Monday, April 9, 2012

Teaching Science Using Guided Inquiry as the Central Theme: A Professional Development Model for High School Science Teachers

Banerjee, A. (2010). Teaching science using guided inquiry as the central theme: A professional development model for high school science teachers. Science Educator19(2), 1-9.


Summary:
This article describes a three year study focused on training physical science high school teachers to incorporate guided inquiry labs into their practice. A major focus was on workshops where teachers could practice inquiry based labs and learn about how to structure similar labs in their classrooms. 


The researchers found the while guided inquiry labs were used more often, there were barriers to implementation such as time constraints, pressure to structure classes to complete the course, pressure to prepare students for state level testing, and difficulties associated with motivating all students to participate in inquiry.


Finally the authors conclude that: 
"There is no silver bullet for inquiry: Science educators need to have patience and understand the factors that impede implementation and transition to inquiry."


The article also included a useful example of a guided inquiry lab, as well as a structure for guiding post lab discussion. Both are reproduced below.


A guided inquiry lab in physical science/chemistry


Hint for teachers: this is not a lesson plan. You will develop flexible lesson plans for teaching this topic after you do the investigation yourself. Identify the national and state science education standards. This guided inquiry lab is to be done by students with minimal teacher support. So, have patience and help students to explore and come up with their own questions, results, and possible explanations. Provide hints/help when needed.


Objectives:

  1. To understand the process of investigative approach to science inquiry
  2. To understand how knowledge of content and skills are important to conducting inquiry processes
  3. To identify content, process, and nature of science standards which  could be taught using this lab
Guide inquiry procedure:


  1. Take a piece of magnesium ribbon & identify physical properties before burning
  2. Observation is a very important step in science inquiry. You will make observations while doing this lab. What equipment do you need? (Mg ribbon, tongs, test tubes, dilute HCl, watch glass safety goggles)
  3. Burn the magnesium and record all observations. 
  4. What questions do you have based on these observations? Write them down. (Lead questions: What are the major observations? Is burning Mg a chemical or physical change or both? Is the product different from the reactant mg metal?)
  5. Selecting one question at a time, discuss these topics in your group and suggest a method and procedure you could use to investigate that question. Discuss your proposed methods with the teacher and finalize your plan.
  6. Question: Is the product different from reactant Mg metal? Place small amounts of Mg metal and the product left after burning in two separate test tubes. Add 10 drops of diluted HCl acid to each test tube. Observe and record what happens. (Hint - possible observation - gas comes out when Mg metal reacts with HCl but no fizzing takes place with the product. The gas released is hydrogen. To verify this, put a burning match over the mouth of each test tube. If hydrogen gas is produced a popping sound will be heard.)
  7. What are your inferences? Does the product contain Mg metal? (No - not in it's metal form)
  8. Question: What does the product contain? Does it contain Mg in some other form? If yes, in what form? (Discuss this topic in groups and then generate a whole class discussion. What do we do to investigate the possibility that Mg is present in some other form in the product? Discuss with students the need for content  knowledge and abilities to engage in inquiry. Then demonstrate to students a lab test that detects Mg ions in a known sample and perform the same test on the residue left after burning Mg. If the test shows the same results in both known and unknown samples, what do you infer?
  9. What do you conclude?
  10. Challenge students to come up with a possible explanation of how the Mg metal became the Mg ion in the solid product after burning in air. Is this a chemical or physical change?
  11. Use this lab to develop concepts of chemical and physical changes, chemical reactions, ionic bonding, and the transfer of electrons from Mg to O2 during the formation of MgO.
Post lab discussion

  1. Organize a post-lab discussion for 30 min after each guided inquiry lab.
  2. First, organize group discussion on lab results and interpretation, followed by presentation of group reports to the whole class.
  3. Ask students why different groups think different ways and how they would resolve the differences. Encourage each group to synthesize their findings and conclusions based on whole class discussion. 
  4. Then you (the teacher) should summarize the post-lab discussion and offer your ideas/comments, being sure to connect the inquiry -based lab activities to the academic content being covered.
  5. Wrap up post-lab discussion with questions such as:
    1. What are "data" in your lab today?
    2. What are the evidences you collected?
    3. If a scientist were to perform the lab you did today, would he/she complete it in the same way? If not, what do you think the scientist would do? (Hint - scientists follow similar procedures to discuss and share their viewpoints)
    4. Do you see any similarity between you and a scientist? (Both raise questions, hypothesize, design experiments, collect data and evidences, and develop explanations/theories.)




