It doesn't matter!

So the last research meeting with CK, JK and BF was very a compelling discussion - about what is hierarchical structures and are students really exhibiting a sense of hierarchical data or are they merely coding efficiently. Well for me the one line summary of this discussion is "It doesn't matter!"

I have felt since the very first few representations began trickling in from our pilot subjects - it doesn't matter whether they are row by column or not. It is the computer that makes the row by column fully normalized flat table be the "best" data organization for capturing all the information in the most flexible way. NH in one of earlier SERG meetings mentioned that he is really tired of the tyranny of the rectilinear data structures!

In a recent administration to a large group of students, of all the representations we received, only about 40% were flat tables. Yet with the exception of 1 student, everyone captured all the information they needed to construct a fully-normalized structure. The sheer variety of structures that were on display by the students were mind-boggling. After having thought about all the ways in which we can structure the data and what makes for an efficient organization, we continue to be surprised at how many different "exhaustive" organizations the students can create.

We went into this work with a hypothesis that students would have trouble creating structures for hierarchical data and the only really "correct" - as in exhaustive in terms of capturing the data and case-centric in terms of maintaining the correlation amongst various attributes of a single object - structures would be fully normalized, flat row by column tables. We have instead seen so many different structures that are both exhaustive and case-centric that as software designers, the path to me is very clear.

Our software needs to provide a way for users to enter and organize data in many different ways and make transparent to the user the isomorphism between the three-way nested table and the partitioned
plot space and the fully flat row by column table for example.

The three representations above all record all the information in the situation and they maintain correlation among the values of the different attributes for a single object (the case). Any of these representations allow us to answer multi-variable correlation questions like - Are westbound trucks faster than eastbound cars? In that sense, they are equivalent representations and the user should be able to record data in one of these representations but be able to use the data in any of these forms or other forms that they may create.

Now to make that happen in software...

The Eagle has landed! 4 times now...

PHEW! Lunar Lander landed in DP's class one Thursday. Then on a Wed a week or so later,  the eagle was on a marathon run - 3 classes in as many hours! Here is what their activity looked like at a glance.

There is so much more to say because you know for the first time, we have nearly a hundred thousand data points that are being cleaned and "dashboarded" by BF - the data magician. Watch this space for more...

Tool-Symbol, Attention-Perception

Finished two more chapters of Vygotsky's Mind in Society. It is not dense - in fact the introduction was far more dense than these actual chapters. the first two chapters are all about how the use and development of language affects the development of tool and symbol use in children as well as the development of attention and perception.

In thinking about why this should be at all relevant to the work that we are doing with data - here is what I come up with:

1. What language are the students using to organize their data?
2. If we can discern the "words" in their language will it help us to build tools that can aid their "expression"?
3. To tie back tightly to what Vygotsky says - how does the development of a "data sense" proceed in tandem with the development of a "data language"?

If we are to be a data processing environment akin to a word processor then it does seem important to know how the language works so that we can provide all the necessary tools to craft a well formatted and thought-out narrative in data.

The last thought to keep in mind as I read through more of the book is I guess where and how the does the "social" aspect fit into our conceptions of what we hope to build and learn? Is it simply that the collaborative data analysis space will contribute to learning or something more deep that arises from being in a classroom rather than by your self?

all for now...

References:
Vygotsky, L. S. (1978). Mind in society: the development of higher psychological processes. Cambridge, Mass: Harvard University Press. 

Two more data structures...

At long last, we are done "piloting" our materials for the interviews. I conducted two interviews yesterday at GHS - real deal. A sad commentary that pulling kids out of class for 30 mins means I get many more volunteers then an offer of lunch! (DP - the teachers says - so long as their brains are engaged in some hard thinking, he's fine with me pulling people out of class). In any case, two kind souls R and J agreed to come.

R was quick - and organized all the information in a sectioned fashion. Kind of hierarchical but not strictly organized in the nested table fashion that we are thinking of. He created a partitioning of the space by categorical variables that were "above" the vehicle in some sense and then proceeded to code the vehicle type and speed together for all vehicles. He then did a second pass through both segments and added the information about the distance from the preceding vehicle. He had some way to answer all questions but did not go so far as to set up a two way correlation for the last two questions. The flat data structure for him appeared to be more organized and "detailed"  - not that he had missing values but the information was "clearer" he said.

