January 2019
« Dec    

Logarithms, lunar eclipses, and learning

Posted: January 21st, 2019, by Marina Milner-Bolotin

The photo of a Lunar Eclipse on January 20, 2019 (courtesy of Tania Toth, Chilliwack, British Columbia)

Last week while preparing myself for writing a research paper, I was reading about the invention of logarithms by John Napier of Merchiston (1550-1617). The story of logarithms is a fascinating story connecting mathematics, science, and our everyday life. You can find a lot of information about it online, including many excellent videos, books, and papers on teaching about logs and teachers’ and students’ understanding of the logarithmic function. This is an excellent opportunity for a creative teacher who wants to help students make meaningful connections between mathematics and science.

Reading the paper by Christof Weber (Weber, C. (2016). Making Logarithms Accessible – Operational and Structural Basic Models for Logarithms. Journal für Mathematik-Didaktik, 37(1), 69-98. doi:10.1007/s13138-016-0104-6) on the topic made me rethink it once again. First, it drew my attention to the choice of words – Logos+Arithmetic=logarithms… Somehow, the word ratio (one of the meanings of the word logos in Greek in a ratio) was hidden in the name of logs… And I am not going to discuss the word “arithmetic” here. Second, this paper made me appreciate not only what the invention of logarithms allowed people to do in the 17th century, but also how the logs were invented and that they were not invented as an inverse function of the exponent! They were invented as a connection between the arithmetic and geometric series… Think about it again… Historically, logs were invented BEFORE the exponential function… The connection between the logarithmic and the exponential functions was made later by another mathematical genius – Leonhard Euler (1707-1783). While this was a groundbreaking discovery, it hides the main reason for the invention and in some way, the power of the logarithmic scale. One of the main goals behind the invention of logarithms was to help astronomers with the calculations of trajectories of heavenly objects – like the trajectory of our Moon, Mars, Earth, etc. I am sure you know where I am going with that now. We will come back to that…

However, for me personally, the story of logarithms started more than three decades ago when my dad, who is an engineer, showed me how to use a strange device that could help me multiply and divide numbers very fast – a slide rule. In Russian, it is called a logarithmic rule, which in my view is a more appropriate name for this amazing invention, because slide rule uses logarithms to convert multiplication and division into addition and subtraction. A logarithmic rule was invented by William Oughtred using Napier’s logarithms in 1622! Yes, it is almost 400 years ago and the ripples of this amazing discovery keep changing our lives today. As you can find on this web site from the Centre of Computing History in the United Kingdom:

“After John Napier invented logarithms, and Edmund Gunter created the logarithmic scales (lines, or rules) upon which slide rules are based, it was Oughtred who first used two such scales sliding by one another to perform direct multiplication and division; and he is credited as the inventor of the slide rule in 1622. Oughtred also introduced the “×” symbol for multiplication as well as the abbreviations “sin” and “cos” for the sine and cosine functions.”

This is very exciting and it is not surprising that I have written about it in my earlier post here. Today, as a science teacher who teaches future teachers, I discuss with them how we can teach students about the magnitudes of earthquakes (Richter scale), pH scale, sound level (dB), radioactive decay, geological scales, and many-many other phenomena. The mathematics behind all these phenomena require a deep understanding and appreciation of the power of a logarithmic scale. I am fascinated by logarithms…

Yet, back then when I was in my late teens I didn’t fully appreciate Napier’s invention or even the slide rule. I realized that somehow Napier’s invention opened doors to “converting” the problem of multiplication to the problem of addition. But was it such a big deal after all? For example, among other things Napier also invented Napier’s bones – another cool pre-calculator invention:

YouTube Preview Image

And here astronomy comes to mind. As I was observing a breathtaking phenomenon of a lunar eclipse last night (this is the reason I place Tani’a photos of the lunar eclipse here), I was thinking how we take for granted our ability to predict the exact time and duration of these phenomena. We just take it for granted that we can know exactly when the eclipses are going to happen, as we have computers and other tools to help us with it.

