Sunday, November 16, 2014

Thoughts on communicating mathematically and professional development


I didn't mean to put the PD speaker on the spot last week, but I thought it was important to at least attempt to convey that there are other types of communication, different from the linguistics forms that were the focus of that session.  In mathematics and science, a large part of our study is focused on helping students learn to communicate using symbolism.  I was happy that the speaker seemed to understand what I was trying to say, but now that I’ve had more time to think about it, and the initial shock and frustration has worn off, I’d like to journal a few additional thoughts here.

During teaching, there are many, many variables to be considered simultaneously.  (These are not listed in any particular order, because I believe that they are equally important.)  The content taught should be accurate and factual, with an underpinning goal of preparing students to succeed at the next level, so that they are able to make well-informed choices based on their level of interest in various subjects.  Teachers also need to be mindful of the range of ability levels of each class, as well as students’ many different preferred learning styles and communication preferences.  In order to help students acquire knowledge of content that may not be their current preference, caring teachers encourage struggling learners as an integral part of the teaching process.

As a practical matter, the length of our school day and each class period is limited, yet we traditionally require students to have a minimum number of courses in various areas because we want them to be prepared to make informed choices regarding their future plans to become productive and happy members of society.  I believe the underlying assumption, which we can all agree upon, is that a minimum amount of knowledge in these areas is needed as a basis for effective decision-making.

In order for our students to have opportunities to learn effective communication skills in mathematics and science, I believe it’s important to foster the development of these “languages” of symbolism in few classes which are built upon these nonlinguistic forms of communication.  Mindful teachers have made efforts to convey content, as well as its necessary symbolism, through many modes of communication in recent years, but few courses throughout a students’ day include non-linguistics as a basic skill required for content acquisition as do math and science.  For this reason, I believe it’s important to encourage teachers of those subjects to build upon the symbolism of the content, and not avoid it in an effort to incorporate more linguistic forms of communication.  Those skills are appropriately utilized in most other subjects to a much higher degree, and rightly so.

It doesn’t seem practical to me that math and science teachers are often encouraged to utilize classroom activities that are designed to improve students’ linguistic acquisition of content knowledge, because the content that we teach is of a nonlinguistic nature.  Some teachers feel frustration during “professional development” sessions that fail to recognize this important aspect of their profession, and that is unfortunate because I believe that our most district leadership teams really do seek continuous improvement in all areas, but they may not realize that their teachers can provide extremely valuable feedback that is necessary in moving toward that goal. 

High-quality feedback is integral to the continuous improvement process.  I believe that most local school systems seek to hire dedicated professionals who are prepared to elicit timely and accurate feedback and incorporate it into practices that enable schools to “learn” and grow, but problems can arise when the system is not utilized to its full capacity.  When leaders don’t have the right types of feedback, sometimes decisions may not produce the desired results toward improvement.

If you want to receive feedback that's helpful to the improvement process, I believe it's important to survey teachers and students to better understand current realities and their beliefs on what is needed in moving forward. 

Sunday, November 9, 2014

CA Unveiling #CommonCore Schedule ~ #Liberty and #Freedom in #Edreform


Unveiling Common Core Event Schedule

Events are free and open to the public although RSVPs are required


Monday, November 10: San Juan Capistrano
7:00 pm forum
Capistrano Unified School District Trustees' Meeting Hall,
33122 Valle Rd.,
San Juan Capistrano, CA



Tuesday, Nov. 11: Montrose/Glendale
7-9pm forum
Light on the Corner Church
1911 Waltonia Dr.
Montrose, CA 91020

Please RSVP through EventBrite

Wednesday, Nov. 12: San Diego
7:00 pm forum
Town & Country Hotel
500 Hotel Circle N.
San Diego, CA

Please RSVP through EventBrite

Thursday, November 13: Chino Hills
7:00 pm forum
Calvary Chapel
4201 Eucalyptus Ave.
Chino Hills, CA 91710

Please RSVP through EventBrite

Saturday, November 15: Murietta
6-8pm Forum
Promise Church & Preschool
25664 Madison Ave.
Murietta, CA 92562

Please RSVP through EventBrite

Sunday, November 16: Palos Verdes
3-5pm Forum
Peninsula Community Church
5640 Crestridge Road
Palos Verdes, CA 90275

Please RSVP through EventBrite

Monday, November 17: Costa Mesa
6-9 pm "Common Core on Trial" Hearing
OC Office of Education
200 Kalmus Drive
Costa Mesa, CA 92626

Thursday, September 25, 2014

Interest, apathy, and empathy...

I used to put up a poster in my classroom that said something to the effect,

What's the difference between apathy and empathy?
 
I don't know and I don't care...

I realized a few years later that posting it may not be helpful to all students.  What I mean by that is some students will understand my intent in posting it, my hope that we all desire to learn, but some may be affected only by the last part and think that I don't care... merely because it was the last part

I decided not to put that on the wall in the classroom anymore.

We have new teachers in our mathematics department this year, and I shared my extra posters that were in the storage cabinet with one of them, thinking that she may need some for her classroom since she was "new" to our building.

She choose very few from that collection that I shared. Maybe she didn't feel comfortable with many of them.  Maybe she is more insightful than I was at the time I purchased some of them. 

I'm not offended at all, because those were my extras... and I had decided at some point to no longer display them also.  They were simply a resource that I thought might help... no big deal. 

I know she wants to do what is best for her students.

My entire collection of posters, some on the walls in my classroom now, and some stored in the cabinet, come from three sources...

1)  My mother has been retired for a number of years now, she was also a math teacher.  She actually has a wealth of knowledge of many topics that she loves to share. 

I'm not exactly sure what is on her transcript... but I believe she is very intelligent.  She enjoys working and absolutely loves gardening!

2) When I started teaching at my school, a math teacher who had decided to become a librarian, was at the end of her math teaching career and was working in the library at the time.  She also attends my church. 

She shared an entire cabinet full of resources with me that she had organized perfectly over the years - at least it was easy for me to understand how she had organized things.  In fact, my first classroom was actually her old math classroom.  I am very thankful that she chose to share her work.  It saved me so much time and gave me needed guidance during the first few years of my career.

3)  Over the years, I have purchased many of my own posters.  At the time of each purchase, it seemed like a good idea to put them up on the classroom walls.  Over the years though, my ideas have changed about what should be displayed. 

It seems minor to some, but I think these are very important decisions, mainly because I am also a busy person and I don't plan to change the posters often, or anytime soon... Unless I change my mind... of course.

I try to display posters that feel right to everyone.  My hope is that students will understand why I chose the posters that are displayed by my actions.  I don't always achieve the goal of conveying the fact that I care deeply about students' personal goals and how the math fits into that and can help them achieve them, but I keep trying...

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."



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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.


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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"

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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. 

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