>> Welcome to today's online office
hours from the Library of Congress.
Today we're going to be exploring
math and primary sources.
And we're so glad that you can join
us either live or by recording.
If this is your first time joining us, welcome.
And if not, welcome back.
So, just so you know these
office hours are short
and they are meant to be informal sessions.
There's going to be about
a 20-minutes presentation.
And we'll be recording the session so you
can watch back later, or of course share
with others that may be interested.
You'll also have the opportunity today to
talk to each other and the presenter via chat.
So, we want to get started trying out the chat.
So, if you can go to that chat box, and
tell us your name, where you're joining us
from and what [inaudible] you teach.
And Mike if you can go to the next slide
everyone can see what we're asking them
to put in the chat box.
As I mentioned, today's focus
is on math and primary sources.
And we're joined by Mike
Alphadorf [assumed spelling]
who is also from Learning Innovations, Inc.
So, please enjoy.
If you have any questions at any
point, please put them in the chat box.
I'll also be posting links there as Mike is
going through his presentation, and either I
or any of my colleagues who are on the chat
will be more than happy to answer questions
or point you in the right direction.
Now, I'm going to pass things over to Mike.
>> Thanks, Collina.
And can you just let me know before you
bounce off if you can see my screen okay?
>> I can see it fine.
Thanks.
>> Okay, well thanks everybody for coming.
As Collina mentioned, we're going
to spend the next 20 minutes
or so talking about math and primary sources.
And by that, what I really mean is what
are some possibilities for students looking
at primary sources through
the lens of mathematics.
So, this doesn't necessarily have
to occurring a math classroom.
It also doesn't mean that they're not looking
at another lens like a historical lens.
So, it's just one more tool or
one more skill that they can bring
to the analysis of primary sources.
And so, while they are processing math skills,
they're also, as a result of math analysis,
they're also building, or unlocking
fresh cross-disciplinary insights.
And we'll look at some examples
to show how that might happen.
If you notice on the screen,
the sub bullets here,
numbers and operations, measurement, etcetera.
I'm going to be sort of referring
to those terms throughout
because those are the national math standards.
And I want to sort of root
what we're doing and sort
of what specific math skills
they're going to bring.
So, let's jump right into it.
We're going to look at the first example has
to do with how can we look at primary sources
in math to think about how
technology has impacted American life.
And we're going to look specifically
at sending messages to one another.
Now, our kids, obviously, they
live in an instantaneous world.
They can send text, it goes halfway across
the world in a snap of a finger, right?
We know it wasn't always like that and
so we can go back into historical record
and see mail deliveries using
different technological formats.
So, this is from the Thomas Jefferson
papers, bits of resources right
after the Louisiana Purchase, 1806 .
And it shows you the mail delivery
between Washington, DC, and New Orleans.
If you look closer at this, not only can
you enjoy Jefferson's beautiful script,
you also see all the elements
here that we need to start
to actually calculate the rate of mail delivery.
We have origin city, destination city.
We have dates and times.
And I can see here, in a very just kind of
rough way that to get from Washington DC
to New Orleans, I can send
a letter in 13 days 7 hours.
Okay, now I can obviously translate that
to only days, or all in terms of hours.
I could also, if I had a map I could say, well
here's how many miles were handled per day.
So, I'll show you a little bit later
some maps we can use to do that.
But in one way or another student can start to
get to level set this idea of communication,
rate of delivery and mail through this
kind of very early primary source.
And then we can start bringing in
other sources, for instance this.
This is by the mid-19th century now,
the train is transforming American life.
And you can see even the document itself
and remember I mentioned we're going
to analyze this not just through math lens,
but even through our historical lens too.
So, you see this document even
just looks different, right?
It's nice and printed.
It's an advertisement, it's telling you can
buy a ticket to ride with the mail as well.
But in addition to that we can
actually start to quantify this change
by having students calculate once
again, the rate of mail delivery
and start to think well how much faster?
How many letters could I have?
How many times can I go ack and
for between DC and New Orleans now
within that 13-day, 7-hour period right?
So, how can I quantify this
rate of change, or this change?
And what sort of insights might that
provide me looking at a historical period.
