Saturday, June 28, 2014

first grade math instruction

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.

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.

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.

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.

Sunday, May 18, 2014

Learning Targets

Connie M. Moss and Susan M. Brookhart's book, Learning Targets: Helping Students Aim for Understanding in Today's Lesson, reinforces some of my thoughts and introduces some interesting refinements. To start, they identify learning targets as uniquely different from objectives. As someone who went to college in the 80's taking special education classes, objectives are something with which I am intimately familiar and skilled at developing and assessing. The idea that objectives are not broken down far enough is intriguing. Moss and Brookhart see the differences as illustrated in the chart below:


objectives for the teacher
learning targets for the student
span one or more lessons
span one lesson
describes content knowledge and skills students should be able to demonstrate
asks, “What am I going to learn?”
teacher language based
language, model, illustration and/or demonstration based
general
specific to the performance chosen for the lesson
includes criteria and performance standards
includes student look fors to identify success
ex. student will be able to solve problems using 3-digit addition with carrying in the one’s place. (p. 166)
ex. I am going to be able to use a method called carrying to solve problems like these accurately and smoothly: 438 + 152 =        (p. 166)
ex.  explain the literal meaning of the Gettysburg Address and make connections among ideas in the Gettysburg Address and other historical documents.( p. 119)
ex. I can put the speech into my own words.
I can explain how the Gettysburg Address echoes some ideas from the Declaration of Independence. (p. 120)



The differences may seem somewhat subtle. The learning targets may be thought of as specifically telling students what they exactly can do and the objectives are more adult oriented. As students get older the two ideas may get closer together. Some of the examples the authors use to illustrate learning targets are leading questions. Students who are not metacognitively aware or are not honest may simply respond, "Yes, I can explain three differences between latitude and longitude," with no basis in reality. The authors never confront this concern. Perhaps it is enough to put it to kids so they know the truth inside.

Grading is a concern the authors address. I have long been against grades that do not reflect what the student can do but rather how compliant, effortful or well behaved he is. As I have explored grading practices, I have become increasingly supportive of standards based grading that reflect the current level of knowledge a student has rather than the mean of his grades or the behaviors he exhibits. For the students that I directly teach material to, I have divorced compliance and effort from content grades. These are definitely areas in which I comment, but they are not allowed to impact grades. For the classes I teach for my homeschooled students, I use a standards based report that lists each objective and where the student performed at the end of instruction on that objective. If I had to reteach a skill, I retaught and then re-administered a summative assessment. If the key is learning the material, it is incumbent upon me to teach the material until some level of success is achieved- not until the time for learning that objective per a curriculum map has passed. The authors concur. They support content and behavior reporting as separate on a report card. They argue for using a median score rather than an average, unless steady progress has led to the decision that a mean would lead to a more accurate report of student knowledge. An entire chapter in the book is dedicated to how to incorporate learning targets into grading. For teachers who are responsible for assigning grades this is essential.

A concern I have is with the time required to plan using the author's guide. Starting with the standards, developing objectives and learning targets that match is only the beginning. Then they describe identifying multiple activities that meet those targets (a task that enables differentiation). The teacher then develops individual descriptions and rubrics for each activity. The process is extensive and time consuming. Planning in teams might help. Slow adoption of the full process might help as well. The easy part is identifying what the students should be able to do at the end of the lesson that they were unable to do at the beginning of the lesson. (This assumes your class does not have any students who could perform the task before the class started.) Creating a series of 1-5 "I can ..." statements for a lesson could be fairly simple. Having a clear direction of exactly what the students should be able to do at the end of the lesson benefits instruction and helps create a road map of learning that helps everyone.

The book offers some interesting insights to the process of organizing and planning lessons. A skilled professional could pull refinement tips and a novice could pull big steps forward from the text. The authors might think of providing a sample set of unit plans across grade and content areas that demonstrate CCSS referenced standards, objectives that meet those standards, learning targets that focus on those objectives, activities that students could engage in to learn those standards and sample rubrics to use throughout. While they do offer a few sample ideas, for many practitioners, this could be inadequate to support their learning and adopting suggested instructional behaviors. The appendix provides some resources for helping plan a lesson or observe one thoughtfully, but time required to use them will be extensive.



