Sunday, November 3, 2013

Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities

Gersten, R., & Chard, D. (1999). Number Sense Rethinking Arithmetic Instruction for Students with Mathematical Disabilities. The Journal of special education33(1), 18-28.

This article draws analogies between phonological awareness and number sense. Although it is written for a specific learning disabilities audience, the information within is useful for anyone who wants to learn more about how number sense is developed. The authors draw analogies between earlier research on ways to remediate mathematical disabilities and earlier research on reading disabilities. Their goal here is to provide a brief overview of phonological awareness concepts and number sense before introducing the concept of number sense, rather than to attempt to provide a comprehensive review of either topic.

Number sense is difficult to define but easy to recognize. Students with good number sense can move seamlessly between the real world of quantities and the mathematical world of numbers and numerical expressions. They can invent their own procedures for conducting numerical operations. They can represent the same number in multiple ways depending on the context and purpose of this representation. They can recognize benchmark numbers and number patterns: especially ones that derive from the deep structure of the number system. They have a good sense of numerical magnitude and can recognize gross numerical errors that is, errors that are off by an order of magnitude. Finally, they can think or talk in a sensible way about the general properties of a numerical problem or expression-- without doing any precise computation. 

It is also likely that some students who are drilled on number facts and then taught various algorithms for computations may never develop much number sense, just as some special education students, despite some phonics instruction and work on repeated readings/fluency and accuracy, fail to develop good phonemic awareness or any sense of the purpose or pleasure of reading.

Saturday, October 19, 2013

The Trouble With Rubrics

Kohn, A. (2006). The trouble with rubricsEnglish Journal95(4), 12-15.

In this article, Kohn analyses rubrics in regard to the assessment of writing and finds them problematic and insufficient in terms of assessing student work. By comparing them to letter grades or scores he highlights the way that rubrics are used to measure student achievement and/or provide extrinsic motivation- rather than provide feedback that helps to improve student work and engagement.

Kohn rejects the idea that rubrics should be adopted because they make assessment quicker and easier for teachers. The fact that it is easier to standardize writing conventions mean that rubrics may often be over-reliant on this one aspect of writing, rather than others. Other consequences of the use of rubrics are, according to Kohn, vacuous writing, lack of confidence and unwillingness to take risks.


“research shows three reliable effects when students are graded:  They tend to think less deeply, avoid taking risks, and lose interest in the learning itself.[2] The ultimate goal of authentic assessment must be the elimination of grades. But rubrics actually help to legitimategrades by offering a new way to derive them.  They do nothing to address the terrible reality of students who have been led to focus on getting A’s rather than on making sense of ideas.”

"Consistent and uniform standards are admirable, and maybe even workable, when we’re talking about, say, the manufacture of DVD players.  The process of trying to gauge children’s understanding of ideas is a very different matter, however. It necessarily entails the exercise of human judgment, which is an imprecise, subjective affair.   Rubrics are, above all, a tool to promote standardization, to turn teachers into grading machines or at least allow them to pretend that what they’re doing is exact and objective."

"But I worry more about the success of rubrics than their failure.  Just as it’s possible to raise standardized test scores as long as you’re willing to gut the curriculum and turn the school into a test-preparation factory, so it’s possible to get a bunch of people to agree on what rating to give an assignment as long as they’re willing to accept and apply someone else’s narrow criteria for what merits that rating." 

"A B+ at the top of a paper tells a student very little about its quality, whereas a rubric provides more detailed information based on multiple criteria.  Therefore, a rubric is a superior assessment.
The fatal flaw in this logic is revealed by a line of research in educational psychology showing that students whose attention is relentlessly focused on how well they’re doing often become less engaged with what they're doing."
"Studies have shown that too much attention to the quality of one’s performance is associated with more superficial thinking, less interest in whatever one is doing, less perseverance in the face of failure, and a tendency to attribute the outcome to innate ability and other factors thought to be beyond one’s control.[7]  To that extent, more detailed and frequent evaluations of a student’s accomplishments may be downright counterproductive."

