Tag Archives: Math

From Finance to Teaching Math: An Interview with Mary Kay Kosnik

What do you enjoy about your role at Hamlin? 

I’m currently teaching 6th grade math at Hamlin.  I have a dream job — I get to learn and help students!  Teaching in the middle school is pure magic. I witness great thinking, creativity, growth and joyful collaboration every day.   My students and colleagues are rock stars! The thread of excellence that permeates through Hamlin is what drew me into this diverse, dynamic and soulful community.   Everything that happens at Hamlin is aligned with best practices and continuously scrutinized for improvement.

Tell us about your career before Hamlin. What did you most like about that work?

My professional background is in analytics, research and consulting to the financial services industry.  I began my career at the Federal Reserve Bank of San Francisco and later worked on Wall Street as a buy-side equity analyst.  For the bulk of my professional career I worked as a management consultant for KPMG Peat Marwick’s National Financial Services Consulting Group. All of these jobs had a steep learning curve, were entrepreneurial and enabled me to collaborate with very talented people. In consulting I traveled extensively and worked on really unique and exciting high impact projects.

How did you make the decision to go into teaching?

I consider myself a life-long learner and have always been passionate about stepping into service to support students.  While I was working professionally and raising a family (my husband and I have three grown children), I taught and volunteered in classrooms, tutored, and coached and managed youth sports.  I also collaborated on fundraising projects to improve schools and provide scholarships. In higher education, I serve on the Dean’s Council at my alma mater, the University of Michigan. I also mentor undergraduates.  

So I guess I would say that becoming a teacher was a natural progression of my lifelong interest in helping students. I knew that becoming a teacher would be challenging and deeply meaningful work.  As an educator, my goal is to inspire girls to enjoy math and to develop their competence and confidence as mathematicians. We need more women in STEM fields!

What advice to you have for women who would like to work in finance?

Study math, always apply your analytical skills, be bold and decisive, and expect to become the boss!

Finance is creative and fun — every organization needs competent people who can generate, analyze and understand the numbers that ultimately drive decision making and the business.

How does learning math relate to understanding “real world” finance?

I think there is a big misconception that the goal in math is to learn an algorithm to achieve a “correct” answer.  Sure we need this competency, but math is so much more than that! In math we question, explore, investigate, analyze, collaborate, strategize, build, explain, and problem solve in diverse and creative ways.   “Real world” finance is all of this, whether you are managing your allowance, your household or your company.

Interview with Hamlin Math Enthusiast: Gillis Kallem

Gillis Kallem is our Lower School math specialist, this is her 11th year at Hamlin.

1. When and how did you fall in love with math?

When I was a kid in school I enjoyed math, it came to me easily and made me feel good about myself. I could see relationships with numbers. I fell in love with math again when I was training to be a teacher. I loved the beauty of teaching math.

2. What is your role in the Lower School?

Guiding the grade level teachers, looking at best practices, including how we develop numeracy for students. I also think about students developmentally, how and when do they acquire their skills? I help with differentiation of instruction, and co-teach inquiry sessions where students are given a problem, but no one tells them how to do it, they have multiple entry points and multiple strategies for solving it. I believe in a growth mindset, and work to elucidate what math is, for both teachers and students.

3. Explain one way that you enjoy supporting math learning.

I love it when a student becomes fully engaged during an inquiry investigation because the solution is open to interpretation, and they have an entry point. It is very fulfilling to watch a student become a leader really doing math with a purpose.

4. Who has influenced you in the math world?

Cathy Fosnot, Jo Boaler, Pam Harris, Graham Fletcher. These are the people I follow on YouTube and I read their blogs. Cathy taught me that when children are engaged with math in a meaningful context they become fully immersed and curious. These people believe that math should be taught for a reason, for a purpose.

5. Finish this sentence. Exploring math is like_____________________________________

a journey into the known and unknown simultaneously. Along the way you stumble across unexpected places and experiences, and the exploration is exciting and inspiring.

6. What is one goal for a Hamlin student completing our lower school math program?

Macro: They are willing to persevere when confronting seemingly impossible problems.