Thursday, May 8, 2014

The goal of education is becoming

Marc Prensky is an education professional who finds complete dismay with the educational system. His commentary, The Goal of Education is Becoming, demonstrates his lack of respect for learning. He feels that school should be about "becoming a 'good' person and a more capable person than you were before."

Dictionary.com defines learning as the following:
1.  knowledge acquired by systematic study in any field of scholarly application.
2.
the act or process of acquiring knowledge or skill.
3.
Psychology . the modification of behavior through practice, training, or experience.

It also defines becoming as:
1. that suits or gives a pleasing effect or attractive appearance, as to a person or thing: a becomingdress; a becoming hairdo.
2.
suitable; appropriate; proper: a becoming sentiment.
noun
3.
any process of change.
4.
Aristotelianism. any change involving realization of potentialities, as a movement from the lower level of potentiality to the higher level of actuality.

Apparently he sees knowledge and the process of learning as incompatible with any process of change especially those involving realization of potentialities. How he divides these two is intriguing. He criticizes education as being especially test and test prep drive- a fair analysis in some schools more than others. He fails to acknowledge that there is an essential component to assessment. While our methods may be far from perfect, we do need to determine how students are progressing and  how our teachers and schools are doing. Employers do this all the time. They set quality standards that their employees are expected to meet: for example, the cash box must balance the receipt count, there are so many pages that must be edited a day, a police officer must follow procedures precisely. Having standards and accountability is important.

Do educators want students to realize their potential? Yes! Personal growth is a critical component of education. There are not, however, any national standards surrounding this issue because it is both subjective and variable. Quantifying it would be a mistake. Most school mission statements include lines about reaching potential, being prepared for life after school, and nurturing children. The problem may be that the concept character development is different for different people. Social, ethnic and religious groups see character differently. The Jewish school I am currently working in would be offended if we pushed the middle school girls to aspire to high powered career lives rather than only motherhood. If I deprived fathers and male relatives from attending concerts in which their daughters performed in a public school, I would lose my job, but in the Jewish school to not do so would also lose me my job. Some schools are more overt in their push for developing character. These are usually small private schools who draw their populations from homogeneous cultural bases. In our society, it would be wrong to impose these beliefs on everyone. Mr. Prensky can argue for "becoming" something greater and I would respond that when you truly learn to critically think about things that you know and learn- a goal of the CCSS, you become something greater than you were before. We may need to reform our methods of instruction to further critical thinking, self-regulation and personal development, but we also need a population with a baseline level of cultural and intellectual knowledge. We truly cannot have one without the other.

Saturday, May 3, 2014

Why won't you just tell us the answer

Bruce Lesh's "Won't You Just Tell Us the Answer?" is an interesting text describing an investigational approach to social studies classes. He begins the thesis with a rationale for teaching history differently. For over a hundred years, he contends, we have bored students who recall little of what is "taught" and who feel that the class is useless. The method of instruction that history teachers have utilized for this time period is lecture and reading. If we want a different outcome- students who are engaged, interested and actually learning history- we must change our presentation method.

Toward this end, he proposes teaching students history in the way that historians approach it: as a study of often conflicting sources that must be interpreted to determine the answer of a question; history can come alive.  Examining primary sources is critical. He describes this methodology as historical investigation

Lesh describes seven American history lessons that he has used, some of which he has presented at a variety of workshops. These lessons cover Nat Turner's Rebellion, Theodore Roosevelt and the Panama Canal, the rail strike of 1877, the Bonus Army March, Custer's last stand, the Civil Rights Movement, and the Truman-MacArthur debate. Five of these lessons use a jigsaw approach. The others use both collaboration and whole class presentation.

Lesh begins his investigations with visual and/or musical pieces to stimulate the students's thinking. He poses a question and sets the class up with a limited number of sources to evaluate. Unlike the traditional DBQ essays which also involve primary sources, Lesh's investigations include no "correct" answer. They demonstrate different sides of an issue and require that students evaluate the text, subtext and the context in order to formulate an opinion that answers the question.  "What is Roosevelt doing on his autobiography (lying, telling a half-truth, exaggerating, rationalizing or obfuscating) and what role did the US play in the acquisition of territory used to construct the Panama Canal?" is one of his questions (p. 60). This open ended question does not have a definitive answer, but does lead to discussion and a deep understanding of the situation.