"What’s our reason for trying to evaluate the quality of students’ efforts?  It matters whether the objective is to (1) rank kids against one another, (2) provide an extrinsic inducement for them to try harder, or (3) offer feedback that will help them become more adept at, and excited about, what they’re doing."

"Neither we nor our assessment strategies can be simultaneously devoted to helping all students improve and to sorting them into winners and losers.  That’s why we have to do more than reconsider rubrics."

This article is a damning critique of those rubrics that are as Kohn describes. While these rubrics may make a rating clearer than just a letter or number grade, they show children where they are on a scale that is problematic in its composition and may well have the same detrimental effect that simple grades have. 

However, Kohn's forceful critique of rubrics seems to be limited to a narrow definition that does not fit with the different ways that I have seen rubrics used. Rubrics are not always about sorting students but can be useful in terms of making it plain to students what a teacher is looking for.

Kohn's article appeals to me because ranking kids seems to be the opposite of what a teacher should do. Assessment of children into grades or numbers or categories is time consuming and what are you left with? At best you have a list from which you can formulate next steps. At worst, you have learners who spend more time comparing themselves to others, bruised egos, fixed mindsets and disengagement. Surely it is better to assess children based on what they are doing well and what they need to improve on?

However, I do think that it is good for any learner to have a clear idea about what makes a great piece of work. A rubric can help draw this out. It should be a tool for the student and the teacher in formulating next steps - rather than measuring.

Tuesday, October 15, 2013

Supporting Self-Directed Learners: Five Forms of Feedback

Costa, Arthur L., & Garmston, Robert, J. (2013). Supporting Self-Directed Learners: Five Forms of Feedback. ASCD Express, 8 (18).


This article describes five forms of feedback, ranked in order of effectiveness for developing “student’s capacity for self-directedness:”

1. Reflective questioning.
2. Nonjudgmental data.
3. Inferences, causality, and Interpretations.
4. Personal opinions and preferences.
5. Evaluations and judgments.  

The authors define each form, offer examples, and explain how it may promote or discourage self-directed learning.   The fifth section, “Evaluations and judgments,” is twice as long as any other; here,  with reference to relevant literature, the authors discuss the possible effects of praise and rewards on learning.  The authors conclude that the first two forms of feedback support self-directed learning while the remaining three work against this goal.  Apart from the examples of each type of feedback, the article provides no quantitative or qualitative data; it is a series of reasonable hypotheses around language and cognition, as opposed to a full research study.  In the final section, “Feedback for Learning,” the authors explain the importance of self-directed learning for nurturing creative, resilient, and successful children.


“Posing mediating questions has the highest potential for developing self-directedness, as the intent is to alert the students to the data that will serve to provide self-feedback, process that feedback, construct meaning from it, and set goals to self-modify as needed to achieve desired results.”

“Evaluative feedback makes the smallest contribution to learning and behavior change. When the teacher makes value-laden comments, this sends a signal that she is the final arbitrator of what is good or bad. The teacher may think that making judgments—either positive or negative—is helpful or reinforcing for students, but the opposite is true. Such comments shift the focus from feedback to evaluation.”

“Our wish is for creative students who are eager to learn. Having this disposition means always striving for improvement, always growing, always learning, always modifying. Experiencing problems, situations, tensions, conflicts, and circumstances provides valuable opportunities to gather feedback and to learn.”

U.S. Elementary and Secondary Schools: Equalizing Opportunity or Replicating the Status Quo?

Rouse, C. E., & Barrow, L. (2006). US Elementary and secondary schools: equalizing opportunity or replicating the status quo?. The Future of Children, 16(2), 99-123.

