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I taught all of my kids math using several methods because learning differs. Here are some:
I made worksheets with hands on them to demonstrate making 5 (fingers up + fingers down), making 10 (same concept but with both hands), and adding to 5 (using the same diagrams as for making 10)
I got a curriculum called Math U See with block-style manipulatives. This system comes with a great scope and sequence as well, the blocks are color-coded, and the lessons are all centered around "Decimal Street" which focuses on place value.
Another curriculum called Life of Fred puts math into the context of daily life in an engaging and compelling way. This is great for those who ask "When will I ever use this?" and for those who love a silly story. There are other lessons embedded in the stories as well, mostly academic, but also critical thinking and philosophical thinking.
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When we learned our multiplication tables in school, we had to stand in front of the class and recite them to a vinyl record with background music.
2 times 2 is [pause]
2 times 3 is [ pause]
…
2 times 10 is [ pause ]
We had a “tracking dog bone” with 2 thru 10 or 12.
If you recited them all correctly, then the teacher would use a hole punch to mark the number off. It was on a volunteer basis, but in hind sight, each student was super attentive to see if the reciter messed up or succeeded so the whole class was reinforcing each recital. Even people who never recited in front of the class were proficient by the end of the year.
The next year we did a 3 minute timed test everyday progressing through addition, subtraction, multiplication, and division.
Once you aced 3 tests, you moved to the next operation.
Once you aced 12 tests, the teacher would call “pro time” at two minutes.
The tests were very simple, basically a folder that you would wrap around a sheet of paper. It had holes to write your answers. Flip it the other way and it became the grader.
I remember that my weak spot was 7x8. I would always answer 48 or maybe 54? Blocked me for weeks!
Memorize memorize memorize!
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Math Blaster 
Also.. Numberblocks (youtube)
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Our kid had a grade 2 teacher who used math as a punishment when his classroom got out of control.
Over the following years we worked past the anxiety with mathematical activities that are not obviously school work, like music and baking to name a couple.
Also: candy works well, even with adults, as an immediate reward for getting something right. We used M&M's on an empty music scale; name the note first try, eat the note.
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For me, there is no one thing that works
Some calculations are memorised, some with patterns which still requires recalling what the pattern was
9s, are related to summing the number
anything with 9 is 1 less, but 9x2 or 9+9 is memorised as 18, not the pattern of move 1 over
Some is using "simpler" math like addition to solver multiplication.
Visualisation is mixed in sometimes
And then there attempting to make it THEIR fun. Do they have lots of books. Use that, how many pages can you read in a hour. So if you have 2 hours a day. How many days will it take to read the book.
If first person shooter games, explaining the K/D ratio - how many klls to deaths you have.
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Use M&M's for addition and subtraction. When they get it right, they can eat one.
Bond
Keep all things as simple as possible, but no simpler. -said someone, somewhere
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Just reading up on the new C# record keyword and nondestructive mutation[^] and wondering:
When was a time you used this concept? Anyone? Anyone...? Bueller...? Bueller...?
Just curious.
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If it ain't in C# 3, I ain't used it. 
Added:
Back in 1996 (?) I developed a system (DEC C on OpenVMS) which ran 24x7 and controlled a manufacturing process.
It had a configuration file. I wrote a simple editor for the configuration file. After the editor read the configuration file, it held two copies: a clean one and one to modify.
When the user exited the editor it would compare the two copies. If there were changes it would save them and then signal the main process to re-read the configuration file.
If there no changes, it wouldn't save and it wouldn't signal the main process to re-read the configuration file.
(Bear in mind that OpenVMS has a versioning file system.)
modified 17-Aug-23 11:58am.
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I think you are like 4 versions behind the 8 ball, here. I know you don't care, but just saying...
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I'm with you, there's just to many moving parts. KISS
I don't think before I open my mouth, I like to be as surprised a everyone else.
PartsBin an Electronics Part Organizer - Release Version 1.1.0 JaxCoder.com
Latest Article: Simon Says, A Child's Game
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I agree. I'm actually reading through the book, C# 10 In A Nutshell - Albahari (O'Reilly pub)[^].
The book is 1058 pages long and I can't believe how many concepts are in C# now.
It's amazing and crazy. And, of course, overwhelming.
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The last I got was C# 6.0 in a nutshell and it was overwhelming.
I don't think before I open my mouth, I like to be as surprised a everyone else.
PartsBin an Electronics Part Organizer - Release Version 1.1.0 JaxCoder.com
Latest Article: Simon Says, A Child's Game
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I tried two things from C# 6 a while back, but found neither compelling enough to use it regularly.
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Yeah I'm more of a brute force programmer, I don't use a lot of fancy stuff.
