Tuesday, September 16, 2014

It's not about politics!

On progressive ideals and reform math...

Alice Crary and W. Stephen Wilson. The Faulty Logic of the ‘Math Wars’. New York Times, New York, NY, June 16 2013.

"it would be naïve to assume that we can somehow promote original thinking in specific areas simply by calling for subject-related creative reasoning"

"It is easy to see why the mantle of progressivism is often taken to belong to advocates of reform math. But it doesn’t follow that this take on the math wars is correct. We could make a powerful case for putting the progressivist shoe on the other foot if we could show that reformists are wrong to deny that algorithm-based calculation involves an important kind of thinking."


W. S. Wilson. SBAC Math Specifications Don’t Add Up. 
Flypaper, Thomas B. Fordham Institute, September 19, 2011.
It's [23] on the Professor's website here.

The conceptualization of mathematical understanding on which SBAC will base its assessments is deeply flawed. The consortium focuses on the Mathematical Practices of the Common Core State Standards for Mathematics (CCSS-M) at the expense of content, and they outline plans to assess communication skills that have nothing to do with mathematical understanding.

Sunday, September 14, 2014

"Adaptive Reasoning" in Mathematics Education

Adding It Up page 129-131

Adaptive reasoning refers to the capacity to think logically about the relationships among concepts and situations. Such reasoning is correct and valid, stems from careful consideration of alternatives, and includes knowledge of how to justify the conclusions. In mathematics, adaptive reasoning is the glue that holds everything together, the lodestar that guides learning. One uses it to navigate through the many facts, procedures, concepts, and solution methods and to see that they all fit together in some way, that they make sense. In mathematics, deductive reasoning is used to settle disputes and disagreements. Answers are right because they follow from some agreed-upon assumptions through series of logical steps. Students who disagree about a mathematical answer need not rely on checking with the teacher, collecting opinions from their classmates, or gathering data from outside the classroom. In principle, they need only check that their reasoning is valid.

Research suggests that students are able to display reasoning ability when three conditions are met:  They have a sufficient knowledge base, the task is understandable and motivating, and the context is familiar and comfortable.37

Principles of Effective Instruction and the 3rd Common Core Standard for Mathematical Practice

This list is adapted from Principles of Instruction: 
Researched-Based Strategies That All Teachers Should Know

1. Begin a lesson with a short review of previous learning:  Daily review can strengthen previous learning and can lead to fluent recall. 

The most effective teachers ensured that students efficiently acquired, rehearsed, and connected knowledge.  Many went on to hands-on activities, but always after, not before, the basic material was learned.

2.  Limit the amount of material students receive at one time.  Present new material in small steps with student practice after each step, and assist students as they practice this material.

3.  Give clear and detailed instructions and explanations.  Provide many examples.

4.  Think aloud and model steps.  Providing students with models and worked examples can help them learn to solve problems faster.

Many of the skills taught in classrooms can be conveyed by providing prompts, modeling use of the prompt, and then guiding students as they develop independence.

5.  Use more time to provide explanations.

6.  Ask a large number of questions and check the responses of all students:  Questions help students practice new information and connect new material to their prior learning.

7.  Provide a high level of active practice for all students.

8.  Guide students as they begin practice.  Successful teachers spend more time guiding students’ practice of new material.

9.  Check for student understanding at each point to help students learn the material with fewer errors.

The most successful teachers spent more time in guided practice, more time asking questions, more time checking for understanding, and more time correcting errors.

10.  Ask students to explain what they have learned.

11.  Obtain a high success rate:  It is important for students to achieve a high success rate during classroom instruction.

12.  Require and monitor independent practice:  Students need extensive, successful, independent practice in order to develop well-connected and automatic knowledge and skills.

13.  Provide systematic feedback and corrections, reteach material when necessary.
Construction viable arguments and critique the reasoning of others. 
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments.  They make conjectures and build a logical progression of statements to explore the truth of their conjectures.  They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples.  They justify their conclusions, communicate them to others, and respond to the arguments of others.  They reason inductively about data, making plausible arguments that take into account the context from which the data arose.  Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is.  Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions.  Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades.  Later, students learn to determine domains to which an argument applies.  Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.


