Dyscalculia
Anyone who tries to make gains in the field of mathematics education is a friend of mine, unless someone is attempting to make the case why dyscalculia makes it impossible for a student to learn. Even in the case that a student has a learning disability, there are always methods for overcoming them through a variety of means.
No one needs to place unnecessary obstacles to success in their way as they strive to learn. However, there are some institutional issues or policy issues that need to be altered or scrapped entirely in place of better ones to help students learn. Those of us in the field of mathematics education know this and we are always willing to examine what we do to increase our efficiency and our students’ ability to perform.
Schmidt’s Article
Do math teachers have the obligation and expertise to tinker with what they do to determine what math gets taught and when it gets taught? This is a two-part question; it questions whether math curricula should change over time and a math teacher’s ability to make those changes.
According to William Schmidt’s article, Springing to Life in American Educator (2013) he argues on both sides.
He reflects on the Common Core State Standards: Mathematics (CCSS-M) and the need to have a national mathematics curricula. In doing so, he stated, “…teachers are not necessarily trained content experts, and they shouldn’t be expected to make these decisions.” This was his rationale for math teachers to take their marching orders and simply accept the CCSS-M without debate.
With regard to mathematics textbooks, however, Schmidt wrote, “Better prepared and more experienced teachers may recognize the problems with their textbooks and, when permitted, may reorganize the material presented in the textbook or search for supplementary materials.”
Does Schmidt believe teachers have the expertise to change the curricula? Yes, unless you are talking about a debate concerning the CCSS-M.
Schmidt’s mindset is very clear: math teachers are to take their marching orders and do what they can with them.
Mathematics Professionals: Accomplishments
The part of being a mathematics teacher that is so intriguing is we ask the ‘why’ and the ‘how’ questions. Few people would doubt that we base our decisions on sound numerical principals. In doing so, it has provided us with a thorough understanding of what we teach.
Consequently, math teachers have learned how to make some interesting changes over the years. According to Woodward (2004), mathematics education has gone through these changes or included these elements: Excellence in Education (The New Math), Slow Learners, Equity and Excellence in Education, and Large Scale Research in Basic Skills. The list goes on to include Cognitive Science as a New Framework, Mathematics Interventions for Students with Learning Disabilities, Excellence in Education (Again), and The Challenge to Teach All Students.
Math teachers have experimented with traditional learning (direct instruction) and various methods of conceptual or child-centered learning (cooperative learning, discovery learning, …) (Rillero, 2012). Interestingly enough, Lewin (2008), had this to share regarding the dichotomy of traditional versus conceptual learning:
It has also been shown math teachers have incorporated research from Bloom, Tennant, and Gardner (University of Washington, n.d.).
Mathematics Educators: Should They Take Orders or Be Problem Solvers?
It should be quite apparent to the reader that these methods have been included within the mathematics curricula over time as a matter of finesse. Such skill requires attention to detail, manipulating teacher resources (like textbooks, workbooks, manipulatives, and hand-designed works) to achieve precise objectives. It is clear that such work is the result of dedication to career, know-how, professional development, and teacher-training. It is not the result of simply following orders, like Schmidt outright suggests should occur.
What is most disconcerting is Schmidt’s top-down style of curricula analysis and design. If one were to form a parallel to math education, Schmidt’s vision of mathematics education would be one of a teacher who is authoritative and using only direct instruction, which is hardly on par with modern approaches to math education.
Steen’s Research
According to Steen (1989), these elements reflect current demands on mathematics learning: engage students, encourage teamwork, stimulate creativity, and encourage discussion. Top-down, autocratic decision-making is hardly the role-model approach for instilling quality mathematics education.
Even more interesting is Steen’s point on increasing breadth. Steen says math learning occurs in an approach that is too narrow. Yet, CCSS-M has acted predominantly like a winnowing tool [confirmed in Schmidt’s article] in abandoning various skills/concepts, which contradicts Steen’s views on breadth.
