Musings on life & math

I am very gruntled after listening to Michael Enright’s

Reflections in a Bay of Fundy tidepool

interview with Andrew Hacker, Professor of Political Science at Queens College in New York City about teaching advanced algebra in high school and college. In part I am delighted to have learned a new word – gruntle, opposite of disgruntle. How cool is that.

But let me focus on the conversation about algebra and why it might be a good idea to drop our insistence on advanced algebra in high school and college because it is the single biggest cause of students dropping out and not finishing their education.

I couldn’t agree more with the premise that we are wasting far too large a proportion of the intellectual capital of our young people by insisting on dragging forward old ideas about what constitutes a good education. Wake up people; start thinking differently instead of simply plodding forward with historical beliefs that are never re-examined.

When life is more than the sum of its parts!

I spent the first 30 years of my life being a math-phobe. I didn’t finish high school because I was terrified of having to do algebra and trigonometry in Grade 13. I had several math teachers who were horrific in terms of their inability to teach and their concomitant ability to humiliate those of us who were slow on the up-take. Except for Mr. Dube, my grade 9 Math teacher. I simply couldn’t cotton on to the notion of x and y. This poor man worked with me for 6 weeks before the light bulb finally went on. I am eternally grateful for his persistence because I may not have made it to Grade 12 otherwise.

University came late in life to me. I was 29 when I began my studies in the social sciences (39 when I got my BA) and I put off the required stats course as long as humanly possible. But having begun a degree on a part-time basis my work fortunes improved dramatically. I got myself a job as a manager in a major telecommunications organization. The horror was that I was hired into a department filled with statisticians, economists and systems analysts. One of my bosses thought it was pathetically funny that when I was presented with a graph with several lines on it my first response was to panic, followed very quickly by tears. Talk about embarrassment and feeling intimidated.

After several years of this nonsense I forced myself to take an introductory economics course. It was perhaps one of my most uncomfortable educational experiences but I persisted. I was fascinated by the assumptions made by this social science that pretends it is a hard science. And some of the math even started to make sense. At one point we had a take home exam which I did fairly well on except for one question that was worth a large number of marks. As the professor was reviewing the assumptions to the question I realized that I had read the assumptions quite differently. I found the courage to put up my hand and let him know that to me the question meant x, not y as he had stated it. He worked the numbers through based on my assumption and it turns out I had the right answer based on that different starting assumption. When he checked with the class, about 20% of us had read the question differently than he had intended. He was a big enough man to give us full marks if we had either an x or y response. Yay!

From that moment forward a huge portion of my math phobia fell away. Because I realized that what I had been calling ‘math phobia’ wasn’t that at all. I wasn’t afraid of numbers: I was afraid of looking like a total loser because I clearly didn’t understand and couldn’t play with them the way I could with words. My moment in Economics class showed me that I did understand; I just often started from a different point than more mechanically oriented brains seem to.

A couple of years later I could no longer avoid that dreaded stats course so I very reluctantly signed up. Lo and behold I got a young lecturer who didn’t believe that traditional statistical analysis were the only way to gain results. Sure we did a bit of stuff around chi squared, etc. but mostly we looked at qualitative rather than quantitative survey methods. What a brilliant course that turned out to be.

By then my job had migrated into the marketing domain and doing customer surveys was a big and important topic. This qualitative approach to stats was a massive benefit to me because it taught me how important language is to creating great, useful and bias free questions. I also discovered that it was okay for me to focus on that stuff and leave the actual manipulating of data to the statisticians who could do it with elegance and accuracy. In this course I also learned a saying that has stayed with me to this day. I think of it always when I hear ‘experts’ flogging their data to prove a point. It is:  If you torture numbers long enough, eventually they will confess.

By this time I was married to a man with an advanced degree in statistics and an undergraduate minor in English. Interesting combination. And he helped me to recognize that mathematics is a language where number combinations rather than letter combinations carry meaning. I am clear that it is a language that I have only the most rudimentary knowledge of, kind of like my knowledge of German. And yet, despite having only a basic understanding of the manipulation of numbers, I get many of the messages that math has to offer us. Before I ended my corporate career I had actually become quite formidable in the boardroom for asking tough questions about the math behind positions, policies and propositions people were putting forth.

I love Professor Hacker’s idea of liberal art courses on, say, the history of mathematics or what’s so important about certain mathematical concepts or even how qualitative and quantitative approach support one another. I’ve kept a small book by John Allen Paulos on my bookshelf for decades now. Whenever I begin to doubt my mathematical abilities I have a read of one of its chapters and it reminds me that I am far from a mathematical dummy. Get hold of Beyond Numeracy is you want to read about math in a way that makes sense to the non-mathematical mind.

I’d also like to thank my ex husband for helping me to understand this domain which used to terrify me so much. Greg is a part-time math tutor whose specialty is working with adolescent boys who aren’t doing well with their math studies. A big part of his success comes from the fact that he treats them as adults, but a bigger part comes from the fact that he finds out what their world is about and then finds ways to make math relevant to their lives or potential futures. I’ve watched as he’s helped steer many young men and women onto a productive and meaningful path after they’ve teetered on the edge of educational failure for some time. We need more math teachers like him.

