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The Mindset thaat Masters Math (Norms & Nobility - 11e) · The Grammar of Classical Education

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  SPEAKER_00: Welcome to The Grammar of Classical Education,
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  a podcast that examines the philosophical foundations of
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  classical education and
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  then seeks to help classically-minded educators bring those
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  ideas to life in their
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  SPEAKER_00: classroom,
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  SPEAKER_00: co-ops,
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  SPEAKER_00: or homeschool settings.
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  SPEAKER_00: I'm your host,
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  SPEAKER_00: Dr.
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  SPEAKER_00: Darlene Gomes from Leading to Wonder,
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  SPEAKER_00: and I am so glad you've joined us today.
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  Welcome back to our podcast,
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  or if you're joining us for the first time,
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  welcome.
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  SPEAKER_00: I'm really glad you're here.
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  We are in the process of working through Norms and Nobility by
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  David Hicks.
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  SPEAKER_00: And in fact,
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  SPEAKER_00: we are almost coming to the end of chapter 11,
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  SPEAKER_00: which is entitled Three Schools in One Academy.
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  SPEAKER_00: Now,
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  SPEAKER_00: Hicks has spent a good deal of time on two of those schools,
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  SPEAKER_00: the Arts and Languages,
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  SPEAKER_00: as well as the Humane Letters.
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  SPEAKER_00: And today,
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  we finally get to tip our toe into the third of the three
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  schools in the Academy,
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  SPEAKER_00: which is the Maths and Sciences.
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  I will tell you before beginning this research adventure that
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  I'm thoroughly
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  SPEAKER_00: enjoying in preparation for these podcasts,
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  I always have seemed to consider that last squall of maths and
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  sciences somewhat
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  SPEAKER_00: unattractive.
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  SPEAKER_00: I am clearly so much more of a word person, but I have to say,
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  After reading through books like The Liberal Arts Tradition and
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  Beauty for Truth's
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  SPEAKER_00: Sake,
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  SPEAKER_00: both of which I've had the opportunity to go through on this podcast,
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  SPEAKER_00: I am actually beginning to see the value and importance of this school.
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  SPEAKER_00: Dare I say that?
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  SPEAKER_00: even the truth, the beauty, and the goodness in math.
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  SPEAKER_00: Now, admittedly, I have always enjoyed science.
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  SPEAKER_00: It's more math that has been my hang-up.
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  SPEAKER_00: Now,
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  while we could try to cram both part five and part six of this
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  chapter into one
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  SPEAKER_00: podcast,
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  as Hicks is spending his time demonstrating why these two
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  sister subjects of maths
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  SPEAKER_00: and sciences not only have a place in the academy,
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  SPEAKER_00: but they deserve the recognition of that place.
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  But since it's kind of a weighty topic and math may make some
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  of you shudder as it
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  SPEAKER_00: did me,
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  I figured we'd handle the math portion this week and then look
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  at the science
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  SPEAKER_00: portion next week.
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  SPEAKER_00: Hicks starts out,
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  SPEAKER_00: though,
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  by laying the foundation for the importance of a solid maths
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  and sciences program.
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  He states that a good math foundation will determine how well a
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  student can use
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  SPEAKER_00: that mathematical reasoning in other subject areas.
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  And how quickly that student will gain a sense of almost a
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  second sense of numbers
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  SPEAKER_00: and functions.
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  And how deeply he will delight in,
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  as Hicks calls it,
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  quote,
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  the science of numbers,
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  end quote.
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  SPEAKER_00: Overall, the benefit of a good math program can be summed up by M.W.
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  SPEAKER_00: Lumanosov when he said,
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  SPEAKER_00: quote,
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  one should study mathematics simply because it helps to arrange
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  one's ideas,
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  SPEAKER_00: end quote.
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  SPEAKER_00: So with that thought in mind,
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  Hicks begins to lay the foundation for a solid math program
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  beginning in seventh
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  SPEAKER_00: and eighth grade.
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  SPEAKER_00: My question then becomes,
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  SPEAKER_00: if this foundation is so important,
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  SPEAKER_00: should we not consider it actually being laid much earlier?
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  And when you consider the fact that Hicks really stresses that
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  math has to be
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  SPEAKER_00: taught properly and taught well,
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  SPEAKER_00: so it does not have to be a relayed foundation in upper school.
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  SPEAKER_00: With that in mind,
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  SPEAKER_00: I would say,
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  SPEAKER_00: yes,
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  it's even more important that we are laying this in the earlier
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  grades as well.
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  SPEAKER_00: By the way, this is also a solid support for a unified math curriculum.
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  When you consider that students are spending years on their
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  educational adventures
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  SPEAKER_00: in math,
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  SPEAKER_00: there is little worse than changing terminology midstream.
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  SPEAKER_00: Imagine waking up tomorrow and suddenly a spoon is called a catch call.
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  A knife is still a knife and a fork is still a fork,
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  but a spoon is now a catch call.
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  If you call it a spoon,
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  you will either get mocked or treated like a complete doofus.