F

Out of the Labyrinth: Setting Mathematics Free

QUOTES:

"Now math serves that purposed in many schools: your task is to try to follow rules that makes sense, perhaps, to some higher beings; and in the end to accept your failure with humbled pride."

"To teach it now as if it were A Rule, or (even more intimidating), The Law, is to pretend that what took years of experiment and ingenuity is as obvious as your nose. And then, because you never really had a chance to understand what was going on ("A negative times a negative is a positive, because that's the way it is!"), whenever you need this rule again it will come as just that - an arbitrary fiat, enforced by Them...The only reasonable conclusion for a struggling student to draw from such pretense is that he is irremediably stupid, of that Mathematics works in mysterious ways, its wonders to perform." (p. 9)

"...and so a teacher, who is supposed to develop our powers of inquiry, becomes instead a messenger of Received Truth." (p. 9)

"Even when designing less extreme teacher-proof curricula, an inevitable consequence is that the texts become learner-proof too; the problem-writers so want to guarantee that their unseen students will succeed, that they can't leave them to figure out relations for themselves, but merely check them. Problems intended to foster discovery are given in such small spoonfuls that you needn't see the idea behind them at all (or even realize there was an idea) in order to answer each question in the sequence." (p. 136)

"So teaching is not about 'lowering' the level of the material to meet the kids, but rather about looking at it from the same angle they are." (p. 232)

Kaplan, R., & Kaplan, E. (2007). Out of the labyrinth: Setting mathematics free. New York, NY: Oxford University Press.

Sunday, April 8, 2012

Habits of Mind: An Organizing Principle for Mathematics Curriculum

QUOTES:

"For generations, high school students have studied something in school that has been called mathematics, but which has very little to do with with way mathematics is created or applied outside of school."

"Much more important than specific mathematical results are the habits of mind used by the people who create those results, and we envision a curriculum that elevates the methods by which mathematics is created..."

"The goal is not to train large numbers of high school students to be university mathematicians, but rather to allow high school students to become comfortable with ill-posed and fuzzy problems, to see the benefits of systematizing and abstraction, and to look for and develop new ways of describing situations."

"A curriculum organized around habits of mind tries to close the gap between what the users and makers of mathematics do and what they say. Such a curriculum lets students in on the process of creating, inventing, conjecturing, and experimenting...It is a curriculum that encourages false starts, calculations, experiments, and special cases."

"The thought processes, the ways of looking at things, the habits of mind used by mathematicians, computer scientists, and scientists will be mirrored in systems that will influence almost every aspect of our daily lives."

Cuoco, A; Goldenberg, E. P., and J. Mark. (1997). Habits of Mind: an organizing principle for mathematics curriculum. Journal of Mathematical Behavior, 15(4), 375-402.

In Search of Understanding: The Case for Constructivist Classrooms

QUOTES:

"Traditional processes, which tend to emphasize "rightness" and "wrongness," are no longer helpful. Assessment processes must instead link the learner with the teacher, provide nonjudgmental feedback, provide for teacher monitoring and observation, and include activities that assess while learning is still occurring."

"We construct our own understandings of the world in which we live. We search for tools to help us understand our experiences. To do so is human nature."

"I propose situations for people to think about and I watch what they do. They tell me what they make of it rather than my telling them what to make of it."

"When asking students questions, most teachers see not to enable students to think through intricate issues, but to discover whether students know the "right" answers."