So in closing I’d like to say that I agree that it is time that we take a long, hard look at the whole domain of algebra in our high school and college system. We’ve stopped demanding that kids know how to spell and write a proper sentence (and even to handwrite, it seems) and they still manage to find work and be productive citizens. Why can’t we lighten up around algebra? If it means that a greater proportion of our children make their way through the school system and actually graduate with some self esteem still intact, who knows how our society will benefit.

And that thought gruntles me very much.

Fear and Aging

Here I am on my balcony last summer. I let my gardening go this year so that I could spend more time solo camping.

I live my life relatively free from fear. I learned a long time ago that fearing the future means that my today is lived with less aliveness than is possible because some part of me is bracing against a negative future. As I often tell my coaching clients who don’t believe that they can envision a future for themselves: if you can worry, you are already adept at creating a vision for yourself. It just happens to be a negative view of what’s possible.

That isn’t to say that I don’t have certain concerns about my future, but I don’t fear it. For example, I’ve chosen to live alone in later life; what biological family I have all live over 1,000 miles away. I’m very mindful that this means that should I ever get sick or otherwise need the support one typically looks to family for, it won’t be there.

I was just chatting with a friend who has just come through a rather prolonged medical situation. She was surprised at just how much self advocacy it took to receive the best attention from the medical system. Those kinds of conversations give me pause to consider the future. Not in a fearful way, but in a way that invites creativity and an awareness that I need to develop alternative strategies for myself.

Making new friends with people younger than me is a key ‘self preservation’ strategy of mine! Sadly, Trish is from Ottawa so we really only spend time together volunteering at Stanfest each July

I don’t know what my answers for dealing with life’s inevitable crises will be, but I do have every confidence that they won’t be fear driven. Rather they’ll be considered and mindful, anticipating alternatives, just like I live my day-to-day life. One thing I’m very clear about, though, is that I have no plans to become one of those fearful little old ladies who sit quietly in their homes and apartments afraid of every knock at the door. I know that the best way to live the future without fear is to live today without it. I also know that the best way to live the future mindfully is to begin to develop plans and strategies today.

Hmmmm . . . .

Twitter has been very, very good to me

My top 10 benefits from regular Tweeting

 Many friends and colleagues think I ‘waste’ a lot of time on Twitter because I can’t claim any significant direct sales. And yet, for me, Twitter has been an invaluable business tool. I’ve developed an international network, gained significant exposure, begun to understand how new-to-me industries operate (social networking, travel, publishing) and built some great business associations.


Here’s a list of 10 specific benefits I’ve achieved over the past 3 years on Twitter:


  1. Guest blog posts – at least 6 covering various aspects of my interests. Guest blog posts are great for highlighting your expertise as well as deepening relationships
  1. Travel agent – found myself a travel agent to handle my client’s bookings
  1. Advertisers – found a woman’s travel site on which to advertise my retreats, plus a retreats site for highly targeted promotions
  1. I’ve been interviewed by several journalists and achieved increased profile for both my coaching and travel businesses. Great credibility builders.
  1. I’ve built in-depth relationships with around 20 specialists in Portuguese travel industry with whom I’m in regular interaction
  1. I’ve arranged free tour and travel opportunities with people I’ve met via Twitter
  1. I’ve sold copies of my Algarve Dining book to Twitter contacts
  1. I’ve obtained great ‘how to’ information about social media, the travel industry and book publishing/promotion by following links and downloading free e-books offered on tweets
  1. Twitter helped me discover a critically important industry conference that I now attend regularly
  1. I’ve been able to help many of my clients on a wide array of topics from articles I’ve read via Twitter. Allows me to offer serious ‘value add’ to clients without any appreciable additional effort or cost.



Too busy living life

A sunset to stir the soul

Well, even with the best of intentions, it has been months since I completed my initial post. My only excuse is that I have been too darned busy living life to take the time to post.

Yet as I wrote that sentence I heard a little inner voice saying “fibber. look at how much time you spend watching TV and just staring at the view out your window. You could be writing instead”. That little voice can take a flying leap. Because every minute I’ve spent doing those ‘wasteful’ things is time well wasted in my book.

I know that one of the reasons I’m as creative as I am is that I give myself permission to hang loose, do nothing useful, chill, drift off, waste time . . .take your pick in terms of your preference for how you think about idle time. I like to think that I’ve let go of my judgements in this department, but clearly I still have a little rule somewhere deep inside that holds unproductive time as a no-no.

So I’m once again reminding myself of the value and benefits of downtime. And while I gaze out my window at the lush greens that are developing on the hillside across the bay, I’m going to take a deep breath and let myself appreciate all that I’ve created in my life. I’m also going to mindfully acknowledge that these times of drifting away are important to to my well-being, to my creativity and to my vitality.

What about you? What are the ways that you take a break from your busy life? Do you have regular down time? How comfortable are you with ‘wasting’ a bit of time each day?