J favoured words over numbers. "I like to describe in words rather in numbers" - his own words. The recording took longer mainly because he was narrating the information and needed more time to write it all out. He initially made the mistake of not recording the vehicle type and recorded all the vehicles as cars. Since the rest of his information was complete, I hazard that this had more to do with our colloquial tendency to refer to any vehicle as a "car", than it had to do with considering an attribute unimportant. This meant that he was unable to answer two of the questions. He went back and fixed this information. Then, he was able to answer the questions that he had missed the first time around. The flat structure for J was more messy and insisted that his was easier to read. But did acknowledge that if you like numbers more then it was a better structure.

Spots that glow:

• Both had a case-centric view of data. They kept the attributes for a case together - even in J's narrative style.
• BF's fear that we are now going to get flat tabular structures is unfounded at least for this small sample
• Protocol was easier to administer this time - had reasonable success with "talk out aloud". So maybe the warmup problems help? Not sure...
• In any case, the task is definitely clear now.

Parents and Polish: Reflections on the DRK-12 PI Meeting

The two memorable revelations for me of the 2010 DR K-12 PI meeting were the exceptionally polished software products on display and the lack of discussion about parental responsibility for learning.

Speaking as a software developer, the quality of the software products was an awakening in that projects are no longer content to create materials that are not commercial production quality. This is a really heartening development because, after all, if our goal is to make the most difference to the most number of students ,then we must look beyond our conventional avenues of dissemination and distribution. As an aside—“publisher” should not be a dreaded word—why should the avenue of dissemination be treated like a condition to be tolerated rather than a partner to be embraced? The presence of the more than a couple of "research products" in the App Store is a good start. Perhaps CADRE can do well to establish a SIG that focuses on product development. Often, when we are presented with the product of a research project, as an emerging researcher you wonder what went into this product. Similarly, when a research project creates a software product, for other projects it is beneficial to be able to discuss issues of how to recruit programmers, graphic designers, and project managers on an NSF budget where you cannot match an industry salary. It was very apparent, at least in a couple of the projects, that the software was not the output of a technically savvy grad student. So, I'd love to see not only more such products emerge but also see a community develop that provides support to projects creating software products.

To move onto my second revelation, I want to begin by saying that at education conferences, I avoid sessions that focus on equity. Equity for me is a topic that should deal with teachers working in heterogeneous classrooms where the heterogeneity is a function of differences in learning styles of students rather than of differences in home environments and parental engagement. It is really strange to me that in this climate of strong calls for teacher accountability there is not an equivalent call for parental accountability. It is not a 10th grade math teacher's job to deal with the fact that a student in her class is failing in math because they cannot read the content—that may seem harsh but I am sorry, that's just not her job. Cathy Black, chancellor of schools in New York City, when touring schools that work said, "Where there’s a strong and effective principal, where parents are committed, you have great schools.”

Why is it OK for a parent to send a child to school with little or no preparation in terms of motivation to learn but not OK for that child's teacher to send that child back home with little or no learning? What’s true of Shanghai's schools, which just outshone American schools in international testing, is also true of the schools that turn out the best (top 2%) talent in Asian countries: families will go to great lengths to ensure that the children have everything they need for doing well in school, and students will put their lives on hold to do well in school. There are no discipline issues; students are in school for exactly one thing and that is to learn. This system of schooling does stifle creativity, and it does ignore those students who cannot keep up, but on the whole, the system raises the level of respect that schools command amongst students. In story after story from teachers, I have noticed that there is a direct correlation between parental involvement and student success.

Sure, it is the job of a school to teach, but then it is the job of parents to provide a safe and encouraging family that prepares the student to learn. Somewhere in all this rhetoric about success for all and differentiated instructions and constructivist learning, we are unfortunately in a state where we are almost afraid to ask parents to hold up their side of the social contract.

"s" not "z"...

