# Tag Info

38

I'm really wondering if this is the end of the world or the beginning of an improvement in the way we teach math. I'll answer this first, and then talk a little bit about the rest of the question. Please excuse my bluntness. I will try to give you the opinion you ask for by weighing what I think may be most important relative to quality of math education. ...

11

Can we include rich math tasks in our answers? If so, look at: http://visualpatterns.org http://graphingstories.com http://map.mathshell.org http://www.illustrativemathematics.org/ http://threeacts.mrmeyer.com http://www.estimation180.com/ http://www.dailydesmos.com/ http://betterassessments.wordpress.com/ http://maththinking.org/ http://www....

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Edit (7/17/14): You can find a very informative flow chart about CCSSM here to show dependencies among standards. At the time of posting, the page covers the standards included for K-8. If by "material" you mean CCSSM lesson plans, then it is important to draw the distinction between standards and curricula. JPBurke makes this distinction in his ...

8

Your question is kind of two parts: one about a convention Is the constant term a "coefficient" and one about a philosophy, which I perhaps find to be a more important question to answer. Isn't mathematics supposed to be non-arbitrary and consistent? Different fields of mathematics have different conventions; this can lead to some mathematicians ...

8

Your teacher decided it was not as important to learn as the topics they chose. Textbooks publishers put in everything the teacher might possibly want to use. If you never learn matrices until a Linear Algebra course, you'll still be fine. You will learn matrices there. They are a tool for solving systems of equations, among other things.

7

From http://www.corestandards.org/Math/Content/K/introduction/: Counting and Cardinality Know number names and the count sequence. Count to tell the number of objects. Compare numbers. Operations and Algebraic Thinking Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Number and Operations ...

7

Social promotion is an interesting topic, and I know my personal views are unpopular in my school. So they probably will be here too, but I'll go ahead. Due to developmental issues with children I think that social promotion is acceptable before high school. It should be coupled with remediation, but I think there are too many issues that can arise from ...

6

Working in a district that has been "ahead of the curve" in preparing teachers about the CC, I feel confident in what the Core has to offer. On the other hand, the parents are still unsure about it. The negative feedback is the typical stuff you see on FB, etc., coupled with the statement, "My kid already knows how to ______ (in math)." The reality is that ...

6

There is a point at which material is so far beyond students' skills that they learn less. Imagine a freshman calculus student plopped into a graduate topology seminar: they will learn almost nothing. Consider Csikszentmihalyi's flow model: We'd like students to be in that upper right corner, where they are highly skilled (relative to the task) and highly ...

6

Not a completely satisfying answer, but there is this from the FAQ at corestandards.org, emphasizing that the onus is on the states: Who will manage the Common Core State Standards in the future? The Common Core State Standards are and will remain a state-led effort, and adoption of the standards and any potential revisions will continue to be a ...

4

One of the drawbacks to the Common Core Standards is the implied assumption that students will not need revision on previous material. All classes need reteaching on certain topics at times, and teachers will need extra time for such remedial instruction. Clearly if students are lacking foundational material that was supposedly taught in previous years, the ...

4

The Common Core State Standards for Mathematics (CCSSM) provides a list of standards that should be covered; the inference that a topic not mentioned in the algebra strand should, therefore, be omitted does not necessarily follow, although time constraints no doubt ensure that will be the case for many courses. Rather than going into the process for ...

4

The standards that you identify actually do cover the things you assume are not covered. The formal properties of logarithms, for example, are proved using exponents, thus: F-BF.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. Exponential functions of ...

4

It sometimes happens that slightly different definitions of the same word each have advantages and disadvantages. In such cases, I wouldn't be surprised to see some people supporting one definition and other people supporting a different definition. In the case at hand, though, I can't think of any advantages for defining "coefficient" to exclude the ...