Micro: They are able to work with numbers easily and figure out efficient strategies appropriate for a given mathematical situation.

To learn more about Ms. Kallem’s approach to math, please read: http://www.hamlinblog.org/blog/2014/10/03/first-comes-number-sense-gillis-kallem/

 

 

Baking Math Into Cakes

Today Grade 5 students had the opportunity to bake a cake and learn about fractions as part of the process.

Students began by completing various math problems in order to determine the quantity of an ingredient required for their specific cake.

Example:

Ingredient 1:

Bennett had 1 & 1/12 hours to play. He walked to the park for 1/2 of an hour. He played at the park for 1/3 of an hour. He ran to a friend’s house for 1/6 of an hour. What fraction of an hour does he have to play at his friend’s if it takes him 1/4 of an hour to walk home from his friend’s house?

The answer (to the above problem) provides the amount of vegetable oil needed for the cake.

Students completed a series of math questions, unlocking the ingredient amounts needed to make a successful cake.

The girls then answered questions related to their recipes, followed a procedure, while also making a couple of hypotheses about the project.

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First Comes Number Sense by Gillis Kallem

number-icon-setAt Hamlin, we want to cultivate a rich math experience, which includes a vibrant mathematical adventure into the world of numbers and reasoning, problem solving, and creativity, as well as real-life applications. At the foundation of this important work is number sense. In its most general definition, number sense is the ability to intuitively work with numbers. It reflects an understanding of numbers, their magnitude, and relationships. As educators, we expand the meaning of number sense to include a well-organized concept of numbers that allows a person to solve mathematical problems accurately and efficiently in a variety of ways that are not bound by traditional algorithms. (Bobis 1996)

Number sense involves the understanding that numbers are flexible. For example, a number is malleable like a ball of clay. You can change its shape – make it long and skinny, or short and fat—or you can break it apart into smaller pieces and in the end roll it back to its original ball. The same is true for any number. Take 28, it can be seen as 2 groups of 14, 4 groups of 7, or as 20 + 8 or 10+18 or almost 30. Take your pick. Having this ability to see 28 or any number in its many forms allows the user to think freely and creatively when asked to solve problems involving operations with numbers.

When we are presented with a problem such as 131 – 28 in which we might be tempted to write it out in the standard algorithm, then regroup/borrow/cross out numbers and so on, we can instead think about the many forms that any number can take and find one that makes sense for solving this problem in our heads:

Think of 28 as 20 + 1 + 7.
We can first think: 131 – 20 = 111
Then, 111 – 1 = 110,
Finally, 110 – 7 = 103.
In this method, we break apart the subtrahend.

Or we can think that 28 is almost 30 by adding 2 more.
We can change the problem: 131 – 30 = 101
Then we add back 2:101 + 2 = 103.
In this method, we adjust the subtrahend to make a friendly number or a round number, and then add back what we added to the subtrahend.

Or we can play even further!
Change both numbers by adding 2 to each.
Thus, 131- 28 becomes 133 – 30 = 103.
In this method, we adjust both sides, keeping the distance the same but making the numbers easier to work with. This method is known as constant distance.

What about 28 x 5? How would we efficiently and accurately solve this mentally?
One way might be to think of 28 as 20 + 8
Then, 20 x 5 = 100 and 8 x 5 = 40
Combine, 100 + 40 = 140.
This makes use of the distributive property of multiplication.

Another way might be to think of 28 as 30.
Then, 30 x 5 = 150.
Now, subtract two groups of 5: 150 – 10 = 140.
Again, this is using a friendly number and then adjusting afterwards.

Or you could think of the problem in an entirely different way!
Turn 28 x 5 into 14 x 10 = 140.
This is a clever method called doubling and halving.
Various classroom activities and lessons in Grades K-5 at Hamlin support the development of number sense and flexible thinking.  Additionally, our assessments measure the girls’ learning of robust number sense. Building computational fluency is a core skill that fluid and flexible number sense girds for long-term success in mathematics.

In my next Curriculum Connection, I will highlight the specific classroom practice of Number Talks/Number Strings as it relates to number sense.

Gillis Kallem
K-5 Mathematics Specialist