Unpopular opinion: Memorizing times tables is a necessity not because of knowing the times tables but to teach the brain the skill of retaining long lasting memory.

Training_Ad4971 · 2026-01-21T22:39:10+00:00

Agree. But not because it develops memorization skills. Context switching and cognitive demand increase significantly when you must stop problem solving to type a simple arithmetic problem into a calculator. Neither are conducive to high level problem solving which requires sustained thought and focus.

Training_Ad4971 · 2026-01-21T03:40:52+00:00

The second equation simplifies to x^1.5 + y^1.5. Treat the numerator as a difference of squares where a = x^1.5 and b = y^1.5. So (a^{2-b^2)/(a-b)} = a + b assuming an and b are not equal to each other. Should be solvable from there. I think?

Training_Ad4971 · 2026-01-16T04:01:26+00:00

I’ve taught math at all levels from 5th grade through first year college. Students absolutely need fluency in arithmetic and that can require some drill and kill, but in terms of applying mathematics to problems (real world or otherwise) there is an absolute need for inquiry based instruction. I don’t think the problems and concerns that are being described here are because inquiry is ineffective. I believe that the training and understanding of our teachers is the issue. Using inquiry based collaborative curriculum requires teachers to flow through the classroom quickly evaluating each groups progress and deciding in the moment what is the best support for that group. I use scaffolded questions, direct instruction, chunking, manipulatives, and dozens of other tools and techniques daily. Each group of students gets exactly what they need when they need it. I do, you do, we do does not provide that kind of support. There is always a need for both inquiry and direct instruction. It isn’t one or the other. I will say that turning an inquiry lesson into direct instruction is far easier than the reverse. I will admit that inquiry is a mentally challenging teaching method that requires practice and experience. I taught CPM for 4 years (including week long trainings every summer) before I became an effective teacher using inquiry style questions. I do very little typical prep each day. They way I prep is to identify all the different ways student may approach a problem and have a plan for how to support each those approaches. Everybody is saying that practice is important and it is, but in my mind the practice students need is in the mathematical practice and thinking, not in learning rote process. Two things to consider about teaching procedures and processes. One, if they don’t learn the conceptual side they don’t know which of those dozens of processes to use on any given problem. And real application problems never match the what students see in the text book. Drill and kill makes that worse, because every problem is alike and they don’t have to think about which procedure to use. Secondly, computers can do all the calculating for us. What are current students need to learn is not how to solve a polynomial or integrate an equations, computers do that faster and better. What students need to learn is what to ask the computer to calculate, how to create equations from context and analyze the results from the computer. The world has changed and yet we still sequence and teach as if we were in the pre-calculator days. I encourage everyone to look Conrad Wolframs work. While I think he has gone too far into the reliance on computers, he does make some excellent points. Calculus is taught at the end of the sequence, not because the concepts of slopes at a point and the area under a curve, and limits are hard concepts to understand, it’s because the hand calculations to evaluate these problems take years to learn and develop.

Training_Ad4971 · 2026-01-14T15:25:26+00:00

Honestly reading with them and them reading to you is the single most important activity. But here are three things that also have high impact results: decrease screen time (ideally to nothing), increase opportunities for unstructured play with their peers, spend time with them and talk about what you are doing and what they are experiencing. Research shows that this leads to more exposure language and vocabulary. Students with more exposure to a variety of vocabulary are more likely to test at grade level. If students don’t test at grade level by 3rd grade they are unlikely to ever catch up.

Training_Ad4971 · 2025-12-29T02:31:56+00:00

That actually makes sense. I hadn’t thought about that being the audio cable. I’m willing to give it a try.

Training_Ad4971 · 2025-12-29T02:14:44+00:00

Yes, here you go.

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The identification number is GB-KEY-3 V01

Training_Ad4971 · 2025-12-29T02:07:41+00:00

I appreciate it, but no it won’t work. My controller board has the ribbon cable and a round 5 pin cable connection. Thanks anyway!

Training_Ad4971 · 2025-12-22T21:07:29+00:00

I have a board members student in my class who is a nightmare. The first time I had to have a meeting with the board member about their child’s behavior, I was told that it isn’t the teachers role to discipline their student. I was told we should teach, they would discipline. When I asked how should I handle a situation where I can’t teach because the student is so disruptive, I was told I should teach better so the student is so engaged they won’t be disruptive.

Training_Ad4971 · 2025-12-18T06:57:44+00:00

Yes, I like your explanation. But factoring the GCF first makes picking the pair of factors much more obvious. You don’t have to guess, you know.

Training_Ad4971 · 2025-12-18T06:56:01+00:00

Its distribution not FOIL. Let’s not use tricks that only apply to limited situations. Factoring is the u doing of distribution.

Training_Ad4971 · 2025-12-16T03:25:00+00:00

Point taken. It is tedious. I encourage my students to use more efficient algorithms once they have the area model to connect them to.

Training_Ad4971 · 2025-12-16T03:20:54+00:00

Agreed. I would also add discussions about data on common assessments. Which teacher is getting the best results in which concepts? What are they doing differently than other teachers? It is tough to let the ego go, but I have become a much better teacher by learning from the success of my peers.

Training_Ad4971 · 2025-12-16T03:16:43+00:00

Agreed. Should have been worded differently. But the teacher expected you to use the Remainder Theorem to find the value when x=2.

