Books similar to “Teaching Developmentally”, but for high school math

I’ve been extremely excited by my reading of the book Elementary and Middle School Mathematics: Teaching Developmentally by Johan A. Van de Walle et al.

Does anyone know of similar books (or other references) for high school mathematics (grade 9-12), by which I mean either of the following:

  • books that explain in detail how to set up a problem-based classroom in grade 9-12,
  • books that provide a perspective of the mathematical content taught at grade 9-12 together with how teenagers best learn that content.

PS: This question is a more specific version of A good book for Juniors/senior/high school similar to VanDeWalle middle school? which has not been answered.

Como crear variables dinámicamente con un array o similar

estoy creando una aplicación donde utilizo una api de mapas para crear mapas personalizados, estos mapas incluyen unos Iconos esos icono se crean de la siguiente manera con JavaScript:

       var iglesia = L.icon({
            iconUrl: 'img/marker-iglesia.png',
            iconSize: [45, 45], 

        var libreia = L.icon({
            iconUrl: 'img/marker-libreria.png',
            iconSize: [45, 45], 

        var cafe = L.icon({
            iconUrl: 'img/marker-cafe.png',
            iconSize: [45, 45], 

        var marinka = L.icon({
            iconUrl: 'img/marker-marinka.png',
            iconSize: [45, 45], 

pero esa manera es muy estática, lo que yo quisera hacer es traer datos de la base de datos como el iconUrl y el iconSize y crear dinámicamente esas variables con los datos, he intentado hacerlo con un array pero no he logrado ningún resultado.

Espero su ayuda gracias.

How similar are Talmy and Wierzbicka’s theories of semantic primes?

I am an Italian PhD student in linguistics and I am interested in the analysis of the expression of Manner.
I went throught the works of Lakoff, Talmy and Wierzbicka recently and their event semantics raised some questions in me which I am not sure to be able to answer.
So, I would ask to the semanticists on this forum: in your opinion, what is the difference between Talmy’s semantic components Move, Figure, Ground, Path and Wierzbicka’s semantic primes MOVE, I/YOU/THIS, WHERE/HERE?

Is it just a terminological difference? Both authors seem to assert that these semantic “elements” are universally shared and not further decomposable. Am I wrong? Could you make some clarification? Many thanks.

Looking to replace my Samsung S7 with similar or better – but having completely flat display

Long story short, a couple of years ago I swapped my old Sony Xperia Z2 for a Samsung S7 (hero, not edge).

But it hasn’t worked out ideally. The problem is that even my S7, which isn’t supposed to have a curved display, does in fact have a subtle curve to the screen. So the thin hardened glass aftermarket screen protectors don’t fit perfectly – they might protect the screen, but they themselves show cracks within weeks of buying. I’ve tried about 3 different types, including 100% flat, and ones that are said to be “shaped to match the S7 display”, and got the same each time. Not ideal at all.

So I’m hoping to replace it with one that has a tough/robust, but completely flat, display, so that aftermarket protectors are guaranteed to work and lie 100% flat on it, without cracking. This was the case with my old Z2, and I miss it.

It would probably help to give a fairly detailed spec of what I use, and physical/design features needed.

  • Probably a top end, or near-top-end-ish Android smartphone (Samsung, Sony Xperia, HTC, maybe one of the newcomer Asian makes?). Or at least, equivalent to what Samsung/Sony/HTC flagship smartphone spec was like, way back in 2016 🙂 Could be a good model from a year or 2 ago, as I don’t mind buying used. Ideally a decent reputation for build quality.
  • I’m in the UK, so it needs to cope with UK GPRS, UMTS, HSPDA, LTE bands (UK LTE bands are 2,7,20). Probably a UK model, or available/sold into UK.
  • 3GB+ RAM, 32GB+ ROM and fast 64 bit CPU (not fussy about CPU make, probably 6-8 core as I like it to feel fast when used. My S7 is ok on this, if that helps.)
  • I always flash aftermarket OS (LineageOS right now), so LineageOS or similar availability is essential, and able to be unlocked from single network.
  • MicroSD slot essential.
  • USB B or C connector essential, ideally with USB3+ data speeds, if not too restrictive. Copying 40GB of files across the USB port at USB 2.0 speed is painful (WiFi file copying isn’t always practical). If not too restrictive, I’d like to get faster USB 🙂
  • Large-ish display – say 5.3 – 6 inch diagonal, but hand-holdable phone size, so handset size limit of about 80-83 x 160-163 mm, but there’s room to be flexible if a few mm helps. As large a display as possible within that size, but ideally a slim side-bezel, to make the most of the viewable area.
  • Good phone/speakerphone/mic volume and clarity, some phones I’ve had, have had issues with voice, or speakerphone (muffled, echoey, too quiet, mumbly), and I’d like good quality phone calls on my new phone 🙂
  • Ideally dedicated headphone jack.
  • Fast rear camera focus (my S7 uses PD AF and is very fast compared to my previous Z2, I like that), and ideally, also good in low light.
  • Good range of GPS networks (including Galileo, Beidou, Glonass if possible), and good range of sensors.
  • Robust – while I don’t need a commercial build phone with rubber at all corners, or a Samsung “active” range, I’d like a robust phone with a newer generation of toughened glass, perhaps more robust or slightly thicker than my current screen. And IP rated – good for 1m+ depth (current phone is IP68).