Visual Scalability, SOLO, Children's Data Organisation

Yesterday, I talked to CK and J about our upcoming research work on Large N Data. The surprise find for me was a couple of papers from a set of folks originating in Australia about Children's Data Organisation. Note the "s" in the word Organisation - I have looked literally high and low for work in this area as support for our work on Students' Understanding of Data Organization. But I was apparently not speaking the same language - literally. In any case, once I found one paper - I found three others from the tun of the century all talking about children's statistical thinking - one epousing a framework to benchmark learning based on the Bigg's SOLO(Structure of Observed Learning Outcomes) framework, another talking about children's representation of data and the third describing a research protocol where students are asked to create a graphical representation for single variables. Briefly, scanned all three - we'd have to commit to the SOLO framework for this to be useful - CK disagrees with some of the premise of the framework.

Moving on, read the long-put aside  paper on Visual Scalability as a way of laying the groundwork for the work on Large N research. Written by Eick and Karr in 2000, it creates a structure to use as a basis for designing visualization tools to understand large data sets. They survey the software (data structures & algorithms), the hardware (screen resolutions, disk space, network speeds, CPU limits),  and the human factors(perception) that influence tool design then prevalent. They predict the trend on each of these and their increased or diminished influence on tool design int he future. Much of what they predict has already come to pass and systems already exist that incorporate most of their suggestions. However, it is a useful taxonomy to anchor our visualization innovations and a distinct point of view from the currently popular ones rooted in Bertin and Stolte (Tableau et al), addressing the issue of size of the data set.

To round off this round of reading, here is an inspirational and validating note written as a wrap-up for a gathering of folks talking about Massive Data Sets. This was the Massive Data Set Workshop organized by Commission on Applied and Theoretical Statistics in 1996!. Peter Huber makes the case for the "case".

Thats all for now - some interesting ideas on how to "see" large data sets as collections of smaller ones but thats for a whole other post.

Web App, Graphs and Logs

(This should probably be dated yesterday so consider the blog post for Jan 4th 2011)
Today was the first FC session after the holidays - the Three Musketeers all turned up. They played Mini Golf in the web app prototype - it held up beautifully - one hour - no crashes, or serious complaints. It felt very optimistic that this would work!

Some spots that glow:

•  This was the most unprompted use of the calculator that we have seen upto now - and we have the logs to prove it :-)! One kid insisted on using his handheld - said it was much faster!
• I am going to go ahead and claim some transfer of habits of mind. Today all of them asked for a graph before they asked for a table. In the past they have always had to be prompted to look at graphs. 
• They all played for the entire hour in the prototype in the limited screen real estate they had with non resizeable components, with pretty limited functionality, but no real obstacles. So successful first outing in the field.
• I think there is some benefit to this being so similar to Shuffleboard – so to satisfy YK – we have a way in which playing one will make it easier to play the other. This should make it easier for us to create a trajectory of games?

Dichotomous Views of Data

For some time now I have been toying with this idea in my head about an aspect of our thinking on data organization. Recently, there is one issue that recurs frequently - at the heart of which is the distinction between the unit of analysis and unit of observation. Here is my attempt to organize my thoughts and see if they fit in anywhere in our article.

Dichotomy of Data Organization

Expertise in dealing with data is scattered across many different professions - the statistician knows how to synthesize and summarize data, the computer scientist has known for many decades now how to structure and store data for faster search and retrieval, the graphic designer is learning how to communicate insights from this data, journalists are increasingly making data representations the thrust of how they present evidence. All these point to the emergence of a new profession or discipline - that of data science. For the purpose of this section, we stay away from the communication of data and concentrate on the analysis and organization.

As we struggle to identify the process by which students organize the data that they encounter in unstructured forms, we come across the same dichotomy characterized in many different ways:
* Analysis v/s Observation
* Record v/s Represent
* Collect v/s Store

Different concerns justify different organizations. We observe that students routinely create many different data organizations when asked to record data from a traffic protocol.

Snapshot of Road at 8am

Snapshot of Road at 4pm

 Specifically:

• About half organized data in fully normalized "flat" tables with repeated values for attributes - this is the structure that we had in our mind as the only possible way to comprehensively capture all data in such a way that would allow them later to answer questions about relations among attributes. This turned out not to be the case.
• A majority used an organizational method that kept the information about individual vehicles together in such a way that it is possible to determine, e.g., the correlation between distance and speed, employing an organizational method consistent with a hierarchical data model, in that they partitioned information spatially to reflect different case levels (date/time, lane direction, vehicle information). 