This article looks at the correlation between socioeconomic status and educational success of students. It takes a few factors into account, but focuses on the the nature versus nurture dilemma. The article touches on the difficulties in conducting research with human, specifically relating genetics to certain behaviors. The researchers found ways to conduct ethical experiments by observing adopted children placed  families that were not genetically related. It concludes by discussing different ideas that may help equalize opportunities in students with differing socioeconomic statuses.


Researchers have used other strategies to estimate the extent to which family income determines children's educational achievement. Again, because they cannot assume that family income is unrelated to other factors (such as inherited ability) that determine both children's socioeconomic status and their educational attainment, they must look for changes in family income that are unrelated to family characteristics such as whether the parents are highly educated or have high genetic “ability.” (Rouse and Barrow)

The Influence of Teacher Background on the Inclusion of Multicultural Education: A Case Study of Two Contrasts

Smith, R. W. (2000). The influence of teacher background on the inclusion of multicultural education: A case study of two contrasts. The Urban Review, 32(2), 155-176.

Summary: The article "The Influence of Teacher Background on the Inclusion of Multicultural Education: A Case Study of Two Contrasts" focuses on effective preparation for teachers in multicultural classrooms. It is critical of what is not happening to effectively prepare teachers in their teaching programs. It splits the essential needs of teacher into 3 important elements ultimately sating that in order to be successful teachers must take into account their background because it plays a large role in the interpretation of classroom situations, and behavior. The first background area is a combination of race, gender and social class membership. The second being prior experience with diversity and the third is support for ideologies of individualism. These factors are what the author finds to be most important through her study of trying to effectively teach in classrooms that are multicultural.

Quote: "In addition to inexperience with culturally diverse people, members of the dominant cultural groups often view the structure of society from a culturally privileged perspective (Boyle-Baise, 1995). Consequently, preservice teachers often support ideologies of individualism opposing structural explanations of, for example, chronic child poverty (Davis, 1995)."

Comment: This quote struck me because it made me think of my experiences and how it plays a role as to who I am as a teacher. I grew up a latino lower middle class student with family on both sides of the spectrum. While I come from parents who were very poor, I never had to deal with the issues they struggled with daily. That being said, I wonder how things might be different for me as an educator if that were the case.

Creative Community Organizing: A Guide For Rabble-Rousers, Activists, and Quiet Lovers of Justice

Kahn, S. (2010). Creative community organizing: A guide for rabble-rousers, activists, and quiet lovers of justice. Berrett-Koehler Store.

Summary: “Creative Community Organizing” is a memoir from former founder of the non-profit Grassroot Leadership, Si Kahn. Aside from being a working musician, Kahn’s experience with community organizing is rooted in the Civil Rights movement, where he first landed in Mississippi during the summer of 1964 to organize black citizens to register to vote. After that historic summer, Kahn’s work covered other historical social movements, working alongside various labor unions in the 1970’s and 80’s to protesting against the existence of for-profit prisons in the last two decades. His book serves as both a memoir and a how to, as Kahn uses his own organizing experience to provide detailed and accessible guidance on how to affect change in your own community. However, his book and ideas are not merely meant for political activist. Kahn states in his introduction that what separates his work and the campaigns he had led was their creativity. Through the book, he is providing innovative structures in which people can collect, meet, and critically think about their community. Those lessons could not only be valuable for any teacher trying to daily mold the hearts and minds of young students, but also for any school looking to actively and positively engage it’s own community. I have not read the entire book, but simply by the introduction and first two chapters, Kahn lives up to that expectation, blending his own rich narrative with practical advice in the organizer’s tool belt found at the end of every chapter.

Quote: “One of the greatest skills an organizer can have is the ability to frame and ask questions in way that make people not only want to answer them, but also think deeply, and in unexpected ways, about what the answers might be… Creativity community organizing can transform us into visionaries, prod us to learn new skills, and encourage us take risks for our and our children’s future.”

