As a special education teacher much of the math pedagogical instruction included the use of manipulatives to teach concepts. As a teacher I have used them to help explain what is going on. Now I am forced to reexamine this experience as a result of a study by Paul L. Morgan, George Farkas and Steve Maczuga, Which Instructional Practices Help First-Grade Students With and Without Mathematics Difficulties?
Their study looked at over 13000 students with over 3500 teachers. Students were grouped by those having evidence of mathematical difficulties (MDs) in kindergarten (bottom 15%) and those who did not. Each group was further broken down into those who demonstrated one time difficulties or persistent difficulties and those in the top or bottom half of the remaining group. They explained their rationale for looking at this age group as, in part, due to evidence supporting the idea that "students with persistent MD... are very likely-- even as early as kindergarten-- to continue experiencing MD as they age (Morgan et al., 2009), thereby necessitating instruction better tailored to their learning needs" (p. 4). This is especially true in our era of CCSS that push for more mathematical learnings and teacher evaluations based on student performance.
Teachers were asked about their instructional practices and this was matched to student performance. Teacher practices were grouped into two main types: teacher directed and student directed. Each type of practice was subdivided.
The results were interesting. Both students with and without MDs demonstrated increased performance with teacher directed instructional techniques which included modeling and drill and practice. Students without MDs also benefited from student centered practices. Contrary to my expectations, however, there was a significantly negative relationship between use of manipulatives/calculators for and music and movement on students with MDs. For the highest performing students there was also a negative relationship between manipulative/calculator use and performance. I've been taught all along to use manipulatives and here is research that demonstrates that it may not be the way to go.
Clearly more research is needed to assess the value of manipulatives and calculators at higher levels of the education chain. We also need to look at a need for using homogenous groups for some math instruction based on the fact that multiple student centered approaches did have benefits for the middle group. We also need to adjust our use of manipulatives to not interfere with performance of our high and low achievers. It is imperative that we provide effective instruction to our students. We need to carefully examine what that means and follow the research, not our beliefs or tradition.
Saturday, June 28, 2014
Friday, June 27, 2014
mindset
Carol S. Dweck has become a hugely recognized name since the 2006 publication of her book Mindset: The New Psychology of Success- How We Can Learn to Fulfill our Potential. I had read about the book, heard about it and finally have gotten around to reading it. In it she describe two types of mindsets- growth and fixed. I was surprised to see how she sees both in some people. I had thought we were one or the other. I was further intrigued by how limited interventions can greatly influence mindset and the potential for success.
The diagrams below are modifications from p. 245 in her book and describe the slope that each mindset puts a person on.
Throughout the text she describes both well-known people and people from her daily interactions with one predominant mindset or another. She discusses how their mindset either sets them up to learn from their mistakes or implode from their mistakes. These examples illustrate the importance of having a mindset that is open to growth.
In school, all to often we only reward success. We minimize effort, in part because we do not recognize how effort is involved. For my daughter who has refused to study for an exam since I stopped making her in third grade because she has learned it all long before the test, very little effort is involved in school other than showing up. Some of the students with whom I work professionally try very hard and encounter very limited success. Unfortunately we reward the result and often assume a level of effort related to it. We need to be careful how we talk about success so as to see it as a result of work. While everyone has some things which come easier to them than others, it is important to push the kids in their "easy" areas to apply effort so that they learn how to deal with the frustrations related to failure and that we recognize how hard they might have to work in their other areas and encourage them to push through the challenges and see them as stepping stones to success rather than road blocks.
One of the tools of encouragement is praise. Much research has been done regarding praise. We know that we should praise 3-4 times as often as we criticize. We know that praise should be specific. "Your reading rate has improved three words per minute this week," rather than "good job reading." According to Dweck, we need to include the information about mindset as well. We can indicate the work it takes to get there: "You have read this passage four times and each time your reading rate increased. You can see your progress on the chart. More importantly, when you read the new passage your reading rate was higher than on the first time through the last passage. That's hard work paying off." Many authors have recently written about feedback. We need to spend our time giving constructive feedback that focuses in on work leading to improvement rather than a quick thumbs up to signify succcess.
The diagrams below are modifications from p. 245 in her book and describe the slope that each mindset puts a person on.
Throughout the text she describes both well-known people and people from her daily interactions with one predominant mindset or another. She discusses how their mindset either sets them up to learn from their mistakes or implode from their mistakes. These examples illustrate the importance of having a mindset that is open to growth.
In school, all to often we only reward success. We minimize effort, in part because we do not recognize how effort is involved. For my daughter who has refused to study for an exam since I stopped making her in third grade because she has learned it all long before the test, very little effort is involved in school other than showing up. Some of the students with whom I work professionally try very hard and encounter very limited success. Unfortunately we reward the result and often assume a level of effort related to it. We need to be careful how we talk about success so as to see it as a result of work. While everyone has some things which come easier to them than others, it is important to push the kids in their "easy" areas to apply effort so that they learn how to deal with the frustrations related to failure and that we recognize how hard they might have to work in their other areas and encourage them to push through the challenges and see them as stepping stones to success rather than road blocks.