Guess a carry over from using C and C++ for many years.
I don't think before I open my mouth, I like to be as surprised a everyone else.
PartsBin an Electronics Part Organizer - Release Version 1.1.0 JaxCoder.com
Latest Article: Simon Says, A Child's Game
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Yes indeed. You have to know what the feature is doing in the background and what the limitations are.
One example (not a new one of course) is the foreach loop -- in many cases, using a for loop is a better choice (when possible). I use a foreach loop only when there is no other option.
I avoid Linq because it frequently does things which I can do better.
As to C# 6 in particular:
String Interpolation just isn't anything I would ever use. Earlier this year I wrote some code which does something similar though, taking some cues from it.
C# 3 added Object and Collection Initializers (which are good), then C# 6 added Dictionary Initializers, which are really not any better and have no benefit over them as far as I can tell.
A lot of these features make it easier for an unskilled developer to get something working, but at the cost of performance or flexibility.
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The more that goes on behind the scenes the more that ccan go wrong and the harder to debug.
I don't think before I open my mouth, I like to be as surprised a everyone else.
PartsBin an Electronics Part Organizer - Release Version 1.1.0 JaxCoder.com
Latest Article: Simon Says, A Child's Game
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If I understand this correctly, we use nondestructive mutation all the time in JavaScript patterns. The most common scenario is with state management. While it may seem optimal to diff and mutate a state object, it's actually much slower in practice to run logic to figure out what's what. So, in JS land, a lot of times we'll just mutate copies of an object. If we need to diff, we can, but for every update we don't need to. It's much, much quicker.
Oh, and if anyone wants to insult JS, you better be an expert in it first.
Jeremy Falcon
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The reason I find it interesting too, is because of a Sea-Change in the development world.
Back in the day C# OOP meant building classes and eschewing Structs.
Now that has switched up quite a bit -- because of challenges devs face when attempting to alter the state of an object and then wondering if anyone else had a reference to the object also.
This has gone much further in the iOS app-building world where that they say that everything you create should be a struct (not a class) so that you know you are only altering your object's state.
Here's the official apple docs mentioning that: Choosing Between Structures and Classes | Apple Developer Documentation[^]
Note the first item is:
Use structures by default.
Very interesting how things have changed.
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raddevus wrote: Now that has switched up quite a bit -- because of challenges devs face when attempting to alter the state of an object and then wondering if anyone else had a reference to the object also.
That's exactly what we do in JavaScript land. Everything's a reference (for the most part) in JS though, but in a lower-level languages that are multithreaded especially... can totally see the use here.
raddevus wrote: This has gone much further in the iOS app-building world where that they say that everything you create should be a struct (not a class) so that you know you are only altering your object's state
That's cool. And you can still acehieve some OOP-like concepts with them. In JavaScript it's called object composition, but it's a way to achieve inheritance with objects that aren't a class (a struct basically). So, if I'm understanding this correctly, then perhaps the same could be done in other languages while also being non-destructive.
raddevus wrote: Very interesting how things have changed.
Yeah it's pretty cool. Functional concepts are awesome. I mean, even if you love OOP, it's cool just seeing some things done in a different way.
Jeremy Falcon
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Oh, I should say, if you don't care about the deltas in state (so you can walk backwards in time, etc.) then just mutating an object directly is the quickest. But, if you want a paper trail, so to speak, the non-destructive approach is great.
Jeremy Falcon
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We have scenarios where a record associated with a particular entity needs to be copied to as a child of a different parent entity, and the record includes some info on the parent. We clone the record and update its parent info, but we preserve the original record because it's copied and the front-end still needs to show parent info of the original record. That said, this is usually all front-end stuff. But I can definitely imagine a use-case for this on the backend. After all, that's why we have functions for shallow and deep cloning. 
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Marc Clifton wrote: with a particular entity needs to be copied to as a child of a different parent entity
Yes that is the example I thought of.
Like many new features I can only see the new feature being helpful in a limited number of cases.
Where it might be nice is when the original class has many attributes and the set (unfortunately) continues to grow. Then the more manual updates become more of a problem. If only because on a standard screen actually remembering that way down below in the class there is one (or more) copy ctors. Forgetting those can become a problem.
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Great examples and the value of the record keyword is that you get a lot of pre-created functionality as follows (the first one being the big one):
- It writes a protected copy constructor (and a hidden Clone method) to facilitate nondestructive mutation.
- It overrides/overloads the equality-related functions to implement structural equality.
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Graeme_Grant wrote: I find them useful as DTOs or for simple POCOs.
That makes a lot of sense to me.
I will check out the video. Thanks
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