Monday, October 14, 2013

Teacher Characteristics and Gains in Student Achievement

Hanushek, Eric. "Teacher characteristics and gains in student achievement: Estimation using micro data." The American Economic Review 61.2 (1971): 280-288.

The article “Teacher Characteristics and Gains in Student Achievement” was set out to understand exactly what background experience of teachers has to do with how well or poorly students achieve greatness inside the classroom. By using micro-data, researchers placed variables in the place of students and teachers to conduct studies on classroom behavior, achievement, and advancement. Researchers wanted to see if there was a correlation between what the students were learning and how much education the teachers had.
The studies did not prove to be as true as the researchers thought they’d be. The original hypothesis was that teachers with education reaching higher than a bachelor’s had more qualifications to help students succeed in the classroom than teachers with only bachelor’s degrees. The testing was completed over several years in several diverse communities. Researchers studied Title 1 schools, inner city schools, private schools, and predominantly white schools. All of the research came out the same: student achievement had more to do with the teacher’s character than with the teacher’s educational background or experience.
It was also mentioned that teachers with more years experience tried less hard to have the students succeed. Researchers mentioned that this was not on purpose, however, as time passed, teachers were less likely to learn something new and more likely to stick to what they had been doing in previous years.

“There is a suggestion that one can measure other dimensions of teacher and school quality. These include attitudes of teachers and administrators, verbal facility (and perhaps general ability) of teachers, quality of physical plant, quality of teacher education, background of teachers, and more” (Eric Hanushek, 2002).

“The analysis indicates that teaching experience and graduate education do not contribute to the gains of in student achievement scores” (Eric Hanushek, 2002).

In reading this article, I found it fascinating that it spoke so heavily against hiring teachers simply for their educational background. It’s interesting, also, that I work for an organization that focuses less on the educational background of teachers, and more on their ability to connect with students, prepare and produce meaningful projects, and truly understand progressive education. I appreciated that this article looked at all sides of education - from different classrooms, to different teachers, even to different equations (with multiple variables) to try and centralize the hypotheses centered around teacher education vs. teacher background.
I also appreciated how the article specifically states that this should only be taken as a primary (beginning stages) research article. They are admitting that this study only reaches a small educational circle, and that there are plans to expand the study and see other findings. I found it interesting that throughout the article the idea of education can help both the teacher and the students if all are willing to utilize those strengths. It isn’t enough to simply attain a master’s degree if the teacher is not going to use what he or she learned in the program to apply it to his or her students’ learning.

Sunday, October 13, 2013

In Parent Choice Suit, U.S. Department of Justice on Wrong Side of History

Fuller, H. and Chavous, K. (2013). In Parent Choice Suit, U.S. Department of Justice on Wrong Side of History.

This article was of particular interest, after watching and reading discussions of Howard Fuller's with the High Tech schools regarding equity and understanding of race within education. Fuller and Chavous make an interesting argument that quality education trumps the notion of impacting desegregation in schools. I too agree, that should families and students qualify for scholastic scholarships that could potentially advance their education, the DOJ should not interfere with their desire to do so. How is this any different than students who leave other public schools around the US, to go to private or charter schools that best meet their needs- even if they do not go via scholarship?

From Judge Robert Carver, the articles quotes, "The immediate and urgent need of the black urban poor is the attainment, in real life terms and in settings of virtually total black-­‐white school separation, at least of some of the benefits and protection of the constitutional guarantee of equal educational opportunity that Brown requires."

Sunday, September 29, 2013

Perfectionism limits our chances to risk, learn, grow, and succeed

Moussavi-Bock, D. (2013). Perfectionism limits our chances to risk, learn, grow, and succeed. Journal Of Staff Development, 34(4), 62-63.

This article is one that I personally need to read because sometimes I am a perfectionist and I stop myself from doing things if I know they won't be perfect.  This has caused me to miss some great opportunities. The author writes about perfectionism, high expectations, anxiety, fear of failure, opportunity and change.