This motivates a new way to think about how users can record hierarchical data. Note that this is distinct from representing or analyzing hierarchical data. 

Motivation for New Ways to Collect Data
The question that motivates the data collection is often too vague to proactively create a fully normalized flat structure of the kind required by traditional computer programs. Instead, the nature of the situation about which data is being gathered may imply an organizational structure that is very different from the one needed for analysis to answer the motivating question.

We draw inspiration from the student representations to create prototypes for two new data structures:
Nested Tables and Partitioned Plot Spaces. Below are the two prototype data structures populated by the data from the above traffic snapshots.

Nested Table 

Partitioned Plot Space

Compare them to the more traditional "fully flat" table structure required by traditional computer programs.

Our next next task is to create seamless transitions between the two views - that are illuminating while being obvious. Data "munging" - or fitting it to the needs of the analysis is a task that while arduous offers many learning opportunities for delving into the structure of the data. We have to be careful to not lose this opportunity while creating the transitions for the student.

to be continued...

Who am I?

Here is a bio that I wrote for a  NSF fellowship that I recently got. It is a "capacity building fellowship for early career professionals"!

Vishakha Parvate knew at the age of six that she wanted to teach Math - not because she was good at it (though in a conventional sense she was and has been -  "good at Math") - but because she couldn't fathom why some of her most intelligent friends claimed they were no good at it. This basic conundrum of a perceived lack of Math expertise among smart, hard working folks is at the heart of her motivation for working in the area of Technology in Math classrooms. Disillusionment with the meaninglessness of all the symbol manipulation that consisted the bulk of her undergraduate major in mathematics, was mitigated by the exciting mathematical patterns that programming brought during graduate studies in Computer Science.  This dual educational background and a lifelong passion for changing the teaching and learning of Mathematics to be meaningful and exciting means that creating and researching dynamic mathematics technologies was the natural career path for her.  

Is this who I am - I guess so. Too long winded sez my better half but I shrug my shoulders and say this is who I am and can't be condensed any more. There was a bit at the end that I took out coz i wrote it only for the NSF folks about my current project ad so on.

Mind in Society: Introduction

Over this past weekend began reading Vygotsky. I have vague memories of him from my Intro to Qualitative Research course. But turns out I was confusing him with Lave and Wenger. In any case, KM - you are an awesome mentor - this is the second of the papers that you told me to read and the first was really worth the effort! This second one is amazing in that I have read exactly three pages of the introduction to Vygotsky's book Mind in Society and already I am convinced of the value of reading the rest of the book.

The first section that lays out the landscape of the European psychological thought in days before Vygotsky came on the scene is a concise and precise description.

Oh no doubt that this is dense reading but what the heck - this is kind of research weight lifting training I needed for many years now. The secret of getting this imibed is the same as exercise - any exercise is better than none and eventually the effects will show. Patience and consistency! (Now if only I could do the same for exercise :-)).

Learning to Listen (and thence to write)

I have been struggling to read Jere Confrey's paper called Learning to Listen.  It is an account of how to apply constructivist epistemology to mathematics education. It describes an incident of a college student trying to create a timeline for a list of events spanning many millennia, to illustrate how to look for what the student may be thinking.

It should be easy to read - after all I am part of a team right now that is struggling with how to interpret what we see during our data structure interviews. In this paper, it does exactly what our situation is:

A one-one encounter between researcher and student where the student is solving a problem selected for her by the researcher. The problem consists of capturing unorganized information and creating an information organization. The researcher is observing the entire process and gathering the think aloud comments of the student. The researcher later attempts to analyze these comments to see if the students's solution confirms some idea that the researcher went in with. This is the exact process that Confrey describes.

The long initial section on comparing and contrasting the discovery learning  theories and constructivist theories, is dense and most of her references are from the area of education research that is too theoretical for me.  After four failed attempts to proceed past the first section, I decided to go to the end of the paper and work my way back from there. Unbelievably, that seems to have worked. (Though there are still sections that are hard and who is Lakatos(I think I sort of know), and Hegel and Popper these are names I recall from my classmates college Philosophy course!).  Ok there is a lot to be learned here and it is worth the hard slog!