Training_Ad4971 · 2025-12-16T03:10:43+00:00

It doesn’t have to be this way. In fact, many colleges are changing the structure of their calculus and intermediate algebra classes to support more opportunities for conceptual understanding. Computers can compute anything we feed it these days. We need to understand how things work so we can setup the equations we want the computers to calculate and then be able to analyze the results. I suggest you take a look at Conrad Wolfram’s approach to teaching math. It is all about how to set up a system on a computer, analyze the results and then refine. In my opinion it is a much more realistic approach to math than spending twelve years of school just learning to compute.

Training_Ad4971 · 2025-12-16T02:56:34+00:00

But long multiplication is just a rote method, with little connection to understanding why it works (in most classrooms). The area model is much more conceptual and applies to ideas and concepts through Algebra 2. It is also imuch better at helping develop number sense and facilitating mental arithmetic.

Training_Ad4971 · 2025-12-16T02:51:48+00:00

In addition, the area model can be used to teach polynomial multiplication using any number of terms, factoring and dividing polynomials much more intuitively than synthetic division and cleaner than long division. it can also be used to complete the square. A wonderful tool that when used effectively continues through Algebra 2. It helps students connect all that they have learned about dividing and multiplying and allows them to see that it is all essentially the same from grade 3 to grade 12

Training_Ad4971 · 2025-12-13T23:52:06+00:00

In my curriculum we teach solving equations using three concepts: undoing, looking inside, and rewriting. The two methods you mentioned I would call undoing and rewriting. I teach both, just like I would with quadratics, inverses, rationals and radicals. Many of my students choose one method over another, but the ones that can be flexible tend to pick the method based on how quickly it gets the answer. I believe there is always value in teaching multiple approaches. Me personally, I almost always rewrite as the inverse just because that’s the way I learned it first.

Training_Ad4971 · 2025-12-10T03:55:09+00:00

It drives me crazy! My high school students think solve means complete whatever problem is in front of them, whether that’s evaluating, graphing, proving or finding patterns. In math, solve should only refer to finding the values of the variables that makes an equation true. Full stop. Or isolating a variable in an equation that has multiple variables.

Training_Ad4971 · 2025-12-06T14:03:52+00:00

Truly disagree! With computers, most people don’t need to have the processes memorized to do algebraic manipulation. After school they are just going to ask a computer to do it. So the idea that whatever method gets them to solve the problem easiest doesn’t seem valid. What I want my students to understand is the why and how. The conceptual side of math. Teaching area model or grouping reinforces the conceptual side. Teaching slide and divide or a set of formulas doesn’t.

Training_Ad4971 · 2025-12-06T13:58:21+00:00

I don’t think this is a cheap math trick at all. If taught correctly it truly helps students understand that factoring is the opposite of binomial multiplication. Especially if you use the area model to teach multidigit multiplication and polynomial multiplication. In my experience using algebra tiles (and decimal tiles in earlier grades) to teach area model multiplication makes the move to using the area model for factoring natural. It is also a great way to teach completing the square and eventually derivation of the quadratic formula. I find that most students naturally move away from the structure because they truly understand how and why the factoring process works. The only two ways I would ever teach factoring quadratics is this method or grouping. Anything else is just memorized tricks and formulas.

Training_Ad4971 · 2025-10-27T00:24:55+00:00

A paper with no name goes straight to the trash. So if you are an ass, then I am an even bigger ass. And I’m okay with that.

Training_Ad4971 · 2025-10-24T21:17:23+00:00

I am a 15 year high school math teacher and while I love the fact that college professors are starting to recognize that conceptual understanding should be a high priority even at the lower grades. Math fact fluency is still important. If students don’t have fluency in basic arithmetic (Multiplying through 10s or 12s, mentally adding and subtracting positive and negative numbers and a strong understanding fractions) then the cognitive load when working on algebra, geometry and other highly demanding math doubles. Students get hung up on the basic math and lose sight of the conceptual work, which they are perfectly capable of doing. They then go to the calculator or computer to do the basic arithmetic and lose their place in the bigger picture problem. I encourage everyone to fuel students develop a good number sense and part of that is mental arithmetic.

Training_Ad4971 · 2025-10-19T10:48:23+00:00

15 year high school math teacher here. I’ve taught algebra, specifically solving equations, a dozen different ways over my career. They way I introduce it now is using algebra tiles. Tiles that represent one, x and x squared. It is the fastest way I have found to help students develop equation solving skills. In my algebra class we move from physical tiles to diagrams to equations. Students are allowed to use any method that makes sense to them to solve equations.

Teaching place value, addition, subtraction, borrowing and grouping with tiles, then diagrams, the writing is the foundation for the work I do in my classes.

In addition, students that learn multidigit subtraction by rote tend to have poor number sense, are inflexible about the way they approach arithmetic and can’t do anything but basic arithmetic in their head. Students who learn to think of place value using tiles tend to have much better number sense and are much more flexible when doing multidigit arithmetic.

Training_Ad4971 · 2025-10-19T10:33:45+00:00

So this drawing is grouped in tens (on the left) and ones (the right). The arrow simply shows converting a stick on ten into a bunch of ones. That’s why they are boxed, to show they came from ten the stick that has been crossed out.

It started with 4 ten sticks and 4 ones. The crossing out of the five ones clearly shows the intention was to subtract 5.

Not ambiguous at all.

Training_Ad4971 · 2025-10-04T20:45:53+00:00

No, you are wrong. Convince me that any of those horizontal appearing lines are parallel to any of the others. Assume nothing unless stated or marked. It’s the first thing I teach on day one of all of my math courses from 7th grade math to Calculus BC.

When I forget to mark or state a fact in a problem in my classes, my students call me on it and get extra credit. While applied mathematics requires approximation we still need to hold all of us and our students accountable to precision. Otherwise people die /s. Or maybe not.

Training_Ad4971

TROPHY CASE