WitCH 58: Differently Abled

Like the previous post, this one comes from Maths Quest Mathematical Methods 11, and is most definitely a WitCH. It can also been seen as a “contrast and compare” with WitCH 15.

Subsection 13.2.5, below, is on “differentiability”. The earlier part of chapter 13 gives a potted, and not error-free, introduction to limits and continuity, and Chapter 12 covers the “first principles” (limit) computation of polynomial derivatives. We’ve included the relevant “worked example”, and the relevant exercises and answers.

WitCH 57: Tunnel Vision

The following is just a dumb exercise, and so is probably more of a PoSWW. It seems so lemmingly stupid, however, that it comes around full cycle to be a WitCH. It is an exercise from Maths Quest Mathematical Methods 11. The exercise appears in a pre-calculus, CAS-permitted chapter, Cubic Polynomials. The suggested answers are (a) \boldsymbol{y = -\frac{1}{32}x^2(x-6)} , and (b) 81/32 km.

WitCH 56: Fuzzy Dots

Has it occurred to anyone else that these WitCHes are a blogging Ponzi scheme? As long as we keep posting new WitCHes, no one bugs us about not polishing off the old WitCHes. What the hell; we’ll keep going until someone calls the Blog Cops. And, to continue with the scheme, this WitCH comes from the Cambridge text Specialist Mathematics 1 & 2, in the section titled Linear Diophantine equations. Happy hunting.

WitCH 55: Oregonian Dreamin’

It must be something in the water.

This one, with due credit to Bill and Melinda, will be appearing in plenty of right wing snicker-rags in the very near future. It’s really a PoSWW. However, given the previous (and much more important) post, we decided to make it a companion blivit-WitCH. (As well, we’re working on another post on this stuff, in defense of it.)

Courtesy of the Oregon Department of Education, teachers there are being offered a “micro-course” on Equitable Math Instruction. More specific links are below. Good luck, and Good God.


1. Dismantling Racism in Mathematics Instruction

2. Fostering Deep Understanding

3. Creating Conditions to Thrive (zip file)

4. Connecting Critical Intersections

5. Sustaining Equitable Practice

Whole Course (zip file)



WitCH 54: California Dreamin’

OK, this is one of those blivit WitCHes. Yeah, sorry, but what are you gonna do? We don’t have the time (or the stomach) to give the stuff below the full-blown critique that it warrants, and there is a stormfront much closer to home.  Given the thing has been brought to our attention, however, it also seems an error to not raise it on this blog. And so, here we are.

The inestimable Jo Boaler is one of the writers for the California mathematics curriculum review, and the proposed new “framework” is now up for public comment. The screenshots below are from youcubed‘s newsletter, and further below are links to individual chapters of the new framework (all also available here, along with other relevant material). Good luck.

CHAPTER LINKS (Word files, because making PDFs is apparently so damn hard)

(There’s also grade level brochures on this page, but, at posting, the links weren’t working.)

1. Introduction

2. Teaching for Equity and Engagement

3. Number Sense

4. Exploring, Discovering, and Reasoning With and About Mathematics

5. Data Science

6. Mathematics, Investigating and Connecting, Transitional Kindergarten through Grade Five

7. Mathematics, Investigating and Connecting, Grades Six through Eight

8. Mathematics, Investigating and Connecting, Grades Nine through Twelve

9. Supporting Equitable and Engaging Mathematics Instruction

10. Technology and Distance Learning in the Teaching of Mathematics

11. Assessment in the 21st Century

12. Instructional Materials

13. Glossary

WitCH 52: Lines of Attack

Yes, we have tons of overdue homework for this blog, and we will start hacking into it. Really. But we’ll also try to keep the new posts ticking along.

The following, long WitCH comes from the Cambridge text Mathematical Methods 3 & 4 (including an exercise solution from the online version of the text).

UPDATE (07/02/21)

Commenter John Friend has noted a related question from the 2011 Methods Exam 1. We’ve added that question below, along with the discussion from the assessment report.