"Schooling is premised on the notion that there exists a fixed world that the learner must come to know."

"Teachers who value the child's present conceptions, rather than measure how far away they are from other conceptions, help students construct individual understandings important to them."

"The only discernible aspect is, once again, the student's behavior, but a different type of behavior. In the constructivist approach, we look not for what students can repeat, but for what they can generate, demonstrate, and exhibit."

"Piaget suggested that the creation of new cognitive structures springs from the child's need to reach equilibrium when confronted with internally constructed contradictions."

"This is not to say that she will necessarily construct the understanding held by the teacher or other thinkers in the class, just that the new understanding will likely be somewhat more sophisticated than the prior one."

"Although designed to foster students' algebraic skills, these types of textbook problems often interfere with students' desire to engage in future mathematical endeavors and, over time, erode students' confidence and self-esteem."

Brooks, J., & Brooks, M. (1999). In search of understanding: The case for constructvist classrooms. Alexandria, VA: Association for Supervision and Curriculum Development.

Classroom Instruction That Fosters Mathematical Thinking and Problem Solving: Connections Between Theory and Practice

QUOTES:

"Doing mathematics cannot be viewed as a mechanical performance or an activity that individuals engage in by solely following predetermined rules. Mathematical activity can be seen more as embodying the elements of an art of craft than as a purely technical discipline." (p. 293)

"...mathematics is a rational human creation. It is a vast collection of ideas derived as a consequence of searching for solutions to social problems. The abstractions and inventions help us make sense of our world and ourselves." (p. 297)

"The 'intended' curriculum can only include our best guesses about what will both interest students and lead all toward development of mathematical power. At the same time, the 'actual' curriculum depends on teacher choice, and the 'achieved' curriculum depends on each student's interest and prior knowledge." (p. 300)

"Nussbaum and Novick suggest a three-part instructional sequence designed to encourage students to make the desired conceptual changes. They propose the use of an exposing event, which encourages students to use and explore their own conceptions in an effort to understand the event. This is followed by a discrepant event, which serves as an anomaly and produces cognitive conflict. It is hoped that this will lead the students to a state of dissatisfaction with current conceptions. A period of resolution follows, in which the alternative conceptions are made plausible and intelligible to students, and in which students are encouraged to make the desired conceptual shift." (p. 298)

"Classrooms should be places where interesting problems are explored using important mathematical ideas…This vision sees students studying much of the same mathematics currently taught, but with quite a different emphasis." (p. 302)

Romberg, T. (1994). Classroom instruction that fosters mathematical thinking and problem solving: Connections between theory and practice. In A. Schoenfeld & A. Sloane (Eds.), Mathematical Thinking and Problem Solving (pp. 287-304). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.

Reflections on Doing and Teaching Mathematics

This chapter in the "Mathematical Thinking and Problem Solving" compilation tackles the epistemological issues questions of "what does it mean to know mathematics" and "what does it mean to do mathematics." There is a questioning of mathematical certainty and a response that mathematics, like other sciences, is actually a theory in progress; new discoveries upset old theories and are reconstructed to match our "reality."

As a result, there is a suggestion that it is foolish and socially unjust to let mathematical authority reside in the hands of any teacher. Instead, classrooms should resemble microcosms of the larger mathematical community, one in which students are doing mathematics and are the arbiters of mathematical correctness.