The photo of a Lunar Eclipse on January 20, 2019 (courtesy of Tania Toth, Chilliwack, British Columbia)

But how was it done 400 years ago? Here logs come back into the picture. Another scientist who changed how we think about the world around us was Johannes Kepler (1571-1630). He was Napier’s contemporary and he was the person who used Napier’s logs and the logarithmic tables to make sense of Tycho Brahe’s (1546-1601) astronomical observations. Without the logs and the ability to simplify calculations, who knows if Kepler was able to derive the laws of planetary motion we teach in school today? And who knows by how many years these astronomical discoveries would have been delayed.

And it all comes back to learning. When you learn about mathematics and science as a collection of facts, without appreciating the context of these amazing discoveries, you lose sight of the achievements of people who lived before us… You also make these achievements abstract and unrelated to you. But if you start making these connections, you realize how these discoveries came to be and how they were the product of many amazing minds… To me these stories to come a full circle like the stories of O’Henry. Ideas, discoveries and our lives come together in fascinating and often unexpected circles, but when you start to see the connections things beging to make so much sense. So for me, the logs, the lunar eclipses and learning came together in such a circle last night.

For more information, read:

Berezovski, T. (2007). Exposing pre-service secondary mathematics teachers’ knowledge through new research designed methodology. (Ph.D.), Simon Fraser University, Burnaby, Canada.

Berezovski, T. (2004). An Inquiry into High School students’ understanding of Logarithms. (M.Sc.), Simon Fraser University, Burnaby, Canada.

Lunar Eclipses Vancouver, BC:

Teaching Online Graduate Courses for Teachers

Posted: January 10th, 2019, by Marina Milner-Bolotin

This semester I am teaching an online course in our fully online MEd in Science Education Cohort: This is very exciting as my colleagues and I have been working for a long time to make our dream of having a graduate online science education cohort become a reality. I also have heard from my colleagues that the previous course went really well. So I am looking forward to teaching the course and getting to know the teachers!

I have spent a lot of time preparing my online course for this cohort: Teaching Mathematics and Science through Technology. And now, as I am teaching it, I am trying to reflect on the challenges I face as an online instructor and think how I can overcome them and how I can make the next course even better. I am also trying to monitor my own time used for teaching this course: I record the time I spend on the course in an Excel sheet to know for myself how it goes. This will also help me to make sure that teaching two courses a term and doing research would be a doable task for me. The worst thing is to burn out and not to be able to enjoy teaching.

While preparing, I found an interesting article about it “Online Teaching: 4 Unique Challenges and How to Solve Them” by Karen Quevillon (from January 2018). So here is a brief summary of the challenges as she sees them (the papers suggests some solutions):

  1. Disengaged – passive students
  2. Responding to students’ questions
  3. Encouraging student collaboration
  4. Technical difficulties

I also decided to look online for professional development resources on online teaching. Here is one that I found useful. I think they give some practical suggestions and while I do not believe in the “best practice”, I do think that becoming familiar with some teaching ideas that others found useful is helpful:

YouTube Preview Image

Happy New Year!

Posted: December 26th, 2018, by Marina Milner-Bolotin

As 2018 is coming to a close, I kept thinking what made it interesting and exciting for me. While family for me always comes first, my work comes a very close second… Making a very rough estimate, I have spent at least 2200 hours working last year… This is a huge amount of time and it is about a quarter of the hours we have in a year. Considering that I am a person who loves to sleep (I can easily sleep 10 hours a day if I am allowed…, so maybe I was a koala in my previous life), this is a huge chunk of time. So loving what I do at work is hugely important for me. And luckily this was a very exciting year for me. I would like to list a few of the most exciting work-related events and activities that made 2018 a very special year for me:

