# Tag Info

1

To answer (2): MHF4U is a co-requisite of MCV4U so there nothing stopping a student taking all 3 courses at the same time. Further more, many Ontario high school operate on semester bases - a student could take MHF4U in first semester and MCV4U in second semester in Grade 12.

1

Identify what you want you'd like to teach the students for the class. Maybe more importantly, identify the goals of the course. What do you want the students to know and what do you want them to be able to do once the course is over? Write up a reasonable calendar for the course. Put the lessons you want to give in a reasonable order and designate which ...

7

The centroid, circumcenter, and orthocenter are concepts that I teach in Grade 10. It is part of the analytic geometry unit, and is where we relate knowledge on slope and distance formulas to geometric concepts. A textbook that includes this topic is Principles of Mathematics 10 by Nelson. Here is a set of sample teaching notes. Reference: Grade 10 ...

1

This may be a case where falling back to more primitive technology makes things easier. Print out (on paper) each of the pages the student uploaded. Mark and comment on the paper copies as you normally would. Re-scan the page or pages from each student as a separate document, and mail that document back to the student. This may not work well if you have a ...

2

An iPad with an Apple pencil- I can hand write comments and corrections on the .pdf and then upload it back to the LMS so that the student can see the feedback.

8

If you have access to a device capable of touch input (like a tablet), then I would highly recommend using a stylus to annotate the pdf document. It should take almost the same time as if you were marking assignments on paper. Foxit PDF and Gimp have in-built support for touch input. OneNote is also good for mobile and tablet devices. If you don't have ...

7

My technique is pretty low-tech. I distribute solutions to the homework after it's due, so students can mostly tell what they did right or wrong by looking at the solutions. Then I reply to each student's email with any additional comments that they need in order to get feedback that they can't get just by reading the solutions. E.g., #37 -- What went ...

2

I am recommending MyOpenMath (MOM) for this. It is a free, open source, online course management system for mathematics and other quantitative fields. [Note: There are other systems out there, such as WeBWorK, which have similar functionality. I am recommending MOM for its quick set-up for those transitioning to systems like this.] MyOpenMath supports "...

3

We use Gradescope, https://www.gradescope.com/ Basically, you upload the scans to Gradescope, and as you make comments on one student's paper, you can assign point values to those comments and re-use the comments on every other student's paper. If you decide at some point that you want to change the point value, you can just do it, and all of the students' ...

1

The Art of Problem Solving has plenty of problems involving pre-calculus tools, some of them quite challenging. However, the best way forward might not be computationally challenging exercises. You said they lack mastery. Please correct me if I'm wrong but I interpret this as they cannot reliably perform said computations and use said pre-calculus tools ...

0

I had a poster of Jake the Dog (from Adventure Time) in my high school geometry classroom, with this phrase: I also gave frequent closed-notes quizzes, and then made my students correct their quizzes on an error analysis sheet like this one (source): I had a poster with a description of different types of errors, in order to encourage them to analyze why ...

2

Age should not be confused with ability. Cognitive understanding of mathematical principles is indicative of higher-order thinking which in turn is ability and skills based. The fact that this student is 16 is irrelevant in terms of ability or skills. Regarding ability, ability is defined by an understanding of key foundational concepts and the development ...

2

Based on my own experience as a learner (and occasionally 'teacher'), I can think of a couple of other possibilities: She may objectively be able to understand maths and even intelligent, but lacking the confidence to believe that she can. I remember it from myself, on occasion, but also from children I have helped a few times. If that is the case, then she ...

6

Most people tend to only understand math when they can translate it to the real world, something they can understand. You've given several examples of theoretical concepts that look like magic to someone who can't translate it into something meaningful. But most of these (still somewhat elementary) concepts can easily be shown using real world examples. ...

3

It's a very broad question (to do the comparison you want). And made even more difficult when you consider that best pedagogy for any of the stages is not agreed on. My personal opinion is that much of the methodology should be similar, because humans are similar. Much more than people think. There's probably some social sensibilities that are ...

11

One of the skills that math education (or any education, for this purpose) includes is the ability of the student to learn on his own. Judging by your description, your student lacks this skill. I have also found from my experience with teaching teens that these students often also lack retention skills and do not ask meaningful questions during the ...

5

A warning: I have read some of the books I mention here but I have not tried them on actual students. I recommend getting your student some of Danica McKellar's books. Your student might want to start with "Math Doesn't Suck" which is targeted at ages 9-12 and covers fractions, decimals, and percentages. If this is too difficult, then try "Do Not Open ...

2

Beast Academy is for younger kids, but she might still like it. The format is "guide books" that are like graphic novels, where the beast students are taught by beast teachers, along with practice books. You can see examples on their website. It has levels 2 to 5. But it was designed for gifted kids, and it offers plenty of interesting challenge, whatever ...