QUOTES
"Our classrooms are the primary source of mathematical experiences (as they perceive them) for our students, the experiential base from which they abstract their sense of what mathematics is all about." (p. 53)

"When mathematics is taught as received knowledge rather than as something that (a) should fit together meaningfully, and (b) should be shared, students neither try to use it for sense-making nor develop a means of communicating with it." (p. 57)

"The issue is the character of mathematical knowing: whether mathematicians can always be absolutely confident of the truth of certain complex mathematical results, or whether, in some cases, what is accepted as mathematical truth is in fact the best collective judgement of the community of mathematicians, which may turn out to be in error." (p. 59)

"The activities in our mathematics classrooms can and must reflect and foster the understandings that we want students to develop with and about mathematics." (p. 60)

"The means are social, for the approach is grounded in the assumption that people develop their values and beliefs largely as a result of social interactions." (p. 61)

"They have little idea, much less confidence, that they can serve as arbiters of mathematical correctness, either individually or collectively. Indeed, for most students, arguments (or proposed solutions) are merely proposed by themselves. Those arguments are then judged by experts, who determine their correctness. Authority and the means of implementing it are external to the students." (p. 62)

"I hope to make it plain to the students that the mathematics speaks through ll who have learned to employ it properly, and not just through the authority figure in front of the classroom. More explicitly, a goal of instruction is that the class becomes a community of mathematical judgement which, to the best of its ability, employs appropriate mathematical standards to jedge the claims made before it." (p. 62)

"The implicit but widespread presumption in the mathematical community is that an extensive background is required before one can do mathematics." (p. 65)

Schoenfeld, A. (1994). Reflections on doing and teaching mathematics. In A. Schoenfeld & A. Sloane (Eds.), Mathematical Thinking and Problem Solving (pp. 53-70). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.

Fire Up the Learner Within

Pant, Atul. (2010). Fire Up the Learner Within. London: Timeless Lifeskills Limited.

Summary/Analysis:

I chose this book because of the subtitle, The Art of Self-Directed Learning. In my opinion this book is simply a short how to book for anyone, any age that wants to be a lifelong learner. In the introduction, I was drawn to the idea of a framework for self-directed learning: learning, knowing, understanding, and performing. The book is set up to address supposed strategies or examples of how a person can employ the framework as stated. The book clearly defines what it will take to be a self-directed, lifelong learner in the 21st century. Each chapter focus is one of the elements of a self-directed learner: to learn, to know, to understand, and to perform.

The author of this book cites many practitioners who in one form or another addresses self-directed learning such as Carol Dweck, Malcolm Gladwell, Ellen Langer, Daniel Goleman, Chris Watkins, George Siemens, Howard Gardner, Peter Senge, Daniel Pink, Mihaly Csikszentmihalyi and many more. I found that this author cited the works of these individuals connecting their works to the concept of self-directed learning. He cites their work to support his ideas and claims about his framework. Citing these other authors was helpful because each citation led me in a direction to pursue further studies and works. I’m not exactly sure if the author completely gave me strategies for lifelong learning, but I was able to pursue examples of the works of others.

Quote:

“To continually expand your personal mastery of a discipline or life pursuit, the first ingredient is a vision. A vision is not a goal it is derived from sense of purpose, an individual’s sense of why the individual lives. Vision must have an underlying sense of purpose. Conversely, purpose without vision has no sense of appropriate scale. Vision gives energy, enthusiasm and ability to persevere even in the face of frustrations and setbacks. Vision pulls you towards itself.”(p. 98)

Comment:

This quote struck me because I feel in order for someone to truly be able to self-assess, they have to know where they were going. A person who can look into himself or herself as a learner is aware of their ignorance and knows where they need and want to grow. This is what I want students to be able to think about and try to envision for themselves. Knowing that people need a vision, lets me pursue an idea of having students set short term and long-term goals periodically throughout the school year.

Quote:

“Just as metacognition is thinking about your thinking, metacognition is being aware, through reflection, about the process of learning as you learn something. In other words, while you are learning something you reflect on your learning process and draw out general principles and explicit understanding of how you learn best. You then apply this knowledge when you next learn something new and thus keep improving your learning process.” (p.47)

Comment:

This quote pushes me think about how I will improve how students assess themselves. I am drawn to the idea of students be able to reflect on the process of their learning. I have always felt that teachers and students focus too much on the end products students create when I feel the real learning that is taking place is during the process of a project or lesson. It is in the discussion, the trial and errors, the reading to gather information, the steps one takes to solve a problem that teachers tend to miss. I want students to focus and hone in on how they learn best. I want to groom the process, not just the product.