One of the tools of encouragement is praise. Much research has been done regarding praise. We know that we should praise 3-4 times as often as we criticize. We know that praise should be specific. "Your reading rate has improved three words per minute this week," rather than "good job reading." According to Dweck, we need to include the information about mindset as well. We can indicate the work it takes to get there: "You have read this passage four times and each time your reading rate increased. You can see your progress on the chart. More importantly, when you read the new passage your reading rate was higher than on the first time through the last passage. That's hard work paying off." Many authors have recently written about feedback. We need to spend our time giving constructive feedback that focuses in on work leading to improvement rather than a quick thumbs up to signify succcess.
Common Core Standards and Gifted Education
It has been a year of growth and development as my children's school struggled to implement the CCSS using the NY state provided modules in ELA (and math, but my youngest to be advanced enough to be lucky enough to be a year ahead of the roll out for high school subjects). As I predicted, the modules were implemented slowly with little regard to my daughter's skills. The English teacher refused to differentiate the lessons because they were "challenging to her," a misunderstanding at its best. She was truly overwhelmed trying to teach the modules, especially with all the extras they decided to put in and the scaffolding for the struggling learners. It took a mere 4 months to read To Kill a Mockingbird. My daughter, who read the book in a week, was so frustrated she wanted to scream, but as a child who plays the game of school well, she did not. I am not saying the modules are bad. They have some wonderful lessons to pick and choose from. Slavish devotion, however, is a misuse.
The National Association for Gifted Children published an article that was picked up by NY's gifted organization AGATE entitled Common Core State Standards and Gifted Education. They not only acknowledge that the CCSS are more rigorous but how they fall short of meeting the needs of gifted children, a viewpoint my daughter's experience supports. The authors pull out the CCSS statement that "The standards do not define the nature of advanced work for students who meet the Standards prior to the end of high school." My experience is that some schools will do everything in their power to prevent students from achieving the standards early so they do not have to deal with the issue. There is simply a failure in the mainstream educator population to even acknowledge that these highly capable students should move at a rate any different than their less academically capable peers. There is a belief that age is the only important determinant in appropriate educational placement.
How do we get appropriate educations for our gifted children? We have to advocate strongly, some might even say fight, for an education that moves beyond CCSS. The problem is that our teachers are overwhelmed with learning the common core and the new curricular materials that go with it. Asking them to then go a step further is logistically unlikely. Therefore, we need our gifted teachers and coordinators to be enabled to help with differentiating the material in the same way we differentiate for our struggling learners. We sometimes need to advance them outside of their grade level or establish separate classes for these precocious children. Most of all we need a testing protocol that enables testing appropriately. If a child is taking 6th grade ELA , she should not be required to take the 4th grade test just because that is how old she is. The math student taking geometry should not be asked to take the 6th grade test because of his age. We need to teach and assess in a smart way or we will lose our smart kids.
The National Association for Gifted Children published an article that was picked up by NY's gifted organization AGATE entitled Common Core State Standards and Gifted Education. They not only acknowledge that the CCSS are more rigorous but how they fall short of meeting the needs of gifted children, a viewpoint my daughter's experience supports. The authors pull out the CCSS statement that "The standards do not define the nature of advanced work for students who meet the Standards prior to the end of high school." My experience is that some schools will do everything in their power to prevent students from achieving the standards early so they do not have to deal with the issue. There is simply a failure in the mainstream educator population to even acknowledge that these highly capable students should move at a rate any different than their less academically capable peers. There is a belief that age is the only important determinant in appropriate educational placement.
How do we get appropriate educations for our gifted children? We have to advocate strongly, some might even say fight, for an education that moves beyond CCSS. The problem is that our teachers are overwhelmed with learning the common core and the new curricular materials that go with it. Asking them to then go a step further is logistically unlikely. Therefore, we need our gifted teachers and coordinators to be enabled to help with differentiating the material in the same way we differentiate for our struggling learners. We sometimes need to advance them outside of their grade level or establish separate classes for these precocious children. Most of all we need a testing protocol that enables testing appropriately. If a child is taking 6th grade ELA , she should not be required to take the 4th grade test just because that is how old she is. The math student taking geometry should not be asked to take the 6th grade test because of his age. We need to teach and assess in a smart way or we will lose our smart kids.
Saturday, June 7, 2014
Start with why
I was recently talking with a colleague about the need to change education but the challenge being that a change needed to be a complete redo, not redressing the same thing. Such a change would require a huge cultural shift. In order to achieve that there would need to be a Martin Luther King Jr. for schools; someone to inspire and lead the pack to change society. Someone not afraid of beating his head against the wall. Someone charismatic who could lead the charge to move schools to the 21st century. That someone has not emerged yet.