I confess to a degree of perfectionism that used to prevent me from having much-needed conversations for fear of saying the wrong thing or saying it wrong. These days, I just say it and let the chips fall where they may. I encourage you to do the same. It will probably go better than you imagined. And if there are chips, well, keep your shoes on, and no one will get hurt. Susan Scott

Saturday, September 28, 2013

A study of an after-school art programme and critical thinking

Lampert, N. (2011). A study of an after-school art programme and critical thinking. International Journal Of Education Through Art, 7(1), 55-67.

This article is very interesting to me, because I have been trying to introduce Project Based Learning in Tijuana, Mexico, and it has been hard for me explaining that a Project is not just a craft. Teachers seem to believe that they can design a project based on what they think students must learn and mix a craft and an exhibition in there, but sometimes the projects designed are not meaningful to the students, and they are not motivated. As I read this article I was able to think of strategies for teachers to link art to critical thinking, thus making the projects meaningful and important.
The article describes a study done in a community arts programme designed to enhance critical thinking skills in children by engaging them in enquiry-based art lessons. Ten urban elementary children participated in the 12 week study. Eight undergraduate students enrolled to be part of the programme. All of them had worked with children before and all had interest in serving their community. The children were assessed in their critical thinking skills two times, at the beginning and end of the study. The results of the test showed significant increase in the children´s average critical thinking from the pre-test to the post-tests.
I found the definition of enquiry-based or open-ended lessons very useful. The author says they are "classroom activities that require students to solve problems and answer questions that have more than one possible resolution" (p. 56). I think that if teachers who are new to project based learning focus on this kind of classes, they will be able to reach more useful and meaningful results.
The programme lasted twelve weeks, two afternoons a week, for one and a half hour sessions. It had three components: open ended, enquiry-based artmaking lessons; the children had time to talk about artwork with the group; the atmosphere in the classroom was friendly and welcoming (p. 57). These components seem to me like a recipe for success. If any class was planned this way, there is a guarantee that it would be interesting, motivating for students and reflective.
The undergraduates showed the children a variety of cultural examples when introducing lessons, but they did not suggested that they imitate the examples. They encouraged the children to develop their own personal visual expressions. I have learned at HTH that having models and examples prior to working is very useful because it gives students a guide and it motivates them to focus on their own work, without wasting time finding out what is expected of them.
At the beginning of each lesson, the undergraduates would show PowerPoint presentations with artwork from several artists and "the children interpreted what they saw and explained it to the group, as a form of critical enquiry. Also, for most lessons the children completed worksheets prior to artmaking. For these worksheets students sketched or listed ideas for their art prior to creating it" (p. 57) I believe that brainstorming before starting is key to creating true work. When it comes from reflection, it shows the person´s true identity and it becomes important, meaningful and intrinsically motivating.
The author gives a synopsis of the first two lesson plans, their description and examples of the children’s works, general thoughts about the experience, and summaries of the undergraduates’ written reflections of what they thought, observed and heard in the community art classroom (p. 58-62). The synopsis was very detailed and included pictures and dialogues from the classes. This was very helpful for me to understand how the mood and feel of the lessons was.
It also included an explanation on how the discussion of the art pieces was conducted. The author mentions Barrett´s (1997) three critical enquiry questions about art: What do I see? What is the artwork about? How do I know? I find these questions very appropriate to use with people of any age, from kindergarteners to adults.
“…for the group discussions about the children’s artwork, a child would get in front of the group with his or her work, and often we would only need to ask, ‘What do you see?’ and the children were off and running – eager to have a chance to talk about what they saw in the artwork and what it meant. Sometimes the young students talked over one another, and sometimes they joked rather than give worthwhile interpretations of the piece, but for the most part, we had enlightening discussions with the group.” (p. 60)
“Our understanding of the boy’s art deepened through the group’s critical analysis of it. This was true with most of the children’s boxes.” (p.60)
“I hoped that the mixed signals they got would impress upon the children that things are not always as they appear, and that people often see the same thing in different ways. In other words, I hoped that we were opening the children’s minds to think critically.” (p.60)
“Through the course of the programme, we saw a steady increase in the children’s ability to communicate their ideas with words and images. And as the children learned more about themselves, we learned more about the children.” (p. 63)
“…by the end of the programme the children were far more comfortable with problem solving and analysis when it came to choosing and discussing images that were representations of their identities.” (p. 64)
“…amongst the teaching of manual skills, formal elements, and the various other necessary components of most US public school elementary art curricula, units that
are interlaced with enquiry may sharpen students’ critical thinking skills…” (p.64)
This article was both inspiring and helpful for me.   I had not been able to express to teachers what a good project, a good class or even a good discussion should look like, and the article gave me a lot of ideas on how to introduce critical thinking and a reflective environment in the classroom.  I personally have been very interested in introducing art in schools, but had not found a way to do it in a meaningful way.  The ideas given by the author are very detailed. 
The only thing I would say is that I was left wondering a bit about the testing and the results.  Te author mentions that they used the Test of Critical Thinking (Bracken et al. 2003a), which is free and available to the public. I would have liked to see more of the results of the children both in the pre-test and the post-test since only one graphic was presented to explain their improvement on critical thinking.  She does mention that future research might be necessary and it would replicate the study with a control group. 
Cited sources of interest:
Barrett, T. (1997), Talking about Student Art, Worcester, MA: Davis Publications,
Bracken, B., Bai, W., Fithian, E., Lamprect, M. S., Little, C. and Quek, C. (2003a), Test of Critical Thinking, Williamsburg, VA: The Center for Gifted Education, College of  William and Mary.
Bracken, B., Bai, W., Fithian, E., Lamprect, M. S., Little, C. and Quek, C. (2003b), Test of Critical Thinking: Examiner’s Manual, Williamsburg, VA: The Center for Gifted Education, College of William and Mary.
Danko-McGhee, K. and Slutsky, R. (2007), ‘Floating Experiences: Empowering Early Childhood Educators to Encourage Critical Thinking in Young Children Though the Visual Arts’, Art Education, 60: 2, pp. 13–16.
Lampert, N. (2006a), ‘Enhancing Critical Thinking with Aesthetic, Critical, and Creative Inquiry’, Art Education, 59: 5, pp. 46–50.
Walker, S. (2001), Teaching Meaning in Artmaking, Worcester, MA: Davis Publications.