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  SPEAKER_00: How frustrating would the easiest things be in the kitchen,
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  SPEAKER_00: a place where you are or you thought you were completely comfortable?
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  It now becomes fraught with frustration as you constantly have
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  to translate the
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  SPEAKER_00: word spoon in this newly declared word of catch call.
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  SPEAKER_00: Now, multiply that frustration for our students on their math journey.
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  For example,
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  in an elementary classroom,
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  they are working with these things called numbers.
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  Everyone knows what a number is after some blessed kindergarten
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  or first grade
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  SPEAKER_00: teacher teaches them.
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  SPEAKER_00: But suddenly in higher grades, a math teacher is talking about integers.
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  SPEAKER_00: Like, well, of course, everyone knows what an integer is.
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  SPEAKER_00: By the way, an integer is simply another word for a whole number.
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  But do you see how valuable it is to have a curriculum that
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  introduces that
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  SPEAKER_00: terminology earlier in their educational journey,
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  SPEAKER_00: allowing the students to be well,
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  SPEAKER_00: at some point,
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  SPEAKER_00: math bilingual,
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  SPEAKER_00: I guess you could say.
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  I think you see the point and the value of working with the
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  upper school math
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  SPEAKER_00: department or teachers,
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  SPEAKER_00: and if you're homeschooling,
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  of getting a clear idea of where they're headed while they're
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  still just getting
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  SPEAKER_00: started on the path.
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  Iggs attributes part of the problem in teaching math coming
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  from the fact that
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  SPEAKER_00: there is,
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  SPEAKER_00: quote,
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  SPEAKER_00: a scorn for the basic ideas,
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  SPEAKER_00: underlying assumptions,
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  SPEAKER_00: and the fundamental skills of paideia,
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  SPEAKER_00: and the consequent desire to teach literature,
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  SPEAKER_00: not literacy,
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  SPEAKER_00: creativity,
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  SPEAKER_00: not discipline,
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  SPEAKER_00: answers,
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  SPEAKER_00: not questions,
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  SPEAKER_00: solutions,
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  SPEAKER_00: not methods.
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  SPEAKER_00: Unquote.
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  SPEAKER_00: Ouch.
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  SPEAKER_00: But what does that look like for a grammar school teacher?
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  SPEAKER_00: Are we teaching math just so they know how to get the solution or so they
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  SPEAKER_00: understand the method?
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  SPEAKER_00: Are we so interested in the what that we brush right past the why?
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  Are we so focused on answers that we really don't want to work
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  through any
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  SPEAKER_00: questions that may arise?
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  SPEAKER_00: To counteract that,
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  SPEAKER_00: Hicks says good teachers must have,
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  SPEAKER_00: quote,
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  SPEAKER_00: a clear insight into the nature of the subject,
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  SPEAKER_00: end quote.
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  So we have to approach math and basically all subjects with a
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  deep and clear understanding.
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  SPEAKER_00: We need to have had our aha moment with the information.
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  SPEAKER_00: We need to be willing problem solvers.
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  SPEAKER_00: Now, some of you may say, that last one, not really.
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  SPEAKER_00: You see, I have an answer key.
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  SPEAKER_00: Well,
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  I would highly recommend that you always go through and double
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  check what you're
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  SPEAKER_00: doing,
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  SPEAKER_00: especially when it comes to story problems,
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  especially when it comes to story problems with upper grammar
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  school students.
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  You should actually be looking for other ways that the problem
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  can be solved.
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  SPEAKER_00: If you are of a certain generation,
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  SPEAKER_00: my hand being raised,
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  SPEAKER_00: math was always done this way,
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  SPEAKER_00: because this way is the way to do this problem.
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  SPEAKER_00: But in real life,
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  SPEAKER_00: it's not actually that cut and dry.
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  SPEAKER_00: There are often many ways to reach the answer.
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  SPEAKER_00: When I first started from a Singapore-based math program,
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  I found it painfully stressful because they never took the most
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  direct route.
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  The do it this way because this is the way to do it that I grew
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  up with and was
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  SPEAKER_00: taught how to teach
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  wasn't being done but because of that i have to say now after
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  several years of
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  SPEAKER_00: teaching it well i've gotten better at math
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  SPEAKER_00: I've learned that math can be, ooh, dare I say it, kind of fun.
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  SPEAKER_00: Yes,
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  SPEAKER_00: it is still hard work,
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  SPEAKER_00: but math according to Hicks has been proven to increase concentration,
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  SPEAKER_00: memory,
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  SPEAKER_00: logical skills.
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  SPEAKER_00: By the way, those are principles that are required in other subjects.
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  SPEAKER_00: It's just more noticeable in math.
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  Higgs also points out that there is a certain discipline
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  required in math.
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  SPEAKER_00: I used to tell my students it was tenacity.
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  And that tenacity is the way that the mind can control the
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  natural tendency to not
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  SPEAKER_00: want to think.
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  It does that by helping us to delight in working through a
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  problem and finding answers.
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  SPEAKER_00: It doesn't mean that it's easy.
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  SPEAKER_00: Tenacity and easy do not go together.