Trudging on - I found five assumptions that Confrey scatters throughout the paper that we maybe can use as a framework to analyze participant data:

1. Constructivists view mathematics as a human creation, evolving within cultural contexts. They seek out the multiplicity of meanings, across disciplines, cultures, historical treatments, and applications. They assume that through the activities of reflection and of communication and negotiation of meaning, human beings construct mathematical concepts which allow them to structure experience and to solve problems. Thus, mathematics is assumed to include more than its definitions, theorems and proofs and its logical relationships - included in it are its forms of representation, its evolution of problems and its methods of proof and standards of evidence.
2. In examining a student’s understanding of a mathematical concept, a constructivist seeks to represent how a student approaches the mathematical content. S/He expects diversity - and idiosyncratic rationality. The interviewer’s knowledge of the mathematical content, complete with multiple representations, competing interpretations, various applications - guides the inquiry, but his/her intent is to examine the student’s use of examples, images, language, definitions, analogies etc. to create a model which may well transform the interviewer’s own understanding of the mathematical content in fundamental ways.
3. Problems serve a crucial role in the construction of knowledge. Problems reside in the mind of the student - not in textbooks or in the mathematics. Problems are felt discrepancies, roadblocks to where a student wishes to be and therefore catalysts for action. To accept a problematic an individual must believe that it is capable of being solved - and act as though the problem and solution were preexistent. The cycle of identifying (noticing) problematics, acting and operating on them and then reflecting on the results of those actions is emotionally charged, motivating and demanding. It is this process of knowledge construction which is the critical site for constructivist researchers/teachers.
4. Problem solving as enacted in interviews or constructivist instruction is an interactive process. The interviewer selects a task for its potential to invite students to engage with a particular mathematical idea. The task will yield to multiple interpretations and resulting approaches. The interviewer must seek out an understanding of the students’ problematic, choices of actions and means of reflection. The interview setting will itself promote more self-reflection and a stronger approach to knowledge construction. The definition of the problem, of what concepts are related and of what constitutes an appropiate answer will evolve over the course of the interview.
5. Students’ responses which deviate from our expectations as research- ers/teachers can appear to he reasoned and well-considered to the student. They may be entirely legitimate - as an alternative perspective, or be effective for a limited scope of application. We must encourage students to express their beliefs, keeping in mind that deviations provide precious opportunities for us to glimpse the students’ perspectives.

Some other glimmers that glow for me:

• the constructivist is engaged in a processs of invention - invention of his/her own models for explaining students’ actions and words.
• s/he(the researcher) begins with the assumption that what a student does is reasonable and then seeks to describe it from the student’s perspective.
• A problem is an intellectual desire ... and like every desire it postulates the existence of something that can satisfy it... (so sez Polanyi)
• Labeling a student’s model as a misconception fails to take in consideration the perspec- tive of the student, for whom the belief may explain all instances under consideration and fail only in cases to which s/he is not privy. 
• Much of the success of the constructivist instructional or research model depends on how willingly the teacher 1) seeks to imagine how the student might be viewing the problem; 2) hears mathematical notions which differ from her/his own but possess internal consistency; 3) examines his/her own mathe- matical beliefs and 4) witnesses and describes the student’s choice of operation (action) and method of evaluation and recording (reflection).
• fit vs match: a conception must fit an experience not necessarily match the researcher's conception
• It is at points of contact, at moments of discrepancy, that we have the highest probability of gaining insight into another person’s perspective.
• Finally, I argued that in examining students’ problems and methods of solutions, one has an opportunity to reconsider the mathematics involved.

On the whole, I made a lot of progress when I decided to skip the arduous theoretical descriptions and the long description of "Suzanne" creating a powers of ten timeline. I read the part focusing on Suzanne later and it was much easier to read once I was no longer looking for deeper meaning.

Same blog, new phase

Since I have always assumed that this blog has exactly one reader - me, I am candid and quick with my thoughts. Should you not be me, let me know if you want me to spend some time cleaning up my thoughts before they make it here.