Opposition to Common Core State Standards
Before the reader thinks CCSS has mass appeal, let it be known there are people who have outright opposed CCSS, that Schmidt professes and for good reason. Look toward the East, at New York, where standardized testing has been around for a long time. They also base teacher evaluations very closely on these standards.
Enter Diane Ravitch (2013), a Ph.D in the history of American Education, is opposed to CCSS. She, too, disliked the top-down, involuntary implementation of these national standards. She indicated states were coerced with federal dollars to accept the state standards. In some cases, better, time-tested standards were abandoned only to chase these dollars. She wrote, “… [the CCSS ]will have a disparate impact on students who are English language learners, students with disabilities, and students who are poor and low-performing” and cited Kentucky schools as an example.
Enter Carol Buris (Strauss, 2013), principal of South Side High School in New York. She referred to CCSS as “…a plane being built in the air — a plane in which the passengers are children.” There is no empirical evidence that the CCSS can be a predictor of college performance, she claims. She also went on to describe how four out of five researchers who were published in Educational Researcher are also employed by Pearson. These proponents for measurement to enhance student learning also produce tests for New York State tests.
There are entire states that are not implementing CCSS (Associated Press, 2013). Several states have placed measures against CCSS to varying degree. This should tell us there is good reason to mark skepticism toward CCSS.
Questionable Funding Issues
Schmidt is fully aware of the costs associated with CCSS. He has pushed Michigan to fund CCSS (Michigan Education Association, 2013). There is also reason to believe CCSS will have little or no affect on achievement within poor communities (Carter, 2013) and not positively affect the achievement gap, despite being a motivating target for CCSS to conquer (Haycock, 2013).
The PARCC test, an evaluative measure for CCSS, is to be given within an online environment. Getting districts up to technological speed requires money to either upgrade current computers or outright purchase more computers. We know 76 percent of districts that use Common Core claimed inadequate funds for implementation was a major challenge (Rothman, 2011).
Strangely enough, years ago there was a landslide of concern regarding No Child Left Behind, its non-funded mandates, and how inner city youths will not gain from the mandate due to lack of funding (Abramson, 2007). Yet, no similar levels of concern have been raised for CCSS, which is odd even though it suffers from the same poorly funded malady.
There is also a quizzical opinion piece that connects the dots between PARCC, Bill Gates, and the company that will produce PARCC assessments that questions how taxpayer monies are being spent (Berger, 2013).
Obstacles to Success
It could be noted that the comments here appear to be negative and they unfairly pound on Schmidt's views. However, it is necessary to acknowledge the obstacles to progress so that schools can overcome them, which is how people with dyscalculia are managed. CCSS-M has obstacles, some of which are massive funding issues for inner city kids who already have a number of limitations to overcome.
The research here should inform the reader that there is no panacea resting in top-down mandates. Consequently, the Herculean task of overcoming issues within certain schools rests with group efforts, creativity, and involving students within the learning process.
It will require teachers to make creative choices that could never be foreseen by members of think tanks or universities. Teachers in the field are always willing to gain advice from researchers who have data that confirm areas of need and methodologies for dealing with them, but no such work has been done with CCSS to help teachers who are in the trenches handling the immediate needs of students.
Schmidt should do more than bark orders and use a limited body of research to affirm his statements [8 out of 11 citations in his Springing to Life piece involve Schmidt (himself), Houang, and/or McKnight]. He could instead offer helpful choices and interesting insights. Teaching by example is exactly what teachers need to witness from education researchers and leaders who can then, in turn, equally inspire the students they teach.
Conclusion
This response to Schmidt’s article is less of an attack on his work and the CCSS-M as it is on those who might be gullible in accepting top-down approaches for their utopian claims. Teachers, especially math teachers, will make the best of these Common Core State Standards. Then, we will be forced to work collaboratively with our peers to make the best of our situations with the limited resources we have to manage.
While the Schmidt’s of the world continue on about their platitudes, we teachers have to negotiate troubled circumstances. Students go without textbooks, have no computers at home, deal with insufficient conditions at home, are a product of low socio-economics, and suffer from language deficits.