  1. Supporting graduate students who have graduated this year: one Ph.D, one M.A. and 3 M.Ed. students. I wish all of them continuing success.
  2. Supporting my science and physics Teacher-Candidates most of whom have found STEM teaching positions and many of whom have received teaching awards in our Faculty. Huge congratulations to them.
  3. Organizing a very successful STEM outreach event in the Faculty of Education in November, 2018 Family Math and Science Day 2018 . More than 100 volunteers helped us to make it all happen.
  4. Attending a very successful STEM 2018 conference in Brisbane Australia in November 2018 and getting ready to organize the 2020 STEM conference at UBC.
  5. Publishing my paper in October of 2018 in Frontiers in Education: STEM education journal – I have been its Associate Editor and I am happy to see journal’s growth.
  6. Continuing a tradition – organization of a 40th UBC Physics Olympics with more than 70 participating teams from all over BC in March 0f 2018.
  7. Collaborating with my very inspirations colleagues – Professors Dragana Martinovic and Yifat Ben David Kolikant to organize of a very successful conference on teacher education at the Hebrew University of Jerusalem in February 2018 – Teachers and Teaching in the Era of Change.
  8. Publishing of two papers in the summer of 2018 in a peer-reviewed international journal LUMAT journal with my graduate student: and .
  9. The publication of a special Physics in Canada Outreach issue (Volume 73) in February of 2018 that I co-edited with my colleague Dr. Sarah Johnson.
  10. The publication of the second edition of our introductory Physics textbook:
  11. Helping to launch our first fully online M.Ed. in science education program.
  12. Receiving a TLEF grant with my husband Valery Milner to produce slow motion physics videos that we will be using in teaching introductory physics and working with future teachers.
  13. Publishing a paper in The Physics Teacher on using Collaborative Learning Annotation System in teacher education.
  14. Publishing new videos on our database of educational videos:
  15. Continuing to learn foreign languages – German and Spanish – I see it as a big part of who I am. I want to keep learning about science, science teaching and teaching and learning in General. Learning foreign languages helps me becoming a better science teacher as it helps me to remember what it means not to know.

So this was an exciting year and I enjoyed learning new things with my students and collaborators. I wish them all a very successful new year. And enjoy this wonderful physics video by one of the people who inspires me.

YouTube Preview Image

Final Thoughts: Winter I 2018

Posted: December 8th, 2018, by Marina Milner-Bolotin

Future physics teachers (one student is missing from the photo) who were my students in the Physics Methods Course 2018

As I am saying good-bye to my students, who will soon be going on a physics teaching practicum in local schools, I keep recalling how I started physics teaching almost 30 years ago. It was not easy, considering I also had to do it in a foreign language (Hebrew) and in a school that had a very different culture than the school I attended as a student.

Not surprisingly, many of my students will face similar challenges. However, they have a strong peer support group and a strong community. This is something I am very proud of. It is impossible to become a good teacher in a few month, but it is possible to star the teaching journey on the “right foot”. I hope my students have done that. A lot of them also have various experiences that will help them in the classroom. So I am confident that our UBC Physics Teacher-Candidates will not only do well during the practicum, but will become very inspiring and knowledgeable physics teachers. I would like to wish them all a very productive and successful practicum experience and of course a very happy and successful new year.  I enjoyed teaching them very much. Good luck!

2018 STEM in Education Conference in Brisbane

Posted: November 22nd, 2018, by Marina Milner-Bolotin

I am very fortunate to be able to attend the STEM in Education 2018 conference organized by the Queensland University of Technology (QUT) in Brisbane, Australia. I am a Co-Chair of the 2020 STEM in Education Conference that will take place at UBC in 2020.

This conference was one of the best I have attended for many reasons. One of them is the keynotes. Dr. Alan Finkel (Australian Chief Scientist) and Dr. Fred Watson were invited to speak. And their presentations were extremely relevant and interesting.