That disclaimer out of the way, this post is a quick one to say that the original purpose of the blog was well-served especially given that life in the way of GSP5 intervened and my only memory of the classroom observation was buried in these pages. It was these pages that stored the spots that glow and aided the process of both writing the paper(6 months later) as well as preparing the presentation(another 6 months later). "Jackie's" struggles were well received and much recognized. But the most gratifying response was the appreciation for the honesty in the presentation - the acknowledgement that I did not see what I set out to see but that it was not a waste and I did walk away with insights for the team. In my role as an educational researcher, this was a setback in that I didn't see "what happens when" because nothing much happened as planned. However, in my role as a software developer(well ok a project manager for a software development team then!), I did "see" important insights.

Moving on, this blog is now no longer the process of writing an ethnography, but rather a place to capture the work I am doing in the classroom, my thoughts on APS(OpenIDEO) work in India, my reading notes, and any other random moderately relevant thought. I do now firmly believe in the power of gathering random dreamy thought and the power of search to be able to use them when I need them to collate them into a coherent whole.

So the tagline for this blog will now read - "Only those attempt the ridiculous can achieve the impossible".

Till the next time...

Surprise! - tracking within the classroom

It was the day of new seating arrangements. Based on test scores from Tuesday - Jackie divided the class into three groups - passing(6), can pass but not there yet(6), need a lot of work(10). she did this, she said to make sure that she can give some undivided attention to the third group.

This is to continue for as long as it takes for them to change their work style. The first group looked pleased, the second was fidgety, the third mostly passive. They worked on taking the test as groups, working through their wrong answers, comparing what they got correct and sharing that with the group as a whole.

I worry that the second group may slide further down instead of rising up? The third appear to be split down the middle into those that know and are willing to engage when called upon in this new situation where they are under a magnifying glass and those are just not willing to take any visible effort.

Spots that glow:
* Thats why you are in this middle group - because you don't want to learn new things. You only want to coast in your comfort zone. You are not willing to put in the effort needed to be in the passing group, but you aren't in the last group becasue you are using what you have.
* No they are not the smartest. They are the best prepared. They don't pass everything they do - they just never stop trying. They are always asking for help. They turn up for office hours. This group has near perfect homework submission rates. That's what will help them succeed in the course.

We collected measures!!!

Second time in a row, the class was in a lab. This time, Jackie appeared more sure of herself. She had had time to pick a problem and prepare a Fathom based worksheet to solve the problem. It was one of their homework problems. The activity that the class was going to model was a simple discrete variable based simulation of creating a sampling distribution. This is problem 7.43 from YMS third edition. It is in the section pertaining to the Law of Large Numbers.

Students were modeling the process of solving this problem on a calculator. In all such problems, the first step is to "assign digits". What that means is given the table of probabilities, you have to create a list in your calculator corresponding to a random variable X (in this case discrete). It is a hard process for them to think through because they haven't practiced enough. Fathom is one more way to model this process.

Class strength was at 17 in place of 25, the rest were on a junior field trip to the South for following a Civil Rights trail. Yet again, a class that was far less disruptive than before. Amazingly the screens mask ratehr than provide the distraction.

Spots that glow:

• "Oh! I get it..." - a boy looking at the way they created the collection - by "assigning digits".
• Get good at Fathom - it is a tool for homework - see how much more we could do - said Jackie
• Pointed out where the law comes into effect, by asking everyone to take one sample of 5. Then asking them to compare how many times they got the number "5" with it's occurence in the distribution of the population. After that, she colected number fo "5"s from the entire class(which was a sample of size 85) and pointed out how much closer it was to the theoritical probability of getting a "5".
  
• In our desire to promote exploration based learning, I realized that our Fathom activities rarely model the typical(and endless number of) AP Stats homework problems.
  

3 collections and a graph!

Today there was a scheduled lab session in which they were to work with Fathom. Jackie said later that she wished she had had time to work with this before hand and create a student work sheet. She mentioned to me that the reason she decided to go ahead and do this session was because she knew I was coming - so there I have influenced the running of the class and in particular with regards to the technology use! Anyways...