Checking for Understanding

Fisher, Douglas & Frey, Nancy. (2007). Checking for Understanding. Formative

Assessment Techniques for Your Classroom. Alexandria: ASCD publications.

Summary/Analysis:

I found this book to be a good resource for helping me understand and define what I mean by self-assessment. In this book, there were many examples of how a teacher can check for understanding, not in a summative way, but in a formative manner. "Checking for understanding," according to Fisher and Frey “is not the final exam or the state achievement tests…. Checking for understanding is a systematic approach to formative assessment.”(p.3). Formative assessments are ongoing assessments that improve a teacher’s instructional practice and one that gives constant feedback to students in the process of their learning. Through thorough observations, teachers are informally assessing student progress minute to minute. That is to say that the teacher is really paying attention which leads me to my action research in which listening to students and their own assessment of their learning will develop self-directed learners. The set of tools for formative assessments given in this resource will help a teacher get to really know their students and will help guide instruction. If students know that they are being heard, then students will develop into self-regulated learners.

Quotes:

“Close observations, deep knowledge of developmental processes, and content expertise had yielded a critical path analysis that anticipated the permutations a learner might take in learning…Checking for understanding should do the following:

  • Align with enduring understandings (Wiggins & Mc Tighe, 1998)
  • Allow for differentiation (Tomlinson, 1999)
  • Focus on gap analysis (Bennett et al., 2004)
  • Lead to precise teaching (Fullan, et al., 2006)” (p.12)

“Oral language development is not simply teaching children to speak. Oral language development must focus on student’s ability to communicate more effectively. Oral language involves thinking, knowledge, and skills that develop across the life span.”(p17)

Comment:

When I think of self-assessment, I think of how a student looks at their own learning, their own work. The student evaluates their own progress, sets personal learning goals, and strives to either improve or challenge himself or herself in what they are learning. . I think focusing on formative type of assessments will help students reflect on their own practices and understandings, and will in turn guide them to be life-long learners.

There were many quotes that struck me and drew me in to read further. The first quote above has made me really hone in on what I specifically want to do as a teacher and how to really listen to students. As the educator, I must create lessons that teach for essential understandings, that are differentiated, that look at closing achievement gaps between groups, and that help me personalize instruction.

Understanding that oral language is an important element in checking for understanding will help me create a culture of dialogue in my classroom. What I saw in the classrooms that I peer coached in was the “initiate-respond-evaluate model’ which is basically when the teacher asks a question, students answer the question, and then the teacher evaluates the response.”(p.22). This type of questioning is apparently typical in most classrooms. The teacher is the central figure in the learning environment. I want to build a classroom of self-directed learners and if this is the typical model, then this model will not work. In the chapter on checking for understanding using oral language, I found several ideas that will help create a culture of dialogue. One example was called “Accountable Talk.” “Accountable Talk is a framework for teaching students about discourse in order to enrich interaction.”(p.23) I like the guidelines of: staying on topic, using information that is true and appropriate, and thinking deeply about what the other person has to say. I have posted on my whiteboard at school ways to engage in scholarly conversations, but I want to add to those posted dialogue stems. This may push student conversations forward. I think I want to add another indicator that includes evaluative/reflective comments or phrases such as: “I want to further pursue this because…. I want to get clarification because I don’t understand…..I feel I know this, and I want to get back to you with evidence to support….”are a few examples.

"A Social Cognitive View of Self-Regulated Academic Learning"

Zimmerman, Barry J. (1989). A Social Cognitive View of Self-Regulated Academic

Learning. Journal of Educational Psychology, Vol. 81, No. 3, 329-339.

