Tag Archives: Common Core

3. Construct Viable Arguments and Critique the Reasoning of Others; ARGUMENTS

File:Einstein 1921 by F Schmutzer.jpg


3.  Construct 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.

Being able to utilize a common algorithm to solve a simple problem remains a skill to be taught and practiced in the classroom. Many parents and teachers are confused regarding this issue. Students must know basic facts and algorithms prior to completion of the fourth grade. This has not changed due to implementation of the Common Core for Math. Being able to solve simple, one-step problems by using common algorithms is only a part of understanding mathematics. A true understanding, and the ability to apply math requires much more.

Solving a real world problem generally requires multiple steps, and can often be approached in more than one way.  This standard encourages students to look at problems in different ways, and occasionally find solutions using unconventional methods.  The ability to apply previous knowledge to problem solving is essential, as well as the ability to solve problems in different ways utilizing analytical reasoning.

The main thrust of the third standard is “argument.” Students need to be able to construct viable arguments of why their problem solving processes work. The ability to argue for a method requires the ability to recognize counterexamples that lead to the same solution. Finding flaws in method is equally important. Those proficient in mathematics must be able to justify their methods and critique those of others. This can often be accomplished through the use of “concrete referents”, such as objects, drawings, diagrams and actions. The ability to reason and write mathematical arguments has becom a necessity for today’s student. Critical thinking, a requirement for today’s information driven world, is being practiced through this method.

James Wheeler – commoncoremath.net


Leave a comment

Filed under Education, Homeschoolers, National Common Core Standards, Primary Education

Critics of the National Common Core Standards


One of the best things about being an American is being entitled to share opinions regardless of their accuracy.  Many have used this right to criticize the relatively new National Common Core Standards for learning.  While some of this grousing is deserved, there is value in the idea of national learning standards.

Complaints have come predominately from conservatives and tea party activists.  Recently the Republican National Committee has joined the chorus of nays.  The conservative Heritage Foundation has stated;

“One of the primary objections by conservatives to the Common Core standards is the view that the Obama administration is intent on controlling what is taught at each grade level in schools across the United States. According to the Heritage Foundation, the Obama Department of Education “has used its flagship ‘Race to the Top’ competitive grant program to entice states to adopt the K-12 standards developed by a joint project of the National Governors Association (NGA) and the Council of Chief State School Officers (CCSSO).”

This indicates much of the criticism has more to do with the standards being developed and implemented during the Obama administration than with any real complaints regarding the curricula.  Of course, there are also folks on the left who question the validity of the new standards, although the reasoning is generally different.

Common complaints regarding the common core include but are not limited to;

  • A national takeover of education
  • Leftist indoctrination of our children
  • Teaching that answers can be wrong as long as they can be explained
  • A movement away from basic facts and the three Rs

These complaints are driven by a great deal of misinformation and partisan politics. While critics complain of the poor job done by educators out of one side of their mouths, they attack almost any attempt to improve education out of the other.

National standards will give every school district in every participating state a baseline to measure against.  In addition, common standards will tend to lower the cost of education through increased efficiencies provided by centralizing a portion of the process.

Nothing in the common core even hints at “leftist indoctrination.”  The core was developed to enhance critical thinking skills through better reading comprehension and a more thorough understanding of basic mathematic processes.  Reading will emphasize non-fiction, not of the “Communist Manifesto” variety, but of documents such as the Declaration of Independence and United States Constitution; hardly leftist rags.

Wrong answers will continue to be wrong, and students will be tested on their knowledge of basic facts in the fourth grade.  Passing or failing will depend on a student’s understanding of the basics as well as an understanding of why math works the way it does.  Written answers will be graded according to a rubric, which will provide points for understanding a mathematical process as well as the answer.  This is hardly revolutionary.  Rubrics such as these have been in use for many years.

Unfortunately, we as Americans have become a divided society.  Partisanship has taken the place of common sense in a myriad of situations.  Opinions are formed based on the rantings of talk radio and cable tv hosts.  Politicians leap at every chance to smear the opposition.  Worst of all, the vast majority never bother to do any research, such as reading the standards themselves, but instead take their views from the rabble rousers.

While I am not 100% sold on the National Common Core, I respect the effort to improve our system of educating k-12 students.  The country would be much better off if everyone pulled toward this common goal.  My suggestion to concerned citizens would be to put in the work required to truly research this effort, and try to put politics aside.

James Wheeler – commoncoremath.net

Leave a comment

Filed under Education, Homeschoolers, National Common Core Standards, Primary Education