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Thursday, September 26, 2013

From Teacher to Student: The value of teacher education for experienced teachers.

Kunzman, Robert. “From Teacher to Student: The value of teacher education for experienced teachers.” Journal of Teacher Education, 54 (3), May/June 2003, 241-253.

Annotation: Teachers that have been in the classroom for quite a while tend to stop reflecting on practice and run off of instinct, past experiences, and the ease of being in a routine. In order to keep up with the ever progressing education field, teachers should find new ways to expand their background (professionally). If teachers had to go through another mini teacher education program after a few years in the field, education may begin to stop being stagnant. New ideas could be shared, and collaboration would be valued among educators.

Job Satisfaction among America's Teachers: Effects of Workplace Conditions, Background Characteristics, and Teacher Compensation. Statistical Analysis Report.

Perie, M., & Baker, D. P. (1997). Job Satisfaction among America's Teachers: Effects of Workplace Conditions, Background Characteristics, and Teacher Compensation. Statistical Analysis Report.

Annotation: America’s teachers have different idea of job satisfaction. The elements that go into this feeling are workplace characteristics, teacher background (personal & professional), and salary. Teachers also have perceptions of what the workplace norms, characteristics, and culture should look like. If this doesn’t necessarily match among faculty members, problems can arise and satisfaction in an educational setting can diminish.

