Textbooks, their history and their future

 Today we'll look at a number of textbooks, new and old, and assess them in the terms listed below. 

As you begin working as a member of a math department at a secondary school, you will be called upon to help assess textbooks that the department and school is considering purchasing. You will also be asked to make professional judgements on various alternatives to textbooks. How might you assess textbooks and their alternatives? That is what we will address in class today.

Some things to start noticing in terms of textual analysis of math textbooks, old and new. (Each observation should be considered in terms of its potential effect on mathematics teaching and learning, and on the ways students might begin to think about mathematics.) Notice:

• The qualities of the physical object. Is it heavy or light, durable or fragile? How does the paper feel and the ink smell? Does it come with a teacher guide? student workbook? CD (seems a bit old fashioned now)? web links? Will it fit in a student's backpack?

• How much does it cost? What would the investment be for a school to take on a new math textbook?

• What is the writing like? Who does it address, and what does that tell you about its view of society and mathematics learning? Does it include definitions, explanations, examples, counterexamples, word problems, instructions, stories, extensions?

• Who are the authors? What is their expertise? Who put the project together, and why? Try reading the introductory material (which hardly anyone ever reads...)

• Is it easy to navigate? Table of contents, index, glossary, answer key, appendices, diagrams, tables, different kinds of pages colour coded, ...?

• What are the graphics like? Photos, diagrams, graphs, boxed information, use of colour or not,...

• How is it designed? Use of white space, sidebars, font size and style, page layout,...

• Any examples of alternatives to paper textbooks, from publishers, or teachers, or organizations, or ...


Interestingly, even a math textbook is very much a reflection of the time, place and society it comes from! No matter that the mathematical content is slow to change -- the social and educational contexts (and printing technologies) change much quicker.
Are there any classes in high schools that don't use textbooks?

Could you imagine teaching a math class without textbooks? What is the future of the lucrative business of textbook publishing? Do you think we will soon be creating teacher-written, collaborative shared materials online that will replace current (retro) textbooks -- or not??

Here is a blog from a workshop on textbooks at CMESG (the Canadian Math Education Study Group). It has fascinating links to many of the earliest math textbooks in English (from the 16th and 17th centuries) and other varied textbooks. We will use several of these today: 

1. Sample pages from Robert Recorde's The Grounde of Artes (1632), one of the first mathematics 'textbooks' in English..and Robert Recorde, The Whetstone of Witte (full text)
   
   
2. Social Arithmetic selections part 1 (US, 1926)
Social Arithmetic selections part 2 (US, 1926)


3. Modern Algebra and Trigonometry part 2 (Dolciani et al, US,1963)
   
   
4.  Mathematics: A Human Endeavor (Harold R. Jacobs, US, 1970) part 1 and Part 2
   
   
5.   Mathquest 8 (Addison-Wesley publishers, Canada, 1988)
   
   
6.  Precalculus 11 (McGraw Hill Ryerson publishers, Canada, 2011)
   
   
7.  Math that matters (Stocker, 2006, Toronto)
   
   
8. Khan Academy Math as textbook?
   
   
9.  Excerpts from Stewart's Calculus

Blog reflection on flow in the secondary math class for Monday Nov 18, 9 AM

 

Hi all! As a follow-up to our exploration of 'flow' , please write a short blog post reflecting on the film we saw in class on Monday: Mihalyi Czikszentmihalyi's TED talk on 'flow' and happiness.

In your post, please reflect on what you take away from this talk and the idea of 'flow':

Have you experienced a state of flow through certain experiences? What prompts it? Is it sometimes connected with mathematical experiences?

Is it possible to achieve a state of flow in secondary math classes? Can we, as teachers, help create the conditions for a flow state for our students as they learn math? If so, how -- and if not, why not?

Looking forward to reading your blog posts, and to following up with more on flow states and ideas about The Thinking Classroom!

Czikszentmihalyi & 'flow', Liljedahl and 'flow' in the Thinking Classroom

 

 Mihalyi Csikszentmihalyi, the late Hungarian-American psychologist, has studied a state he calls 'flow', where people are completely engaged and delighted in a process of problem-solving, and our normal sense of time is suspended. Here is a link to his TED talk on this topic from 2004.  

Professor Peter Liljedahl from SFU Math Education has taken up the idea of 'flow' in both a descriptive and prescriptive way for our math classrooms. Here are his slides shared from his session at the Northwest Math Teachers' Conference in 2015. Peter's books on Building Thinking Classrooms in Mathematics K-12 have resonated strongly with math teachers in Canada and internationally. Here's a link to his website on Thinking Classrooms, an interesting
short article on Edutopia about Thinking Classrooms

How can we, as teachers, promote "flow" and happiness in our mathematics classes? What kind of activities might help students feel immersed and excited in problem-solving and other mathematical undertakings?