That should with luck narrow it down to <10 models.

The final criteria would be “as cheap as possible used good condition on EBay“! 🙂

Volume of polyhedron similar to prism but with different bases

Imagine a polyhedron similar to a prism, with parallel but different bases. Let the bases have the same number of sides, so that every vertex on a base is connected to exactly one vertex on the other base (side faces are all quadrilaterals). See example figure:

Solid similar to prism

  1. Does it have a name? I found the term “prismatoid” but it seems like a more general family.
  2. Is it possible to compute its volume without integrating? By analogy with trapezoids in 2D, I’d be tempted to say $(A1 + A2) / 2 * h$, where $A1$ and $A2$ are the areas of the two bases.

Similar Triangles

I am looking to improve my programming skills with this question. I believe I am making a mistake placing a tikzpicture within a tikzpicture? Any suggestions how to make this better and more flexible so one can vary the output according to ones needs? This is exactly what I want but I want to improve the programming.


node at (-3,0) {begin{tikzpicture}[scale=2]%,cap=round,>=latex]
coordinate [label=left:$B$] (B) at (0:0cm);
coordinate [label=above:$A$] (A) at (60:1.5cm);
coordinate [label=right:$C$] (C) at (20:1.8cm);
filldraw[fill=orange!50!white, draw=black] (B) -- node[above left] {c} (A) -- 
node[above right] {b} (C) -- node[below] {a} (B);
node at (3,0) {begin{tikzpicture}[scale=2]%,cap=round,>=latex]
coordinate [label=left:$Y$] (Y) at (0:0cm);
coordinate [label=above:$X$] (X) at (60:.5cm);
coordinate [label=right:$Z$] (Z) at (20:.6cm);
filldraw[fill=orange!50!white, draw=black] (Y) -- node[above left] {z} (X) -- 
node[above right] {y} (Z) -- node[below] {x} (Y);


This outputs:

enter image description here

Mosfetdriver or something with similar function for Highside back-to-back Mosfet switch

I want to supply a µC with 4x AA alkaline batteries or via USB, with the USB source being dominant. Meaning when USB is on, the batteries should be disconnected.
For the USB path, I intend to use a Schottky Diode.

For the Battery path, I initially thought about using a “oring” IC or one of those “powerpath” controllers. The problem with most of the ones I’ve seen so far is, that they only have one integrated FET, so there could be a reverse current flowing into the batterie, when the batteries drop below the usb voltage and the forward voltage of the FET body diode.

I want to use two back to back FETs with common source, but I’m not sure what driver would be suitable.

One way I thought of would be to use a mosfet driver like MAX1614 and let it drive two Fets. But the Max1614 only goes down to 5V Vin which would be too high. Something like 4V would be better to get the most out of the batteries.
Vin is between 4V and at least >7V, if possible >12V.

But most of the drivers I find are for Lowside configurations and some barely go above 5.5V.

Then there would be ones like the MAX5048 or the MAX15070 that go down to 4V.

Or I could use a oring controller with external Fets, something like a LTC4412 or LTC4359 (looks like the 4359 is hard to get in germany) and then use the enable pin to shut them down when the USB voltage is present.

I tried to design a discrete circuit with Mosfets and Transistors but that didn’t work very well, I lack the experience.

Does someone have tips or ideas on a good approach? Or alternative mosfet driver ICs?

This was my general idea for a discrete circuit, but I didn’t choose proper parts yet. When I simulate this in LTSpice, I get a huge spike for Vout when it switches from USB to Batt. (from ~4.7V down to 0V and back up to 4V)
I think an output capacitor is needed to prevent that spike.


simulate this circuit – Schematic created using CircuitLab