time for as long as scientific evidence allows us and go through the landmarks of development of life on Earth in prehistoric time. Students will have the chance to fill in the important years that they know in the arrow of time. Lastly, we will venture out to space to visit other planets to find out, for example, how long a year on Mars is or if there are seasons in other planets in our Solar system.
The recommended ages for this mini course are 7-10 years old, although it is a fun course for a much wider range of ages.