Push as we may toward Bloom’s pinnacle, but Maslow’s burdens equate to a near Sisyphean duty.
Resources
Abramson (2007) Funding Stagnant for No Child Left Behind Program. NPR. Accessed online on June 3rd at: http://www.npr.org/templates/story/story.php?storyId=13746166
Associated Press (2013) Some States Push Back On Common Core Standards. Accessed online on June 3rd at: http://www.huffingtonpost.com/2013/05/28/states-common-core-push-back-standards_n_3346210.html?utm_hp_ref=politics
Berger (2013) The long shadow of Bill Gates. Rutland Herald. Accessed online on June 3rd, 2013 at: http://rutlandherald.com/article/20130516/OPINION04/705169963
Carter (2013) Beyond the Common Core: Transforming Low-income Housing to Support School Outcomes. Huffington Post. Accessed online June 3rd, 2013 at: http://www.huffingtonpost.com/carol-j-carter/support-school-outcomes_b_3140302.html
Haycock (2013) Closing the Achievement Gap. ASCD. March 2001 | Volume 58 | Number 6. Helping All Students Achieve Pages 6-11. Also available online at: http://www.ascd.org/publications/educational-leadership/mar01/vol58/num06/Closing-the-Achievement-Gap.aspx
Lewin (2008) Report Urges Changes in Teaching Math. New York Times. Accessed online on June 3rd, 2013 at: http://www.nytimes.com/2008/03/14/education/14math.html
Michigan Education Association (2013) No Michigan schools will make AYP if Senate strips Common Core funding. Accessed online on June 3rd at: http://www.mea.org/no-michigan-schools-will-make-ayp-if-senate-strips-common-core-funding
Ravitch (2013) Why I Cannot Support the Common Core Standards. Accessed online on June 3rd, 2013 at: http://dianeravitch.net/2013/02/26/why-i-cannot-support-the-common-core-standards/
Rillero (2012) Deep Conceptual Learning in Science and Mathematics: Perspectives of Educators and Educational Administrators. Research Report for Arizona State University’s Technology Based Learning and Research Center. Accessed online on June 3rd at: http://tblr.asu.edu/images/uploads/ASU_TBLR_RESEARCH%20REPORT_Deep%20Conceptual%20Learning%20in%20Science%20and%20Math.pdf
Rothman (2011) Five Myths About the Common Core State Standards. Harvard Education Letter. Harvard Education Publication Group. Volume 27, Number 5 September/October 2011. Available online (accessed online on June 3rd) at : http://hepg.org/hel/article/513
Schmidt and Burroughs (2013) Springing to Life. American Educator. Spring Issue, volume 37 (1), pp 2 – 9. It is available online at: http://www.aft.org/newspubs/periodicals/ae/spring2013/schmidt.cfm
Steen (1989) Teaching Mathematics for Tomorrow's World. Accessed June 3rd, 2013 at: http://www.stolaf.edu/people/steen/Papers/edl.html
Strauss (2013) Principal warns parents: ‘Don’t buy the bunk’ about new Common Core tests. Accessed Online on June 3rd, 2013 at: http://www.washingtonpost.com/blogs/answer-sheet/wp/2013/04/07/principal-to-parents-dont-buy-the-bunk-about-new-common-core-tests/
Woodward (2004) Mathematics Education in the United States: Past to Present. Journal of Learning Disabilities; Jan/Feb 2004; 37, 1; Academic Research Library, pg. 16. Also available online at: http://www.cimm.ucr.ac.cr/historia%20de%20las%20matematicas/archivos/John%20Woodward.%20Mathematics%20Education%20in%20the%20United%20States%20Past%20to%20Present..PDF
University of Washington (n.d.) Types of Learning. Accessed online on June 3rd, 2013 at: https://www.washington.edu/doit/TeamN/types.html
Anyone who tries to make gains in the field of mathematics education is a friend of mine, unless someone is attempting to make the case why dyscalculia makes it impossible for a student to learn. Even in the case that a student has a learning disability, there are always methods for overcoming them through a variety of means.