So, the idea is the student is at once kind of
practicing math skills and really basic numbers
and operations, looking at rates, and addition,
also sort of gaining insights into history.
And we can layer in additional times of history.
Additionally, you can make this as
elementary or advanced as you like.
You can walk them through rates how to do rates,
or you can walk them through how to do rates,
or you can just give them both resources
and say, how did American society change?
And let them come up with
the solution how to do that.
Now, I want to also show how you can add
other primary sources to continue this motif
of the evolving postal systems while
bringing in different math standards,
specifically measurement, geometry, algebra.
So, here's a map.
This map shows some of the things
we've already talked about.
Post offices, post roads, railroads.
And so, using this kind of resource,
you can layer in other things.
You see there are numbers on this
map so I can bring in measurement.
Now, I can see really how far
it was from different locations.
From there, I can bring in algebra, right.
Because I know I can cover 100 miles in
two days and I know I have to go 500 miles,
right I can solve for the unknown,
which is how many days it's going
to take me to get there, right.
So, you can bring in measurement,
you can bring in algebra.
And of course, you bring in geometry,
because the mail system is a network,
it's not simply always just putting in mail
from two points, which as we know from geometry,
the fastest way between two
points is a straight line, right?
But it doesn't go in a straight
line it's a network right.
So, we can think about now what would
be the fastest mail delivery system?
What would that have to do with geometry.
But then how was it actually created right?
Because there's a very historical context
around this, right the postal system,
the development of post roads, post offices
is in the United States Constitution.
So, on the library's website
you can find bills saying
when that congress established
different post roads.
You can see how that laid itself out.
So, again, you're learning sort of using
the math skills, but also using them
to really reflect on the actual history.
Here's a blog post if you're
interested in this topic.
We have a blog post I think Collina
is going to put it in the chat.
It really kind of looks at
the evolving postal system.
But that's just kind of one
example of something you can do.
Now, in other cases, you're not necessarily
making calculations to understand history,
but there's just kind of an interesting
connection between the source and history.
And so, we're going to look at
a couple with measurement here.
So, this one, you might show your
kids and just say what do you notice.
And feel free to speculate what you notice here.
For me, there's a lot of
interesting things here.
This is actually Thomas Jefferson's proposal,
very early on in the country's history
for a national measurement system and it
could be fun to just notice things here
like the funny words like might and
stone, and hog's head and scruple.
Measurement terms we used to use.
But some that we recognize
right, like pounds and ounces.
And one of the things you obviously
notice is the base 10 system.
Right? Obviously, this proposal was
not accepted, that's why you still have
to always remember there
are 16 ounces in a pound.
However, I don't use hog's head
or scruples interestingly enough.
So, there's a lot of history
of measurement in here.
And there's an interesting
connection for instance in 1791 is
when the metric system was actually first
proposed, wasn't accepted in the United States,
it was accepted in France, interesting
when you think about Jefferson.
And so, you can get kind of
into the history of systems.
Another fun one with measurement
is Rosa Park's pancake recipe,
her peanut butter pancake recipe.
And my colleagues Amara Alexander [assumed
spelling], I don't know if she's on or not,
but she's our Einstein Fellow this
year, she's written a great blog
and I hope Collina you can put it in the search.
And there was also a blog on that Jefferson
research you can put in if you want.
But Amara has suggested that
you could use this recipe
to introduce young children to
the concept or measurements.
They can recognize the symbols
and things like that.
You can even get a little fancier with it,
right, you can say this makes one batch,
what if I have people coming
over and I need three batches.
What if I lost all my measuring
devices except for my teaspoon?
How would I redo this recipe in
terms of just teaspoons, right?
And so, I wouldn't argue that by
doing these calculations you're going
to somehow understand Rosa Parks better.
However, I think this example is a little
different than the post office one.
This is just kind of an example of how you
can use a primary source that's math related
to both teach and practice
math, but also learn something
about an important historical
figure at the same time.
Which can be engaging.
And additionally, I think one of the things I
like about primary sources and famous people is
that it sort of shows them
as a full human being.
And if you haven't had a chance to check out
our Rosa Parks papers online, that really is one
of the great benefits of it, seeing Rosa
Parks as complete person, including a person
who likes peanut butter pancakes.