YouTube Preview Image YouTube Preview Image

I also presented a workshop on innovative technology use which was well attended. It is always exciting to meet inspirational STEM Educators from all over the world and learn from them:


8th Family Mathematics and Science Day

Posted: November 4th, 2018, by Marina Milner-Bolotin

Visitors young and older were fascinated by demonstrations and experiments they participated in during the day! (Photo credit Marina Milner-Bolotin).

Prof. Valery Milner (Department of Physics and Astronomy) shows families how an infrared camera works. Photo credit: Paul Joseph/UBC Brand and Marketing.


For more photos click here.

On Saturday, November 3rd, 2018, we had an amazing 8th Family Math and Science Day. My Mathematics Education colleague Dr. Cynthia Nicol and founded the event in 2010 and it is going strong!Despite the weather, we had almost 400 guests, more than 130 volunteers and lots and lots of fun. This event is becoming a feature in our Faculty and our teacher-candidates are becoming very comfortable leading mathematics and science outreach events. In addition, the kids in the community are waiting for it. We had a few innovations this year: University Transition School students took part in the event and it was fantastic. We had a Virtual Reality exploration room. We had a lot of innovative stations created by teacher-candidates, faculty and staff. We know that our teacher-candidates will be using these ideas during the practicum.

This year we have been supported by the UBC Faculty of Education and Department of Curriculum and Pedagogy, UBC Teacher Education office and UBC Professional Development and Community Engagement Unit, David F. Robitaille Mathematics and Science Education Endowed Chair, Pacific Institute for the Mathematical Sciences, and UBC Department of Physics and Astronomy, UBC Faculty of Science. We are grateful to our sponsors.

And here is some feedback from the families who attended the event this year:

Dear Marina,

I would like to thank you for organizing such a great outreach program. I am a grade three student and I love math and science. I really enjoyed the UBC math and science program this year and last year as well. Next year, could you have it a little bit longer and maybe have it  two or three times a year? It was really good and I enjoyed it but it was too short! Thank you!

Sincerely, A.


Dear Dr. Milner-Bolotin,

This event was fantastic! Well organized, amazing volunteers, and so many activities and experiments to explore. You brought Science world to UBC with the great advantage of eager volunteer students giving a personal, one on one experience for each child. Send your team a big thank you!

B., R., R. and N. K. 


Hi Marina,

Just wanted to say how impressed I was with all the volunteers that you had manning the stations this year! They were so enthusiastic and knowledgeable! I was also amazed by the high school volunteers–they were able to interact with my young kids so well! Thank you for hosting this event every year–I’m sure it’s a HUGE amount of work! Our homeschooling community appreciates this and looks forward to it every year! 

Warmly, Y.


Marina, Volunteers and Team,

A huge and sincere thanks to all of you for organizing yesterday’s event.  It was our first time and our family enjoyed all the hands on discoveries. My 6 3/4 year old son’s favourite was the circuit made with play dough and watching the led light come on. My 9 year old daughter like making the flowers and touching the alive and non alive animals.  They also like playing the math games. Thank you.

The A-D Family


Hi Marina,

Thank you very much for today and all your efforts to arrange this event which I know how much time and work was needed to be done for all. This event is a unique and comprehensive strategy, which engage everybody from kindergarten to parents and adults. Everyone was enjoying, learning and engaging with science and math. 

Thank you and have a great weekend. 


 More photos can be found here.


Feeling Proud of my Students!

Posted: October 19th, 2018, by Marina Milner-Bolotin

These are BC physics teachers who are also my former or current students. This is so exciting to see them loving their profession and coming back to learn more. I am so proud of them!

Today I participated in BC Association of Physics Teachers Professional Development event. It was a very successful event and I wrote about it on the BCAPT web site. However, what made it especially memorable and special for me is that I had an opportunity to meet my former students who are now physics teachers in British Columbia and to introduce them to my current teacher-candidates. Knowing that I made a difference to physics teaching in BC by supporting the next generation of physics teachers is very exciting.