Lesh offers suggestions for identifying sources, selecting questions, and determining time frames (keep the investigation less than 120 minutes). He provides some sample graphic organizers and worksheets to use with the described lessons. Although he offers interesting descriptions of his lessons, lots of room is left for interpretation. The author confirms that setting up investigations is time consuming. Sifting through the volumes of sources available, selecting ones that support understanding differ viewpoints and pieces of information, and preparing lessons around the question takes copious time. Slowly introducing investigations and limiting the number of thorough ones is important. Lesh does assign textbook and survey reading, especially for homework to prepare students for the investigations. He is not using the investigations to present what happened, but rather to analyze why did an event occur, how are events interrelated, which perspective should be understood, and how have things changed over time. This is the higher level thinking we aspire toward that is often missing in traditional history classes.

The book was written while the CCSS were being developed and rolled out. His methodology, while not referencing the standards, is compatible with them. They utilize all the reading standards. For example, the CCSS list the following standards in the 6-8 strand.
  • Cite specific textual evidence to support analysis of primary and secondary sources- he uses primary sources for investigations themselves and secondary ones to set the stage.
  • Determine the central ideas or information of a primary or secondary source; provide an accurate summary of the source distinct from prior knowledge or opinions- if students cannot understand the text, the rest is moot.
  • Identify key steps in a text's description of a process related to history/social studies (e.g., how a bill becomes law, how interest rates are raised or lowered)- the entire approach is process oriented.
  • Determine the meaning of words and phrases as they are used in a text, including vocabulary specific to domains related to history/social studies- Lesh advocates using the language of the source and the writing. Scaffolding in this area is for students who would struggle too much with the source material- handwritten pages can be typed, unusual words and language can be debated in small groups  
  • Describe how a text presents information (e.g., sequentially, comparatively, causally)- Lesh structures his concepts around issues such as causality and sequencing.
  • Identify aspects of a text that reveal an author's point of view or purpose (e.g., loaded language, inclusion or avoidance of particular facts)- this the subtext that is critical to understanding primary sources; one of three aspects of reading primary sources that Lesh focuses on throughout all investigations.
  • Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts- Beginning lessons with images and music and moving on to more wordy sources integrates the visual and the print.
  • Distinguish among fact, opinion, and reasoned judgment in a text- the questions require students to analyze these issues as part of both the text and subtext.
  • Analyze the relationship between a primary and secondary source on the same topic- by providing secondary source homework, occasional lectures and movies, Lesh sets the stage for the investigations. This enables students to see how the sources are related. 
  • By the end of grade 8, read and comprehend history/social studies texts in the grades 6-8 text complexity band independently and proficiently- Although the text is used less than in a traditional classroom, students are expected to read the text or teacher written historical summaries of events.
All of these aspects are evidenced within his structure. Since historical investigations do meet the Common Core standards, this approach should not be as controversial as it was when Lesh began using it over a decade ago. Students have responded well to having to do the process of historians as opposed to having to recall detailed lists of facts.  He has also discovered success with student performance on both AP and NY Regents exams. Using an increasing number of primary sources with ambiguous interpretations enables students to sample the task of historians in an active and engaging method. Being careful to be sure to cover the material that is critical to the mandated state exams, can be done while at the same time presenting history in an manner that students will actually learn the subject and perhaps not dread the class.
 
It appears that premade historical lab information is not as easy to locate as one might desire. Simulations are the most often occurring samples. While some simulations offer insights into why some events occur, students shuffling students into situations so they can try to "feel" the way people did in the past is ingĂ©nue. Empathy is important to develop, but we need to develop empathy in a historical sense. If all we get out of slave ships is indignation, we cannot understand the historical events that led to them and why it took so long to eliminate such events. We do not need to agree with slavery to understand the social complexity of it as an underpinning of early American society.