Now, quickly on to a couple more examples.
We haven't really, of all these math
standards, the one we haven't talked about
yet is data analysis and statistics.
But I think that is actually a pretty good one
for the library's collection, because statistics
and data analysis intersect
a lot with social sciences.
And so, some very simple things you can do.
"Chronicling America" is a
historic newspaper archive.
So, there's millions and millions
of historical newspaper pages.
And within those you can see a lot
in terms of business and commerce.
And some of these are actually very simple,
but they connect to more
complicated economic concepts.
So, for instance, price.
This is a look at old advertisements.
You see in 1935 I could buy
four bananas for $0.15,
in '61 I could buy three
pounds of bananas for $0.29.
So, how do I compare this right?
Do I need to reduce each one
to what one banana would cost?
Do I need to check other newspapers?
You know you could do lots of analysis here.
You could just kind of straight
comparison of these two.
I could look for a data point
every year between 1935 and 1961.
Or, I could just focus on say 1935 and
look for regional differences in price.
Either way, the idea is again doing some math
calculations and I'm going to learn something
about economics as I go, in terms of
inflation and maybe even consumer price index.
If you look at this page it's a much
more kind of sophisticated page, I guess.
Also, from "Chronicling America" from
1953 that really gets into this idea
of consumer price index, which is
sort of the price of an average basket
of goods an American consumer would buy, right.
And economists use this to figure out things
like cost of living increases and policy
as this page shows, actually is written
around this idea of consumer price index.
Interestingly enough that little experiment
we did with the price of bananas is kind
of how you calculate the
consumer price index, right,
you're seeing how these prices
are changing over time.
So, this kind of gives an
example of the ways for kids
to start to kind of looking at the data.
And in sort of this presentation
mode, how is data presented,
how a chart is put together,
how is data presented?
And what is our information
literacy approach in this right?
Like when I first saw this I though how
can I learn about economics and then I had
to pinch myself and say wait a minute I
don't even know if this is bias or not.
And to know that I really kind of have to
know something about math right to know how
to put these numbers and these charts together.
So, this idea of can you really be information
literate without being math literate.
And "Chronicling" has a lot
of good stuff for that.
Staying on the same topic of data analysis,
another good source I would point you
toward is the statistical atlases.
And so, in the late 19th, early 20th century the
US Census Office created six statistical atlases
one every 10 years.
And what it did was it took the census data and
it created literally hundreds of data tables,
graphs, data visualization, showing
what life was like in America, right.
So, this is another good example, another
good way of looking at particularly things
like how do you take data and
communicate it in charts and graphs.
And on the other side how do you see
charts and graphs and really kind
of understand what you're looking at right?
So, that's a lot of what you learn with that
sort of data analysis kind of standard, right.
And it's also very important for
information literacy as well, as we know.
So, I'll just show you a couple screens here.
What does data tell us about
America in the late 19th century?
This is kind of a population chart
showing you how population is increasing
between 1790 and 1890.
But if were to really look at the data we'd
start to see that the urban population is taking
on a little bit bigger part of the pie.
We've got look at where those urban centers
are growing and the darker section is
where the urban centers are growing, not just
in the northeast, but also here around Chicago.
And then I looked at other charts and I saw
distribution of the foreign-born population
of the United States 1890 and
it's interesting to see this kind
of rough correlation between these areas.
These charts weren't put together in
the atlas, but I think as you look
at them together what larger stories are told?
There's immigration, urbanization and so on.
It really brings this home when you look
at the same data given a different way.
So, now I'm going to look at distribution of
foreign-born population put in a chart by state.
You can see how different this
chart looks and how it tells
such a different story than this one, right.
Now, this shows me the geographic
sort of movements.
This one really highlights
state political organizations,
so you can really tell a different story.
Just two more quick examples.
One is, I'm not going to go all off about
this one because I want Collina to talk
about this one later, but a great resource
for geometry and engineering is the
"Historic American Buildings" collections.
And these are the National Parks
Service went all over the country,
they took photos of hundreds,
thousands of historical buildings.
But also, are providing architectural drawings.
So, these are a rich source for looking
at things like geometry and engineering.
Not going to say anything else, because
I don't want to steal Collina's thunder.