0

If you are searching for a website where you can mathematics worksheets for the students of primary class (grade 1 to 5), then I am suggesting you a website where you can get mathematics worksheets for class 1 to 5. I have a daughter who study in class 2. I am taking Maths Homework for Class 2 from here because it provides daily homework with solution also. ...

2

In Spain these things are generally not taught at the university level and there is no course comparable to what you call College Algebra, as these topics form part of the high school curriculum. Some degree programs offer a "Zero Course" that reviews mathematical material from high school, but such a course usually focuses on graphing functions using basic ...

0

Speaking as an A Level physics teacher having seen what maths students do, they do stuff like quotient rule and chain rule. Hell, I even teach exponential decay with caclculus if I have a mathematically inclined class. But to get a C/4/5 grade in the edexcel maths papers you needed 21%. To get a 6/7/B you needed about 45-50%. In the UK schools I've worked at,...

0

I think that high school calculus is not supposed to be too rigorous. Calculus is a subject introduced in high school, and if it is too theoretical, then students can have a hard time understanding it. It is pretty reasonable to think that proofs of rules of differentiation(like chain, quotient, product etc.) must be told. But as far as course is ...

2

Typical topics are the Dijkstra and Floyd algorithms to find the shortest way between two nodes in a graph (used e.g. for NPC wayfinding in games, navigation etc.) or typical problems of IT theory (e.g. https://en.wikipedia.org/wiki/Graph_coloring vertex coloring). You could also cover neural net types that are build upon a graph-like structure. Usually, ...

5

The question really is: how individualized is your high-school calculus course ? If you have a kid who reads Godel Escher Bach and is fascinated by formal logic etc then probably you should offer a pretty rigorous calculus with $\epsilon \delta$ and basic topology and attempts at proofs of most theorems. If on the other hand, your student intends to be ...

46

Not very rigorously at all, but that doesn't (and shouldn't) mean just memorizing calculations. (I should add that I'm basing this on my experience teaching calculus to non-major college students, but I think the relevant issues are similar.) Mathematicians have a bad habit of conflating rigor with conceptual understanding. A lot of this seems to come out ...

6

Students who go on to be math majors will get a later course in theoretical calculus. The vast majority of science and technology students (i.e. non math majors) will NEVER have such a class. And not need it, either (to support their mechE, chemistry, etc. majors courses). So, I think the current approach is fine. The math majors get taken care of with ...

3

Here's a drawing of a house Can you draw it without lifting your pencil? What about if the roof is removed? What about two houses side-to-side? Here’s the floor plan for a house with some doors (some of which lead to the outside) Is it possible to draw a path that walks through every door, without going through any door twice? Then you can talk about ...

12

I study pursuit-evasion games on graphs, so I will recommend using the cops & robbers game as a way to introduce graph theoretic terminology, concepts, and examples. It should also keep the tone informal and recreational, which will do far more (I believe) to actually inspire the students to study more mathematics. Below are the rules of the game, so ...

5

I always introduce graph theory with the Königsberg Bridges, as Joel Reyes Noche suggested in his answer. Years ago, I went to a wonderful math talk that used this problem to describe 5 or more stages of what I'll call mathematizing. There was the physical problem. Then drawing it to be able to "walk" the bridges with a pencil, instead of for real. Then ...

6

I would try to keep it heavy on sugar and light on medicine. In particular emphasize visual representations more than precise terms that students don't know (or even worse, symbol soup). Maybe something like this: https://www.youtube.com/watch?v=iW_LkYiuTKE For what it's worth, I find this very similar to the issue of alkane isomers. Just got done Zoom ...

20

I suggest you discuss the Seven bridges of Königsberg problem (the problem that essentially started the field of graph theory), then discuss the Three utilities problem. For each, discuss the problem first, then introduce the definitions, then perhaps give a sketch of a proof. The first problem allows you to introduce the concepts of vertex, edge, walk, ...

5

You might include results on coloring plane graphs: The Art Gallery Theorem: $3$-coloring. Using Euler's theorem to prove that there must be a vertex of degree at most $5$. From there to $6$-coloring plane graphs. $5$-coloring is more difficult, but there is a nice exposition in Proofs from THE BOOK. Finally, sketch a history of the $4$-color theorem. &...

4

Dave from Boyinaband had a song about all the stuff he found useless in school. While I disagree with some particular things, his opinion in general is right. There are too many things taught that aren't needed by most students. Latex might be good for maths professors. How many people go to that field? Not a lot. Those who go there can learn Latex easily (...

4

First, LaTeX is a markup language and should be taught as such; trying to use it as a programming language would be an exercise in frustration. Second, I believe that all HS students should learn a markup language as an alternative to WYSIAYG. Third, while I routinely use LaTeX both for papers and for short documents, I am not convinced that it is suitable ...

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