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(this is in the US and at a high school level)

why don't we dedicate a day of the week each week to do a lab for math for exploration? I mean we already do that for Earth Science, Physics, Chemistry and Biology.

Examples of mathematics labs would be in applied math or math itself

  • Discovering numbers: constructing the real numbers (probably not by doing Dedekind cuts)
  • Pan balance problem = algebra
  • Proportional relationships (exploring a physics constant/application eg Hooke's Law)
  • Finding pi by measuring circular objects
  • Proof workshop
  • Working on a very very hard math problem or proof (e.g., volume of frustum or motion problems, $d=rt$)

(The examples below are of beyond high school level, but I wanted to include them to show examples of ideas of what I thought would be good labs adjusted to the algebra level despite being of calculus and beyond level):

  • In calculus II, it would be something like: show that $\displaystyle \int_{-\infty}^{\infty} e^{(-x^2)} dx= \sqrt{\pi}.$

  • Prove $\displaystyle\lim_{x\to 0} \frac{\sin x}{x} = 1$.

  • Exploring l'hopital's rule.

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    $\begingroup$ I do. We use swinging pendulums in precalculus throughout the year to record measurements when discussing sinusoids, parametric equations, and linear regression. $\endgroup$
    – Andrew
    Commented Apr 24, 2019 at 5:28
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    $\begingroup$ Your question: "Why don't we do X" presumes "We don't do X." Maybe not in your "neck of the woods", but the suggestions you offer are in fact incorporated in secondary education curriculum in much of the US. $\endgroup$
    – amWhy
    Commented Apr 24, 2019 at 12:23
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    $\begingroup$ When I taught high school geometry, we: - went outside and measured the heights of tall things with similar triangles (this project took a week for them to completely write up) - Designed and then built 3-d objects out of construction paper to "package" some item and computed the amount of packaging material needed (surface area) and the amount of wasted space inside the packages (volume). - Illustrated translations, rotations, and reflections by creating an animation in Scratch. Now, many of these activities just hit middle school standards, but my students were well below grade level.. $\endgroup$
    – Opal E
    Commented Apr 24, 2019 at 17:22
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    $\begingroup$ My AP statistics students worked with the neighboring elective science class to create a 'research poster' with the science students designing experimental methods and materials, and the my students acting as statistical consultants to improve their study design and perform the final analysis. $\endgroup$
    – Opal E
    Commented Apr 24, 2019 at 17:23
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    $\begingroup$ Physics, Earth Science, Chemistry and Biology are sciences. They are based on experiments; the words "theory" and "model" have a different meaning in science and in math. In science you do some experiments, you suggest a law that describe it... (or, more practically in schools, you introduce a law/a theory and do some experiment to verify it). $\endgroup$
    – user5402
    Commented Apr 24, 2019 at 19:11

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