Tuesday, July 22, 2014

#CommonCore and #Sovereignty

Let's start with a couple of recent quotes - (discovered here)

“I can’t think of anything that has had this much controversy,” said Linda Johnson, who served on Louisiana Board of Elementary and Secondary Education from 1999-2011.

“This is the first time there has been anything like this,” said Leslie Jacobs, another former Louisiana BESE member, who played a major role in creating Louisiana’s public school accountability system.


When [Diane Ravitch] testified to the Michigan legislative committee debating Common Core in Aug. of 2013, she told them to "listen to their teachers and be prepared to revise the standards to make them better"

When asked if states were "allowed" to change the standards, Ravitch responded, "Why not? Michigan is a sovereign state. If they rewrite the standards to fit the needs of their students, who can stop them? The federal government says it doesn't 'own' the standards. The federal government is forbidden by law from interfering with curriculum and instruction"


By now, you must be wondering "What's your point?"  It's strange that relatively few people, throughout the political spectrum, have been very concerned about the sovereignty of states, or that of individuals and communities, throughout the FedLed Common Core Standards *Initiative* process. 

If there is a silver lining, it is that growing numbers of citizens are becoming concerned and engaged in education issues.  The "sleeping giant" has awaken just in time, in my opinion, "little dictators" and "social engineers" have infiltrated every political party. 


In March of this year, Ravitch explained...

The reason to oppose the Common Core is not because of their content, some of which is good, some of which is problematic, some of which needs revision (but there is no process for appeal or revision).

The reason to oppose the Common Core standards is because they violate the well-established and internationally recognized process for setting standards in a way that is transparent, that recognizes the expertise of those who must implement them, that builds on the consensus of concerned parties, and that permits appeal and revision.

The reason that there is so much controversy and pushback now is that the Gates Foundation and the U.S. Department of Education were in a hurry and decided to ignore the nationally and internationally recognized rules for setting standards, and in doing so, sowed suspicion and distrust. Process matters.

The Common Core lacks most of the qualities [of the ANSI core principles for setting standards] — especially due process, consensus among interested groups, and the right of appeal — and so cannot be considered authoritative, nor should they be considered standards.  (emphasis added by me)

Another fabulous recent article on this issue can be found here.

Sunday, May 4, 2014

The Tension - Passion and Logic

The Tension. . . (from July 5, 2010)
I was listening to a financial show yesterday, while waiting in the car...
One of the guys talking said something that I think may be a common misperception. 
He said,
Democrats are a party of PASSION
the Republicans are a party of LOGIC
It was such a revelation for me, I had to write it down because I didn't want to forget exactly what he said and the visceral reaction I felt at the time.

It's apropos that it happened on Independence day, too! 

It explains exactly why I haven't been able to identify with either party (and their misperceptions) exclusively, and why I consider myself independent. 
I reject this overgeneralization as an idea used to disparage individuals and minimize their opinions and concerns.  Passion and logic are not mutually exclusive in my life - politics included.  Any good decision that I have been able to make along the way has been a confluence of both logic and passion, rarely in equal parts.
I believe each of us has our own synergism of passion and logic.  Our unique way of interpreting and utilizing the information gathered from the world around us. 

See people as individuals... address issues as issues we all face...
Don't lazily rely on partisan rhetoric...

These are reminders to self.   

Saturday, April 19, 2014

Princeton Study Concludes that American is Basically an Oligarchy

Princeton Concludes What Kind of Government America Really Has, and It's Not a Democracy   
April 16, 2014

A new scientific study from Princeton researchers Martin Gilens and Benjamin I. Page has finally put some science behind the recently popular argument that the United States isn't a democracy any more. And they've found that in fact, America is basically an oligarchy.

This is a familiar topic to those of us who oppose the Common Core Standards Initiative.  I've been scratching my head, literally for years, trying to understand how Common Core took hold, quietly and quickly, in America's representative Republic.  In Missouri, it became clear to me that the "initiative" capitalized fully on the top-down governance structure in our education policies and their implementation.  I believe that Missouri state statutes were violated in the adoption process, but unfortunately, there was no oversight mechanism in place to stop Common Core from the onset.

After researching the opposition to the Common Core Standards Initiative throughout the country for a number of years, there is no doubt in my mind that our American oligarchs were well aware that state legislatures were not equipped to investigate and address adoption of Common Core Standards in 2009-2010.