No one needs to place unnecessary obstacles to success in their way as they strive to learn. However, there are some institutional issues or policy issues that need to be altered or scrapped entirely in place of better ones to help students learn. Those of us in the field of mathematics education know this and we are always willing to examine what we do to increase our efficiency and our students’ ability to perform.
Schmidt’s Article
Do math teachers have the obligation and expertise to tinker with what they do to determine what math gets taught and when it gets taught? This is a two-part question; it questions whether math curricula should change over time and a math teacher’s ability to make those changes.
According to William Schmidt’s article, Springing to Life in American Educator (2013) he argues on both sides.
He reflects on the Common Core State Standards: Mathematics (CCSS-M) and the need to have a national mathematics curricula. In doing so, he stated, “…teachers are not necessarily trained content experts, and they shouldn’t be expected to make these decisions.” This was his rationale for math teachers to take their marching orders and simply accept the CCSS-M without debate.
With regard to mathematics textbooks, however, Schmidt wrote, “Better prepared and more experienced teachers may recognize the problems with their textbooks and, when permitted, may reorganize the material presented in the textbook or search for supplementary materials.”
Does Schmidt believe teachers have the expertise to change the curricula? Yes, unless you are talking about a debate concerning the CCSS-M.
Schmidt’s mindset is very clear: math teachers are to take their marching orders and do what they can with them.
Mathematics Professionals: Accomplishments
The part of being a mathematics teacher that is so intriguing is we ask the ‘why’ and the ‘how’ questions. Few people would doubt that we base our decisions on sound numerical principals. In doing so, it has provided us with a thorough understanding of what we teach.
Consequently, math teachers have learned how to make some interesting changes over the years. According to Woodward (2004), mathematics education has gone through these changes or included these elements: Excellence in Education (The New Math), Slow Learners, Equity and Excellence in Education, and Large Scale Research in Basic Skills. The list goes on to include Cognitive Science as a New Framework, Mathematics Interventions for Students with Learning Disabilities, Excellence in Education (Again), and The Challenge to Teach All Students.
Math teachers have experimented with traditional learning (direct instruction) and various methods of conceptual or child-centered learning (cooperative learning, discovery learning, …) (Rillero, 2012). Interestingly enough, Lewin (2008), had this to share regarding the dichotomy of traditional versus conceptual learning:
“There is no basis in research for favoring teacher-based or student-centered instruction,” Dr. Larry R. Faulkner, the chairman of the panel, said at a briefing on Wednesday. “People may retain their strongly held philosophical inclinations, but the research does not show that either is better than the other.”
It has also been shown math teachers have incorporated research from Bloom, Tennant, and Gardner (University of Washington, n.d.).
Mathematics Educators: Should They Take Orders or Be Problem Solvers?
It should be quite apparent to the reader that these methods have been included within the mathematics curricula over time as a matter of finesse. Such skill requires attention to detail, manipulating teacher resources (like textbooks, workbooks, manipulatives, and hand-designed works) to achieve precise objectives. It is clear that such work is the result of dedication to career, know-how, professional development, and teacher-training. It is not the result of simply following orders, like Schmidt outright suggests should occur.
What is most disconcerting is Schmidt’s top-down style of curricula analysis and design. If one were to form a parallel to math education, Schmidt’s vision of mathematics education would be one of a teacher who is authoritative and using only direct instruction, which is hardly on par with modern approaches to math education.
Steen’s Research
According to Steen (1989), these elements reflect current demands on mathematics learning: engage students, encourage teamwork, stimulate creativity, and encourage discussion. Top-down, autocratic decision-making is hardly the role-model approach for instilling quality mathematics education.
Even more interesting is Steen’s point on increasing breadth. Steen says math learning occurs in an approach that is too narrow. Yet, CCSS-M has acted predominantly like a winnowing tool [confirmed in Schmidt’s article] in abandoning various skills/concepts, which contradicts Steen’s views on breadth.