FREE Virtual Math Ed Pro-D Event - Nov. 15-17 (open to everyone, and especially needed if you missed the October 24/25 pro D!)

  From Erica Huang's 442 blog:

Here is a free, virtual Math Ed Pro-D event that may be of interest: 2024 Make Math Moments Virtual Summit. There are some high-profile math educators presenting at the event, such as Jo Boaler (Mathematical Mindset), Peter Liljedahl (Building Thinking Classroom), and Ben Orlin (Math with Bad Drawings), just to name a few.

Make Math Moments is a popular math education podcast host by two Ontario math educators, Jon Orr and Kyle Pearce. Check out their work if you enjoy podcasts!

Homework reading and response: Arbitrary and necessary

  

For homework, please read this classic and very influential piece by UK mathematics educator Dave Hewitt. Think about what he means by 'arbitrary' and 'necessary', and then please write a blog reflection about how this might affect the way you plan your lessons and units as a math teacher! Blog posts are due Wednesday Nov. 6 at 9AM.

Dave Hewitt 2020 video for the Assoc of Teachers of Mathematics (UK) on awareness and fractions (13:31)

Dave Hewitt 2022 video on Grid Algebra (8:00)

The Giant Soup Can of Hornby Island: A puzzle due on your blog Wednesday Nov 13 by 9 AM

 

  

A geometric puzzle with real-life connections:

On Hornby Island, BC, local artists were commissioned to paint the volunteer fire department's water tanks in a dozen different locations around the island. Artist Pix Sutherland noticed that this tank was in exactly the same proportions as a Campbell's soup can and painted this (controversial) tribute to Andy Warhol's famous 1960s soup can pop art paintings.

Lots of math problems could come out of this story. Here's one: given the size of the actual Campbell's Soup can (of normal size) and the height of the bike in the photo, what are the dimensions of the volunteer fire department's water tank? What is its volume? Does it hold enough water to put out an average house fire?

Your task: work on this puzzle yourself, and let your 'teacher bird' and 'student bird' notice how you approach it, where you can use reasoning and where you need to research, where you get stuck and un-stuck.  

Then work on either: (a) extending this puzzle, or (b) coming up with your own puzzle for secondary math students based on a real-life observation you have made (and include a photo or graphic to support it).

Your unit planning assignment!

   

 

A unit of work in secondary school mathematics (on a linear timetable) generally lasts 4 to 5 weeks, and includes about 10 to 12 lessons. In most courses, there are 9 or 10 units of work per year -- approximately one per month, speaking linearly. Your unit planning assignment should get you started planning for one of the units of work that you will actually be teaching for your long practicum!

Note that each of your sponsoring teachers will have slightly different requirements for unit planning, and for your practicum, you will need to work with those individual requirements.

For this course, I am most interested in seeing your background thinking and planning for designing the unit. I want to see that you can:

•answer the question "why are we learning this?";
•make connections for yourself and your students with the history, social/environmental/Indigenous connections, artistic connections, fascination and beauty of this topic;
•think deeply about the pedagogy of this topic and the possibilities for teaching it;
•work out formal and informal ways of assessing students' progress in learning this topic;
•design a large or small student mathematics project that will be part of the unit.

You will also need to think out the sequencing of your 10-12 lessons and outline this in a chart.

In planning a complete unit for your practicum, you will need to write a lesson plan for each of the lessons. But for our class purposes, I am only asking you for three lesson plans. However, these should be for especially inspiring, creative and actively engaging lessons that do not follow the traditional pattern of lecture/exercises/homework. (I expect that some but not all of your lessons in the unit will follow that traditional pattern -- but I would like to see your plans for ones that do not!)

Please download the template linked here to write up your unit plan, and stick closely to the suggested word counts for each section. You will see that you are asked to produce short paragraphs for each section, but I will expect them to be well-researched and well thought out.

Your first draft of your unit plan is due on your blog on  Nov. 27 at 9 AM. Then we will go through a process of peer editing and revision, with the revised version due for marking on Dec. 11 at 9 PM. 

Please talk with your SA about a unit you will actually be teaching in your long practicum — then post the grade, course and unit topic in the comments here by this Wednesday November 13!

Hope you enjoy the process, and then the teaching!