The irony of this conversation is that I had just begun reading Simon Sinek's book, Start with Why: How Great Leaders Inspire Everyone to Take Action. Simon's thesis is that in order to successfully lead you need an inspiring leader who is focused on the WHY surrounded by people who can plan and execute the HOW in order to accomplish the WHAT. He cites several examples including Martin Luther King, Jr., Steve Jobs, and JFK. These people had a vision that changed the world.
Over the last centuries, the why of education has changed. Women in ancient Sparta were educated to run their family business because Sparta's why was military might to protect and the men folk might be absent. Puritan education was premised on the need to read the Bible to better understand God. Children on the industrial revolution were educated to get them off the streets, provide care while parents were working 14 hour days in factories and to prepare them for the workforce. Today the WHY is foggy. Are we trying to produce an educated workforce? Are we trying to stage kids for college? Are we trying to do as my districts mission statement says: develop "the whole child physically, emotionally and culturally?" Our diverse nation struggles with answering the why of education and so it is no wonder that we can improve education. All the new things we want will only be moderately successful because we do not know what we as a nation want our schools to do.
If we want to educate a populace for the 21st century, we need someone who can inspire and articulate the WHY of education of today. Sinek says, "Passion comes from feeling like you are part of a something that you believe in, something bigger than yourself" (p. 111). Our young people leave college and enter teaching with the passion, but the reality of teaching often tarnishes it quickly out of the start. They need to find the motivation to keep up the hard work of educating children so that they do not simply go through the motions. If we can collect the passion with a leader we can magnify it and change the world. We need to start with a willingness to challenge the status quo. If we want our schools to truly prepare students for the 21st, we need to articulate what that means, get the general population on board and make sweeping changes to the field. Education must cease to be the job you take so you can have summers off and be home with your children of the future, and must become a job where the constant pursuit of professional improvement is essential, where instead of whining about union hours, all teachers put in the time that needs to be put in, the job that spreads itself throughout the whole year because we are fully committed to developing students who can thrive in the ever-changing environment that is our today. If we want life long learners, we must become life long learners. If we want people to believe that the world owes us something, let the era of entitlement continue.
My answer to the WHY of education is to create independent thinkers and learners who can navigate the world of tomorrow. If we all were to be willing to engage in the changes that the goal encompasses, think where we could go.
The irony of this conversation is that I had just begun reading Simon Sinek's book, Start with Why: How Great Leaders Inspire Everyone to Take Action. Simon's thesis is that in order to successfully lead you need an inspiring leader who is focused on the WHY surrounded by people who can plan and execute the HOW in order to accomplish the WHAT. He cites several examples including Martin Luther King, Jr., Steve Jobs, and JFK. These people had a vision that changed the world.
Over the last centuries, the why of education has changed. Women in ancient Sparta were educated to run their family business because Sparta's why was military might to protect and the men folk might be absent. Puritan education was premised on the need to read the Bible to better understand God. Children on the industrial revolution were educated to get them off the streets, provide care while parents were working 14 hour days in factories and to prepare them for the workforce. Today the WHY is foggy. Are we trying to produce an educated workforce? Are we trying to stage kids for college? Are we trying to do as my districts mission statement says: develop "the whole child physically, emotionally and culturally?" Our diverse nation struggles with answering the why of education and so it is no wonder that we can improve education. All the new things we want will only be moderately successful because we do not know what we as a nation want our schools to do.
If we want to educate a populace for the 21st century, we need someone who can inspire and articulate the WHY of education of today. Sinek says, "Passion comes from feeling like you are part of a something that you believe in, something bigger than yourself" (p. 111). Our young people leave college and enter teaching with the passion, but the reality of teaching often tarnishes it quickly out of the start. They need to find the motivation to keep up the hard work of educating children so that they do not simply go through the motions. If we can collect the passion with a leader we can magnify it and change the world. We need to start with a willingness to challenge the status quo. If we want our schools to truly prepare students for the 21st, we need to articulate what that means, get the general population on board and make sweeping changes to the field. Education must cease to be the job you take so you can have summers off and be home with your children of the future, and must become a job where the constant pursuit of professional improvement is essential, where instead of whining about union hours, all teachers put in the time that needs to be put in, the job that spreads itself throughout the whole year because we are fully committed to developing students who can thrive in the ever-changing environment that is our today. If we want life long learners, we must become life long learners. If we want people to believe that the world owes us something, let the era of entitlement continue.
My answer to the WHY of education is to create independent thinkers and learners who can navigate the world of tomorrow. If we all were to be willing to engage in the changes that the goal encompasses, think where we could go.
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