Opposition to Common Core State Standards
Before the reader thinks CCSS has mass appeal, let it be known there are people who have outright opposed CCSS, that Schmidt professes and for good reason. Look toward the East, at New York, where standardized testing has been around for a long time. They also base teacher evaluations very closely on these standards.
Enter Diane Ravitch (2013), a Ph.D in the history of American Education, is opposed to CCSS. She, too, disliked the top-down, involuntary implementation of these national standards. She indicated states were coerced with federal dollars to accept the state standards. In some cases, better, time-tested standards were abandoned only to chase these dollars. She wrote, “… [the CCSS ]will have a disparate impact on students who are English language learners, students with disabilities, and students who are poor and low-performing” and cited Kentucky schools as an example.
Enter Carol Buris (Strauss, 2013), principal of South Side High School in New York. She referred to CCSS as “…a plane being built in the air — a plane in which the passengers are children.” There is no empirical evidence that the CCSS can be a predictor of college performance, she claims. She also went on to describe how four out of five researchers who were published in Educational Researcher are also employed by Pearson. These proponents for measurement to enhance student learning also produce tests for New York State tests.
There are entire states that are not implementing CCSS (Associated Press, 2013). Several states have placed measures against CCSS to varying degree. This should tell us there is good reason to mark skepticism toward CCSS.
Questionable Funding Issues
Schmidt is fully aware of the costs associated with CCSS. He has pushed Michigan to fund CCSS (Michigan Education Association, 2013). There is also reason to believe CCSS will have little or no affect on achievement within poor communities (Carter, 2013) and not positively affect the achievement gap, despite being a motivating target for CCSS to conquer (Haycock, 2013).
The PARCC test, an evaluative measure for CCSS, is to be given within an online environment. Getting districts up to technological speed requires money to either upgrade current computers or outright purchase more computers. We know 76 percent of districts that use Common Core claimed inadequate funds for implementation was a major challenge (Rothman, 2011).
Strangely enough, years ago there was a landslide of concern regarding No Child Left Behind, its non-funded mandates, and how inner city youths will not gain from the mandate due to lack of funding (Abramson, 2007). Yet, no similar levels of concern have been raised for CCSS, which is odd even though it suffers from the same poorly funded malady.
There is also a quizzical opinion piece that connects the dots between PARCC, Bill Gates, and the company that will produce PARCC assessments that questions how taxpayer monies are being spent (Berger, 2013).
Obstacles to Success
It could be noted that the comments here appear to be negative and they unfairly pound on Schmidt's views. However, it is necessary to acknowledge the obstacles to progress so that schools can overcome them, which is how people with dyscalculia are managed. CCSS-M has obstacles, some of which are massive funding issues for inner city kids who already have a number of limitations to overcome.
The research here should inform the reader that there is no panacea resting in top-down mandates. Consequently, the Herculean task of overcoming issues within certain schools rests with group efforts, creativity, and involving students within the learning process.
It will require teachers to make creative choices that could never be foreseen by members of think tanks or universities. Teachers in the field are always willing to gain advice from researchers who have data that confirm areas of need and methodologies for dealing with them, but no such work has been done with CCSS to help teachers who are in the trenches handling the immediate needs of students.
Schmidt should do more than bark orders and use a limited body of research to affirm his statements [8 out of 11 citations in his Springing to Life piece involve Schmidt (himself), Houang, and/or McKnight]. He could instead offer helpful choices and interesting insights. Teaching by example is exactly what teachers need to witness from education researchers and leaders who can then, in turn, equally inspire the students they teach.
Conclusion
This response to Schmidt’s article is less of an attack on his work and the CCSS-M as it is on those who might be gullible in accepting top-down approaches for their utopian claims. Teachers, especially math teachers, will make the best of these Common Core State Standards. Then, we will be forced to work collaboratively with our peers to make the best of our situations with the limited resources we have to manage.