The activity that the class was going to model was a simple discrete variable based simulation of sample means. This is activity 7b from YMS third edition. The gist of the activity is captured below (will try to add it from the book later)

1. Let X be a random variable whose values are drawn from {1,1,2,3,5,8}
2. Take a sample of two values from this set. (Treat the two 1s as separate values).
3. Compute the mean for this sample.
   
4. Repeat this for all possible samples of size 2.

This session took place in the lab. Each student had an individual iMac to work on. The have assigned computers but they can access all their documents from any computer as they have networked logins. The lab is set up as 6 rows of 6 computers each. Each row is divided into two parts by a vertical aisle with four computers on one side and two on the other. There is a screen in the front that is visible from all computers.

Jackie didn't have a student handout for them to work from. She had only that very morning decided that she would use Fathom after she confirmed my attendance. She reported her worry that if she had tried this activity solo then in case she ran into a snag she would get nowhere. Whereas with a physical simulation, she may only do a few runs but she had the confidence that she would get the point across. This appears to be a common worry with teachers who didn't grow up with technology as an integral part of teaching. As it turned out, the only real Fathom help I gave her was to point out that you could escape out of animation when collecting a 1000 measures. At other times, when she looked a bit puzzled, I just waited for a moment and she figured it out (An example being - which menu to choose from and which collection to have selected when wanting to collect measures)

(Development Note : We know this is a problem - trying to figure out which collection is which and when to work with which inspector)

On the whole the students seemed to not have a hard time with this activity and with Fathom. Jackie modeled the process of "putting together a Fathom document". The began with a collection, she called randomVariable. She called the attribute random_var. And created 6 cases using the case table {1,1,2,3,5,8}. She didn't ask the students for input when creating the document. She asked them later "Why do you think I put in those numbers?"

At the end, she asked them to look at their neighbour's computer and see if their graphs looked similar. This led to a bunch of looking around and comparing but not too much engagement or talk around why they may have slight differences.

About three of them were working with a sample of size ten (the default) when the activity asked for a sample size of two. One of them did sampling with replacement - and realized it only because his graph looked so different from others and asked for help figuring out why that was the case.

On the whole, an exciting and satisfying class. even the usual disruptive suspects had less effect on the class - maybe it was the fact they were in front of a computer and all doing something. The individual computer in fact to some extent lessened the disruptive effect because it was easier to stay on task with this screen blocking the distractions.

The person who had caused quite some disruption in the earlier class this time spent a lot of time fooling around but was also one of the first three to finish. So is he disenegaged because he is bored adn this material is too easy? Hard to say...

At the end of all this - they had fun, were more engaged than in any class before this, but did they learn better? Now that is a question for a later time...
Spots that glow:

• Even for a bright and dedicated teacher like Jackie, it is hard to get over the mental hurdle of doing an entire lesson based on technology.
  
• All it took in this case was the knowledge that a "technology expert" would be present for her to take the brave step of plannign this lesson
• "Why does Fathom create the third box?". "I don't know; for fun?"
• "Why do you have different numbers?" "Oh because we got different samples!"
  
• Fathom was very well suited to modeling this simple activity. There was none of the cognitive baggage associated with putting together a probability simulation involving cards or a "real-life" situation. Perhaps for students, whose big hurdle on a AP like test is reading and parsing the question, there are two simultaneous needs fighting for their attention. One is the need to understand the language - the other is to model the situation.
  

This is sooo hard!

Date of class- Jan 29th.

Today's class was a very unsettling experience. Jackie spent large parts of time just dealing with expectations, behaviour patterns and habits of mind. Plenty of spots that glow in terms of how much effort she puts into the class but hard for me to write up in terms of what it meant as class that will work with technology.

Before I forget too much about what happened in this class, I will record a few main themes and then elaborate on them later

• Get Help - use wikipedia, parents, teachers and peers
• Think before you speak and know when you are conjecturing
• Fill holes left by first semester teaching
• Teach new topic for 20 minutes - planned to do Fathom demo but no time
• Use your time - be intellectual - plenty to keep you busy even if you know nothing on quiz.
  