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  But while it is hard work,
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  math must not be seen as,
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  quote,
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  useless mental discipline,
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  unquote.
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  SPEAKER_00: We must help create a foundation where numbers can be enjoyed,
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  SPEAKER_00: where they can be played with,
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  SPEAKER_00: where they can sing.
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  SPEAKER_00: Now, not all students are born with a positive proclivity to math.
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  This difference is clearly seen when comparing my husband's
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  view of math and my
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  SPEAKER_00: view of the same subject.
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  SPEAKER_00: To him, numbers bring something delightful to the party of thought.
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  They are there to mix and mingle with,
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  to enjoy and join in their beautiful melody.
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  SPEAKER_00: For me,
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  SPEAKER_00: numbers all tend to come tumbling into the room,
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  all talking at the same time in obscure foreign languages and
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  all screaming for my
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  SPEAKER_00: attention,
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  SPEAKER_00: especially when they show up for a party and ask a question,
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  SPEAKER_00: as in a word problem.
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  I do find them slightly more tolerable when they come quietly
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  into the room,
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  SPEAKER_00: lined up neatly and standing in order for me to work with.
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  SPEAKER_00: But I am learning to enjoy the party.
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  SPEAKER_00: Do they sing for me?
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  SPEAKER_00: Not just yet.
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  SPEAKER_00: but I can at least put on my party hat and try to enjoy them.
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  SPEAKER_00: So as teachers, our job is twofold.
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  SPEAKER_00: One, we need to find joy in the math we are teaching.
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  SPEAKER_00: Honestly,
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  If we can't do that,
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  how on earth can we expect our students or our children to?
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  SPEAKER_00: If you hate math,
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  there is a pretty high likelihood that your opinions will ooze
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  out in a very
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  SPEAKER_00: obvious ick to your students.
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  SPEAKER_00: So we need to find joy in the math that we're teaching.
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  SPEAKER_00: And then number two, we need to help them find that joy.
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  SPEAKER_00: It is a mindset.
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  SPEAKER_00: Maybe sometime we'll be able to delve into this area a little bit deeper.
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  SPEAKER_00: You see, I understand because I have been through this personally.
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  From a math student who hated math to a math teacher who really
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  disliked math to a,
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  SPEAKER_00: well,
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  SPEAKER_00: I guess it's not so bad.
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  And that change came only because I brushed up against a
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  teacher who helped me see
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  SPEAKER_00: the joy in math.
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  And then after a few years of teaching math with a Singapore
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  model in mind,
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  struggling through it with two other teachers who together we
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  were bound and
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  determined to figure this math stuff out after that kind of
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  effort and that kind of
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  SPEAKER_00: camaraderie,
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  SPEAKER_00: I turned into a teacher that thought,
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  SPEAKER_00: wow, this math stuff is actually kind of fun.
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  SPEAKER_00: And folks, if I can do that, so can you.
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  SPEAKER_00: Remember, a twofold mission.
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  SPEAKER_00: One, to find joy in the math we're teaching.
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  SPEAKER_00: And number two, to help them find the joy as well.
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  SPEAKER_00: Well,
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  SPEAKER_00: next week,
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  SPEAKER_00: we will finally be finishing chapter 11,
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  SPEAKER_00: three schools in one academy as we look at science.
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  And we'll see how it runs parallel to without completely
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  overlapping the math of this school.
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  SPEAKER_00: Thanks for joining us.
• 17:23
  SPEAKER_00: And I look forward to having you around for our next episode.
• 17:31
  SPEAKER_00: I trust that whatever your teaching situation,
• 17:35
  SPEAKER_00: whether it's in a classroom or co-op or homeschool setting,
• 17:41
  SPEAKER_00: that you have found these ideas not only encouraging,
• 17:46
  SPEAKER_00: but challenging as well.
• 17:50
  You can listen to all of the episodes of The Grammar of
• 17:54
  Classical Education on
• 17:56
  SPEAKER_00: Apple Podcasts or Spotify.
• 17:59
  If you would like to add to the podcast a weekly teacher's
• 18:03
  newsletter that includes
• 18:05
  SPEAKER_00: some helpful teacher tips and freebies,
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  you can sign up for the Leading to Wonder newsletter at
• 18:12
  darlenegomes.substack.com.
• 18:18
  To learn more about me and Leading to Wonder,
• 18:22
  please visit the website leadingtowonder.com.
• 18:27
  SPEAKER_00: No spaces.
• 18:29
  I encourage you to reach out if you have any questions or if
• 18:36
  you're interested in
• 18:37
  SPEAKER_00: the virtual or in-person workshops that I offer for schools,
• 18:42
  SPEAKER_00: co-ops,
• 18:43
  SPEAKER_00: homeschool educators,
• 18:44
  SPEAKER_00: and parent groups.
• 18:46
  SPEAKER_00: Again, my name is Dr. Darlene Gomes, and thank you for joining us.
• 18:54
  SPEAKER_00: Until next week, remember, as E.B.
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  SPEAKER_00: White said, always be on the lookout for the presence of wonder.
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  Bye.