So, Collina after I'm done, I'm going
to invite you to come in and talk
about the resource you guys just
released on the website that sort of gets
into this idea of maker space stuff too.
So, that's kind of another
connection we can get into.
The final example, and then I'm going to
pause and let Collina in and sort of open it
up for questions, is computational thinking.
I know this wasn't one of the math
standards, but this is particularly fun,
and it shows you how you can look at these
resources through a whole other lens.
There's some great codes and
ciphers in the collection.
This is the Culper Code, which is a famous
code when the British had occupied New York,
George Washington would use this
code to communicate with his friends
and not only can you look at that from a
historical perspective, you can also think,
computationally how was this code structured?
Sort of a simple substitution code
where a number stands in for a word.
So, it's a fairly straightforward thing.
And you would need a code book to
decode this to write and decode it.
That code book could be lost,
it could be stolen.
Right, so that gives you
kind of, not just the code,
but there's kind of a historical
kind of situation around this.
Now compare that with Jefferson's cipher.
We keep coming back to Jefferson, he
really like math and science, I think.
But you've got Jefferson's cipher that he used
or proposed to use to send messages to Luis
and Clark when they were exploring the west.
And you can see right away, this
is structured very differently.
This is this great big grid.
This is a type of what they call
a Vigenere cipher, it's a square.
And instead of being a simple
substitution cipher, it actually getting
into an algorithm right,
which means it has rules.
So, for instance you're given a
keyword, like in this case antipode.
And you're given a string of numbers to code.
And so, the way this works is if I want
to write my letter t and my first word
of my keyword is a, I shift
one time down the alphabet.
So, instead of writing a t I write a u. Now,
if that first letter would have been a b,
I'm going to shift not to a u to a v.
Right, and that's kind of how it works.
So, it's the idea of there are
rules, here's an algorithm.
Much different situation and you can
put that in historical context as well.
You don't need codebook,
codebook can't be stolen,
but somebody could crack your
code, right, through their mind.
And that's precisely what's happened
in the history of coding and cyphers
and why they've become so sophisticated
that only machines do them now.
Because people were so clever
at cracking them, right.
But as you can see because of this shift, you
can actually, not only can you use these codes
and have kids send them back
and forth to one another.
But kids can express these codes mathematically,
right I could say a equals
1, b equals 2, c equals 3.
Can actually write expressions
articulating what these codes are.
And I can even program a computer
to code and decode these messages.
So, there's kind of a lot more
coding stuff in the collections too.
I just wanted to show you those two for now.
Really only have about a minute left of my
20 minutes because I really wanted to stay
to 20 minutes and then give
you a chance to ask questions,
is this is really just kind of a summary.
And really, I've only kind of shown
you a drop in the bucket here.
But this is kind of where you can learn more.
One of the places I'd start with is a lot
of the stuff that I've shown you is actually
from the teaching's Library of Congress blog.
So, if you go to the blog and search under
mathematics, or choose science, technology,
and mathematics in the left, that
will bring up some ideas for you.
You'll see ideas on computing,
on you know the Rosa Parks
and the Jefferson measurement
and the post office.
You'll find some of those examples
and maybe it will just kind
of help you see some possibilities here.
There's also on the teacher's page section,
a primary source set on scientific data
that could be interesting if you're
interested in the idea of data
and how al the different ways it's communicated.
Again, I'm just kind of repeating
things we've already seen.
But a couple of collections
that are particularly good ,
have pair for geometry and engineering.
The statistical atlas is excellent for
data analysis as is "Chronicling America"
and I would say "Chronicling America"
particularly well for economics.
Kind of more fundamentally, this is a hard topic
to just say I'm going to go to this one section
and find all my math stuff
here in this one section.
Really, kind of like math is kind of a language
that's everywhere, right and so I would just say
that if it's something that if you think
this approach looks interesting to you,
you just always kind of put your
own math lenses on and sort of look
for the evidence of math everywhere you see.
And the maps I know Leeann, I don't
know if she's on she mentioned to me,
I forgot to mention, but scales
and ratio obviously a big part
that you can enter in any of these maps.
But even through manuscripts or photographs,
there's always kind of a lens you can bring.
So, that's it.
I think I've given you a lot of information.