Teacher Educators as Learners: How Supervisors Shape Their Pedagogies by Creating and Using Classroom Videos with Their Student Teachers

Danielowich, R. M., & McCarthy, M. J. (2013). Teacher Educators as Learners: How Supervisors Shape Their Pedagogies by Creating and Using Classroom Videos with Their Student Teachers. Action in Teacher Education, 35(3), 147-164.

Annotation: New teachers need to create a “professional” background in order to take some experience into the classroom. Most of this professional background is developed in a credential or teacher preparation program. Professors in these programs tend to give their own background ideas to these new teachers. One credential program decided that an essential part of gathering a professional background was through video. If teachers were able to see their actions in a classroom setting, it would help them develop a sense of who they were professionally a lot quicker.

Faculty Development as Community Building-An approach to professional development that supports Communities of Practice for Online Teaching

Eib, B., & Miller, P. (2006). Faculty Development as Community Building-An approach to professional development that supports Communities of Practice for Online Teaching. The International Review of Research in Open and Distance Learning, 7(2).

Annotation: Faculty building is an ongoing effort to connect and collaborate with counterparts in our school environment. If a faculty is not connected, the school culture is jeopardized. In order for any innovation or improvement to happen, it is vital that faculty members are on a relatively similar page. Although this piece of literature focuses on University culture, the same research can be applied to elementary, middle, and secondary schooling.

The Influence of Teacher Background on the Inclusion of Multicultural Education: A Case Study of Two Contrasts

Smith, R. W. (2000). The influence of teacher background on the inclusion of multicultural education: A case study of two contrasts. The Urban Review, 32(2), 155-176.

Annotation: Effective preparation for teachers in multicultural classrooms is not happening as effectively as it needs to in teaching programs. Backgrounds of teachers (professional) contributes to what is taught, interpretation of classroom situations, and behavior. Ultimately, personal background plays a dramatic role in teacher’s essential elements of practice. In a diverse classroom setting, is there a “type” of teacher that works better with students than others?

Wednesday, September 25, 2013

Thinking, Teaching, and Learning Science outside the Boxes

McComas, W. F. (2009). Thinking, Teaching, and Learning Science outside the Boxes. Science Teacher, 76(2), 24-28.


This article is looking at redefining the term "interdisciplinary" with relation to the sciences. It begins with the story of researcher Thomas Young, and all his accomplishments. He was referred to as "the last man to know everything" (24). He combined many different aspects of science to solve multiple problems, spanning many different disciplines of science. The article discuss the university approach to sciences, where each discipline of science is learned at separate times, and even have different buildings for each. The discussion then turns to how we can incorporate all aspect of science and offers different levels of blending to accomplish this. The levels represent the extent of blending the disciplines ranging from 0, or no blending, to 5, which requires students to look at a concept and think of all the disciplines relate to that topic, concept, or problem. However, it also discusses the difficulties in creating a true interdisciplinary classroom. Two of the bigger problems stem from the fact that many teachers with a science background are experts in only one of the scientific fields. In addition, since the teachers were never really exposed to this type of learning, how can they teach in this manner? The article address the difficulty in this type of teaching, but concludes in stating that sometimes brillant ideas or difficult to implement.

Relavent quotes/concepts:

"Phenix uses the concept of “ways of knowing” to help focus the definition. In his view, these ways of knowing include empirics (science), symbolics (mathematics), aesthetics (arts), ethics, synnoetics (literature), and synoptics (history). Therefore, it is more accurate to describe interdisciplinarity as the crossing between various ways of knowing or what some might call “schools of thought" (25).

"Rationales can also be found within the pedagogical 
realm. Students may benefit from seeing the world in 
a less-constrained fashion; thus, teaching effectiveness 
is increased when students are permitted to explore in 
ways that have personal meaning" (26).

"Science teachers typically start out as biologists, geologists, chemists, and physicists, and, with few exceptions, rarely gain content knowledge too far outside their initial science realm" (27).