While the Schmidt’s of the world continue on about their platitudes, we teachers have to negotiate troubled circumstances. Students go without textbooks, have no computers at home, deal with insufficient conditions at home, are a product of low socio-economics, and suffer from language deficits.
Push as we may toward Bloom’s pinnacle, but Maslow’s burdens equate to a near Sisyphean duty.
Resources
Abramson (2007) Funding Stagnant for No Child Left Behind Program. NPR. Accessed online on June 3rd at: http://www.npr.org/templates/story/story.php?storyId=13746166
Associated Press (2013) Some States Push Back On Common Core Standards. Accessed online on June 3rd at: http://www.huffingtonpost.com/2013/05/28/states-common-core-push-back-standards_n_3346210.html?utm_hp_ref=politics
Berger (2013) The long shadow of Bill Gates. Rutland Herald. Accessed online on June 3rd, 2013 at: http://rutlandherald.com/article/20130516/OPINION04/705169963
Carter (2013) Beyond the Common Core: Transforming Low-income Housing to Support School Outcomes. Huffington Post. Accessed online June 3rd, 2013 at: http://www.huffingtonpost.com/carol-j-carter/support-school-outcomes_b_3140302.html
Haycock (2013) Closing the Achievement Gap. ASCD. March 2001 | Volume 58 | Number 6. Helping All Students Achieve Pages 6-11. Also available online at: http://www.ascd.org/publications/educational-leadership/mar01/vol58/num06/Closing-the-Achievement-Gap.aspx
Lewin (2008) Report Urges Changes in Teaching Math. New York Times. Accessed online on June 3rd, 2013 at: http://www.nytimes.com/2008/03/14/education/14math.html
Michigan Education Association (2013) No Michigan schools will make AYP if Senate strips Common Core funding. Accessed online on June 3rd at: http://www.mea.org/no-michigan-schools-will-make-ayp-if-senate-strips-common-core-funding
Ravitch (2013) Why I Cannot Support the Common Core Standards. Accessed online on June 3rd, 2013 at: http://dianeravitch.net/2013/02/26/why-i-cannot-support-the-common-core-standards/
Rillero (2012) Deep Conceptual Learning in Science and Mathematics: Perspectives of Educators and Educational Administrators. Research Report for Arizona State University’s Technology Based Learning and Research Center. Accessed online on June 3rd at: http://tblr.asu.edu/images/uploads/ASU_TBLR_RESEARCH%20REPORT_Deep%20Conceptual%20Learning%20in%20Science%20and%20Math.pdf
Rothman (2011) Five Myths About the Common Core State Standards. Harvard Education Letter. Harvard Education Publication Group. Volume 27, Number 5 September/October 2011. Available online (accessed online on June 3rd) at : http://hepg.org/hel/article/513
Schmidt and Burroughs (2013) Springing to Life. American Educator. Spring Issue, volume 37 (1), pp 2 – 9. It is available online at: http://www.aft.org/newspubs/periodicals/ae/spring2013/schmidt.cfm
Steen (1989) Teaching Mathematics for Tomorrow's World. Accessed June 3rd, 2013 at: http://www.stolaf.edu/people/steen/Papers/edl.html
Strauss (2013) Principal warns parents: ‘Don’t buy the bunk’ about new Common Core tests. Accessed Online on June 3rd, 2013 at: http://www.washingtonpost.com/blogs/answer-sheet/wp/2013/04/07/principal-to-parents-dont-buy-the-bunk-about-new-common-core-tests/
Woodward (2004) Mathematics Education in the United States: Past to Present. Journal of Learning Disabilities; Jan/Feb 2004; 37, 1; Academic Research Library, pg. 16. Also available online at: http://www.cimm.ucr.ac.cr/historia%20de%20las%20matematicas/archivos/John%20Woodward.%20Mathematics%20Education%20in%20the%20United%20States%20Past%20to%20Present..PDF
University of Washington (n.d.) Types of Learning. Accessed online on June 3rd, 2013 at: https://www.washington.edu/doit/TeamN/types.html