So, I want to pause for a second
and see if you want to go into any
of the sections I went through deeper.
If you have any questions if you have any ideas.
Among other things, I would love Collina
for you to also share your lighthouse idea.
>> Great. Well, thanks so much, Mike.
So many different ideas and I learned a lot of
fun access points to mapping our collection.
So, thanks for saying that.
Just to piggyback on what you were saying
about the [inaudible] collection,
the light house example.
So, for those of you out there we
just launched a new family activity
and I'll put that in the chat box.
That was actually inspired and kind of based
on research that Mike did in [inaudible]
to connect children to books to primary
sources in the library collection.
And his work focused on children's
books about lighthouses.
And then he found examples of
lighthouses in the collection.
So, a group of us developed this
activity to design your own lighthouse.
And basically, it's an opportunity for
students to get inspired by examples
of lighthouses in our collections.
So, photograph, architectural
drawings, newspaper articles
about lighthouse keepers, that kind of things.
Increase that inspiration
through learning about lighthouses
as primary sources to design
their own lighthouse.
Either by drawing it or creating it with
materials that you may have at home.
So, I'll point you all to that and also
post a few more links related to lighthouses
and primary sources in the collection.
But in the meantime, feel free to
post any questions that you have.
So, Mike, I know I saw a
question, or a comment earlier.
Maybe Mike can go back to the,
there's a comment here that scale
on the CPI graph was not consistent.
So, if you can go back to that slide.
>> Let's look at which one
are you talking about?
>> I think it's the economics example,
the consumer price index graph.
We had a comment here that said
the scale was not consistent.
>> Now, that's very interesting.
Oh yeah. Go ahead.
>> So, I wonder if you know we
can talk about that a little bit,
or just look a little bit
more closely at that to see.
>> I think that's, I'm pulling up the site and
I think that's one of the points that shows sort
of a good information literacy component.
And I applaud whoever said it.
I'm not sure what you meant, I'm assuming that
you meant like there's only 20 between here,
and there's 30 between here, and there's 25.
It's not completely consistent.
And so, when you're looking at a
graph, you're expecting consistent.
And additionally, here, 1951, 1952 when
you're looking at something graphically,
the more even the scales are, the
more accurate the graph is, right?
So, otherwise people can play with
that scale to make it look different.
So, that's actually kind of a good example.
I don't know whoever responded,
feel free to respond in the chat.
But I think that's a very good thing to look
out for in terms of information literacy.
And the way I look at these charts
and graphs is these and also the ones
in the statistical atlases, there's
kind of two sides of it for kids.
One is you know we want kids to be very
information literate and know when they look
at info graphs how to really understand
how they were built and how to read them.
And the other thing is they're also creators of
information right, so we want them to be able
to create information very
deliberately to tell their own story,
and you know obviously you'll
want them to be objective.
So, that was a good point whoever made that.
>> Exactly.
And I think that was actually Jeff and he
followed up to say the compressed horizontal
on the left makes the graph look steeper
than on the right side of the graph.
>> Oh, very clever.
Very good point.
So, yeah, I mean that's a
very good example of the type
of thing we certain want our kids to make.
One of the cool things I like about going and
chronicling for these things is you know we look
at infographics today and it's just sort
of this dizzying among of information.
It is kind of neat when I look at this one
and I look at there's sort of a particular
in moment that we're looking at too.
There are controls and decontrols.
And they're really talking about
something very specific to the time.
And looking at something in a historical
record also gives us the great luxury
of seeing how all this works out, right.
What happened in 1953, and 1954, so
it gives you another lens with which
to judge what's happened here and
even what's being communicated here.
>> Definitely.
Liz asked if we can go back
to the lighthouse slide.
I'm guessing it was the slide with the interior
drawing and then the [inaudible] photo.
>> Yeah, you got it, this one.
>> Yep, I think that's it.
So, Liz if you have a question
about this, let us know.
Maybe you just wanted to
take a closer look at it.
Just so everyone knows these slides
will be made available online.
We'll put them in a PDF, and
they'll be available on our website.
So, you'll have access to them
and to the recording, soon.
>> You know I have a very elementary
observation just when I saw it.
I feel almost embarrassed it seems to simple.