Summary/Analysis:

This article is of particular interest to me. This research review focuses on the social cognitive belief of self-regulated learning. According to the social cognitive theorists, self-regulated learning involves three functions: personal (self), behavioral, and environmental. All three function in reciprocality. For example, the self can affect the environment and vice versa. The example given is “assumed to be determined not only by personal (self) perceptions of efficacy but also by such environmental stimuli as encouragement from a teacher and by enactive outcome (i.e. obtaining the correct answer to previous problems.)”(p.330). Zimmerman goes on to discuss the importance of self-efficacy, the sub processes of self-regulation, and the determinants of self-regulated learning.

Social cognitive theorists see self-efficacy as a key variable affecting self-regulated learning. Students with high self-efficacy showed better learning strategies and self-monitoring of their learning. Self-efficacy can in turn affect how one chooses their learning environments. With this understanding, it is important to help children with their perceptions of themselves. Modeling how we deal with problems or work in class is just as important as the project itself. Teachers need to teach students how to cope with difficulties and challenges, so that their ability to self-regulate their learning doesn’t become impeded by how they view themselves as learners.

I felt the sub processes in self-regulation was of importance because it involves self-observation, self-judgment, and self-reaction (Bandura, 1986). As I read this section of the article it made me think about how I can incorporate time for students to observe themselves. Could I use a video recorder in the classroom for projects that students can use to view themselves with their projects? Maybe in my project design I can set aside time during the process of a project to have students self-observe, self-judge, and self-react to their work. Wonder if this process would encourage students to do this naturally when given projects in the future?

I found the section on metacognitive decision-making processes of particular interest. The self-instruction example by Meichenbaum and Goodman tells of a ninth grade boy in band who could not play a certain sound very well. The boy planned to use a mnemonic word to help him remember the musical staff. The boy then adjusted his environment by positioning himself better to see the notes to facilitate recall. This example shows how a student can plan and control their “use of personal, behavioral, and environmental strategies” to learn. This is what we want for students to learn how to self-regulate their learning.

In the article, Zimmerman also refers to long-term goal setting as a determinant of self-regulated learning. This is of particular interest to me as well because goal setting is important for students because it puts the students in the driver seat for what they are learning. I feel when students set long term and short term goals they become intrinsically motivated to learn and there tends to be a stronger engagement in their own learning. Goal setting is a life skill.

In conclusion, the social cognitive approach to self-regulated learning has three important points to consider: how one views themselves as learner, how one interacts with their environment, and how one controls his/her behavior when learning new and old concepts. These ideas are important to keep in mind when trying to create an environment of self-directed learners.

Quotes:

“The effectiveness of each of the 14 self-regulated learning strategies in Table 1 can be explained on the basis of the proposed triadic model. The purpose of each strategy is to improve students’ self-regulation of their (a) personal functioning, (b) academic behavioral performance, and (c) learning environment. For example, the strategies of organizing and transforming, rehearsing, and memorizing, and goal setting and planning focused on optimizing personal regulation. Strategies such as self-evaluation and self-consequences were designed to enhance behavioral functioning. The strategies of environmental structuring, seeking information, reviewing, and seeking assistance were intended to optimize the students’ immediate learning environment.” (p.337)

“There is a rather extensive body of evidence that training students to self-record can produce a variety of positive reactivity effects during student learning and performance.”(p. 334)

“Self-observation refers to students’ responses that involve systematically monitoring their own performance. Self observation is influenced by such personal processes as self-efficacy, goal setting, and metacognitive planning, as well as behavioral influences.”(p. 333)

Comments:

Much of the article gave me information that I already do in my class, but it was affirming to note that there is a body of research to support my ideas of student learning. I have tried having students keep track of test and quiz scores in their binders, but I think having them record the score and then set a goal for themselves or possibly reflect on their learning may be helpful and may push students toward self-directed learning. Self-observation struck me as well because as teachers I don’t think we give students the opportunity to self-observe. I think this would be great technique to employ in the classroom to help students see how they are progressing or to see how they are doing visually. Like I said above, maybe set up opportunities for students to record themselves practicing performances or speeches or even reading may push them to improve their performance.