4

The CME Project! It's a full four-year high school curriculum. http://cmeproject.edc.org/

4

http://www.corestandards.org/Math/Content/K/introduction/ I am not aware of incoming requirements for Kindergarten but the link above details the learning goals for CC math at grade K.

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Indeed it is futile to expect students to successfully catch up with the prerequisite mathematical understanding for a course if they are too far behind. This is because many students think that they would rather focus on getting their grades for the current course despite not having any proper foundation in prerequisite courses. (This is real and happens ...

4

I have to admit I was skeptical of the OP's claim that contemporary textbooks do not identify the constant term as a coefficient, so I checked the first book that I had handy -- and indeed it does seem to be the case, in at least my sample of 1. Here is some evidence: (Source: McDougal Littell Algebra 2, 2004.) Note however that 2004 precedes the Common ...

3

The correct answer is obviously all reals, since it is an exponential function. I think the big point trying to be made here is that exponential functions are defined anywhere, so even though the graph is (more than likely very purposefully) misleading to show that there appears to be an asymptote at x=0, The key is relying on the student's ability to reason ...

3

There are a lot of sources of information on the history of mathematics education reform, and such sources fill many books. What you may be interested in is knowing that, basically, our understanding of human learning has changed over time. To hugely oversimplify, much of learning that older generations are familiar with is based on ideas of learning linked ...

3

In regards to early education and specifically the math of the CCSS, I have a link. This is a new blog post that ultimately tries to wade in by outlining several OTHER blog posts that all make good points. Some of the main points being offered is that you have to separate the STANDARDS themselves from the question of whether they are being implemented well, ...

2

Here is a github page that details connections between all standards: CCSSM Flow View For example, you can hover over the standards for K and see how they relate to others. Moreover, you can click through to see the description of the standard, its prerequisites, and its dependent strands. Site description: Hover over a standard to see what it depends ...

2

David Wees already mentioned in but I'd like to highlight Illustrative Mathematics - it's designed precisely for this purpose. (It's the brainchild of Bill McCallum, one of the lead authors of the Common Core math standards.)

2

With apologies to those who gave us the CCSS-M and who were well meaning, in my view the CCSS-M have been a "disaster" for mathematics, computer science, mathematics education, and most importantly American public school students. In the years since World War II the world has been transformed by new technologies, in particular those that were driven by the ...

2

This is coming from an educator that isn't fond of common core for various reasons. What I believe is at the heart of common core math tho, is that the "Why?" is important. Math isn't just a series of steps to get to an arbitrary answer that someone says works, but it's a logical method of using order built into numbers to arrive at the correct answer. My ...

2

I rather like The Art of Problem Solving's Beast Academy series. It is a complete curriculum, but in a "graphic novel" format, with problem solving emphasis. This can lead into other resources from AOPS for middle and high school. (I was myself homeschooled, homeschool both of my children ages 5 and 8, and am a mathematics professor. In my experience, the ...

2

The Common Core State Standards for Mathematics can be found here: http://www.corestandards.org/Math/ Besides the mathematical standards, see also about the standards, what parents should know, and whatever other parts of the site that may be of interest. From the about section's FAQ: As to your [edited] post, you write: So is the common core really ...

2

Let's keep in mind that "mathematics" and "mathematics education" are different subjects. This question brings forth this distinction. At one end of the "Piaget" spectrum of mathematical stages of development, explaining that the constant term $c$ is the same as $cx^0$ might be too much cognitive overload. However, towards the other end of the spectrum, say ...

1

After three years of intensive work with the new math standards (as part of the writing team for a new, national common core-based mathematics curriculum), my partner and I began consulting for school districts, training their teachers in the very thing you inquired about....HOW best to teach this new math. Almost without exception the teachers we worked ...

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There are so many mathematical directions you can go. I have found Living Math Forum (a yahoo group) to be incredibly eye-opening. There are about 5,000 members, and questions usually get a variety of answers from other homeschoolers. How do you want to approach math? There are various curricula available, there are "math readers", there are activities that ...

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