You know, to me when I saw this, I wrote
down on the slide what shapes were used
to build this lighthouse and first I was
thinking, well it's just a bunch of circles.
And then I started looking at this lighthouse,
and I thought actually, no when I start to look
at this architectural drawing, I see
these octagons, right with circles inside.
And it just really made me stop and consider.
You know what I mean closer something
that I would have maybe just
spurted out a lot, quickly.
You know what I mean?
And so, I think really pouring
over the architectural drawings can be
interesting whether it's for younger kids,
just making simple geometric
observations, or for older kids too.
>> Yeah, definitely and I think the opportunity
to zoom in, you have a change to zoom
in on these drawings as well as the photographs
to get more of an appreciation for the shape
of things and scale of things
and that sort of thing.
>> Yeah, and I'm thinking
about your maker activity,
obviously, you can scaffold that too right.
it can be just a very simple activity where
you make the lighthouse, or you can really try
to you know achieve certain you know
mathematical similarities to this one,
I guess lack of better word,
which ever you want.
>> Yeah. Definitely.
I'm kind of scoping to see if there
are any other comments or questions.
There are actually Leeann had
a comment he's pondering again
about that "Arizona Sun" article.
And she wondered why the
"Arizona Sun" would choose that
and does the graph now provide greater
support for the gist of the article?
>> Yeah, I agree Leeann.
And I love how Leeann is thinking about this.
And to me it's kind of why I don't know where
this activity fits in terms of a curriculum,
right because you need to think
with a lot of lenses, right,
you're thinking with a mathematical lens, but
you're also thinking with your historical lens.
You know what I mean?
You're looking for bias and all sorts of things.
So, it really is just kind of a
skill that applies everywhere.
So, I agree with you Leeann.
I don't know enough about this picture, but it
makes me want to go back and look at this whole,
all the newspapers around
this one a lot more closely.
>> Definitely.
And Liz says, I was wondering at the top of
the newspaper page it said advertisement.
A lot of times today they try to
I guess trick you into thinking
that it is real, but it is an ad.
So, again, definitely ways to apply
other kinds of lenses and other kind
of literacies to primary sources.
>> Yeah, no, I love this little subtle text
below here, source Bureau of Labor Statistics.
They are then taking the authority
of the Bureau of Labor Statistics.
But we don't know that this graph came
from the Bureau of Labor Statistics.
We just know that they got some
of these numbers from there.
So, that's absolutely a good point.
>> Right. Anyone has any other questions?
People want to share if you have ideas
about how you may use these resources?
Or, if you've used primary
sources that we mentioned today,
or that you didn't mention
that you found to be useful.
Please, please share those.
If you have any other ideas, please let us know.
>> Yeah, and even if anybody wants to
share in their chat for their colleagues
if you have other ideas about how primary
sources in math are related to one another
that we didn't cover, because these
were just kind of a few example.
Feel free to share those in the chat.
This is really something that I think
that our office here, our learning
and information office, we're still really
sort of in the early stages of figuring
out this connection between
math and primary sources.
And so, we'd love to hear from you
guys what looks like it would work.
What would be a good connection with you?
>> So, just to give you a sense
of what's coming up for next week.
Actually, before I do that, I want to say
thank you so much to you, Mike for talking us
through this and just giving us
ideas and food for thought about how
to apply a math lens to primary sources.
Particularly ones that maybe we may not have
approached through using a math lens previously.
And thanks everyone for participating and
for sharing your questions and your ideas
and your observations, and
things that you noticed.
So, for next week, we have two office
hours coming up on Tuesday the 26th,
our physics teacher in residence Jenn Rydell
[assumed spelling] will be taking us on a tour
of Congress.gov and sharing her ideas about how
you might use this resource with your students.
Which about the bill making process?
And then, on Thursday, May 28th, Brian Retch
[assumed spelling] from the [inaudible] Library
of Congress will join us to talk a little
bit about the Spanish flu and Word War I,
looking through the lens
of different manuscripts.
So, we hope that you will join us,
or let colleagues that you know
who might be interested, join us, or just share
with anyone you think might be interested.
So, if there aren't any other questions,
I'll say have a great afternoon,
and have a great long weekend and stay well.