Interview with Anna Maria Tremonti from CBC’s The Current

Posted: October 3rd, 2018, by Marina Milner-Bolotin

Fall Welcome

Posted: September 21st, 2018, by Marina Milner-Bolotin

As we are celebrating the first day of the fall and are wondering what the winter has in store for us, I cannot think of a better science connection to the inevitable change of seasons than a very famous study by Philip SadlerA Private Universe. I use it in my undergraduate and graduate courses as it inspires us to see within us how we understand (or do misunderstand) the world and to appreciate how our students do that. It also teaches us to think about what we know and if to remember not to try to hide our ignorance by fancy words. I have watched this movie so many times, that some of it has been imprinted in my mind. For example, how the students have been taking so many advanced science and physics courses, and yet they cannot explain why we have seasons or why the phases of the moon happen. What troubles me more is that how professors or students at Harvard University instead of admitting that they don’t know, try to hide their ignorance by very vague and purposefully complex words. Is university education a way to teach students how to hide their ignorance? This brings me back to another very inspiration colleague – Dr. Eugenia Etkina. Many years ago I was invited to take her graduate course. There she taught us that we have to understand the concept first and only then to be invited to learn and use a word to describe it. I talk about it with my students today – ideas first, specialized words to describe these ideas – second…

YouTube Preview Image

Happy Fall to everybody!

Beijing Science Festival

Posted: September 17th, 2018, by Marina Milner-Bolotin

During the last few days I was invited to take part in the Fifth Beijing Science Festival (BJSF) that took place at the Beijing Olympic Stadium. It was my first time to participate in such a big and so well organized event that aims at engaging children and the general population in science, technology, engineering and mathematics (STEM).

The view of the Bird’s Nest and the Cube at the Beijing Olympic Stadium (by Marina Milner-Bolotin)

Today I flew back from Beijing and I had a moment to reflect on my very brief, overwhelming, but also very powerful experience. During my visit I was able to see and be a part of the science outreach event on a grand scale that I have never experienced before.

It is hard if not impossible to describe the magnitude of the BJSF without experiencing it. It is about 800 times bigger than our UBC Family Math and Science Day, it is free and open to anybody in Beijing or outside of it. So many families come to participate over the weekend – I saw parents, grandparents, entire families, as well as young couples who I suppose decided to have a date there. During the week, many school students came with their teachers. I could see groups of kids in uniforms running around and enjoying the day.

On Monday, many schools took their students to the Science Festival – these students are from the same school as they wear the school’s uniform.

In addition, many secondary students volunteered during the event and it looked like they enjoyed it as well. They also had an opportunity to speak a little English with us. Hundreds of companies, educational institutions, and governmental agencies took part in this event. The government of China allocates funds for inviting science educators from other countries (that is how we could come), so the exchange of ideas not only inside China, but also on the larger international level is a very big part of it.

As I mentioned earlier, it takes place at the Beijing Olympic Stadium, so the venue is huge, well known, and has many attractions in addition to the BJSF – museums, etc. The BJSF has about 250,000-300,000 visitors during the four days of the festival (this is about 1/3 of the population of Vancouver).

I represented UBC and Canada as every country was invited to have one booth of science activities to inspire young people. The booth of science experiments I brought with me was very popular and the organizers already invited me to come again next year. I think we are doing a very good job with the science outreach here, as the stream of visitors to my booth was always very high. Considering that this is the biggest science festival in China, it is very exciting to know that we were represented (together with the US, many European, Asian and African countries).

While I am a little bit overwhelmed and tired now, I am proud to be able to represent Canada and UBC and make us known for our science outreach. I also met many amazing STEM educators from all around the world. So I hope this will open new collaborative opportunities. All in all, it was a great opportunity and a big inspiration. I hope we will go there next year as well.

Science and curiosity allow you to communicate with people even if we do not speak each other’s language…

Spam prevention powered by Akismet