More encounters of the high school kind

Jackie's class is my first close encounter with a high school classroom in the United States. It is a non-typical situation as discussed in my earlier posts about Memorial High School. But for me, I have no baseline for what is a typical classroom. The interactions that I observe in Jackie's classroom are not very typical I guessed but wanted another experience.

I decided to visit an AP Statistics class in a large comprehensive high school in San Francisco. The school draws it's student population from all over the city. The teacher appears popular (enrollment in AP Statistics has almost doubled since he joined 4-5 years ago). The school itself has undergone a self-feeding upward trend with its scores int he same time period. The student population has undergone a demographic change.

The first difference I observed in this class as compared to the Memorial HS class is the more uniform dressing style. The are about 20% of the accessories that I saw in MHS - on both boys and girls. The other is that out of 25 students, there were 2 Hispanics, 1 Caucasian, the rest are all of East Asian origin. The community appears to have much to do with dressing styles. As someone who came from wearing uniforms to school and liking it, I struggle to come to terms with how much time and effort appears to go into dressing for school. I cannot help feeling as if they would regain a good hour or two each day if only they didn't spend so much time on dressing. This will be the last mention of this issue because this ethnography is not about what they wear but what they do; else I will be guilty of the same time waste.

This class apparently has 60-70% ELL students. But I can't help wondering if that just means that their first language at home isn't English - not necessarily meaning that they struggle with English. In addition, the similarity(with MHS) that here again more than a third will be first generation college aspirants seems amply offset by the difference parental expectations. As Jackie has expressed before one of the big challenges facing her students is an almost complete lack of parenting. Jackie also pointed out that even if they don't speak English at home, the language that they do speak, they speak at a much higher level of sophistication sot hey know what it it to communicate at a "college-level" so to speak. The other significant differnec ein this ELL characterization is the language you hear at break (that is their language of choice for social interaction) is English at this school whereas at MHS you hear Spanish in the break mainly.

So on the whole the students appeared on task, prepared to learn (in the sense that all of them had books and calculators and writing materials), non-disruptive but also jaded. There were situations in which one of them was napping. one was eating and another texting - but the teacher appears to have very strict classroom behaviour expectations and in general thery were met.

That said, the class was in a listening mode and not really in any type of active learning situation.
It was a lecture - they did about 5 problems but all of them were done by him on the board and they took notes and answered when he called on them. I definitely need to go again when they may be doing an activity. They did enter data about penny ages into a Fathom survey during break. They were passign around a bag of pennies during class and had been instructed to take 2 samples - one of size 5 and another of size 10; compute the mean; enter it into the survey. He used this data at the end of class to lead up to the Central Limit Theorem. It was the standard demonstration of how the distribution of sample means approaches the normal as we increase the number of samples - irrespective of the shape of the population. He then moved onto using the CLT document that comes with Fifty Fathoms. He also modified the uniform population in that demo to a bi-modal distribution to better illustrate the "normalization" that takes place as the shape changes int he sampel mean distribution is very dramatic moving from a bi-modal to tri-modal to normal by the time you get to about 25 samples. Even this felt more like a demonstration as it was not preceeded by any active work by the students in the area of building the distribution - they computed the means but that was all.

I took detailed notes of what actually happenned in the class in terms of the activities and use of Fathom but what appears here is a distillation of those notes using a framework of comparison rather than of reporting. I did learn how to answer questions like the ones that appear on the AP exam :-).

Missed opportunity?

The class on January 22nd was an unsettling experience. The students were being walked through a quiz that they had taken on the Tuesday prior to this class. They had all done really badly in that quiz. It was a very basic quiz on reviewing variance and made Jackie revisit her planned scheduling of the chapters. The quiz revealed a lot of "holes" in their earlier learning.

The entire time was spent in going over the quiz and ten the last 20 minutes were allotted to doing homework. Homework not being done is one of the root causes why it is hard for Jackie to ensure that the students get enough practice in basic simulation techniques. Modeling the problem and then converting it to "numbers" is hard when they mostly only do that in class.

I feel that the use of Fathom in this situation would have been a very valuable exercise. It would have been a visual approach to explain a concept that they are having trouble seeing. A way to provide yet another mental anchor for them to recall how it is done.

Maybe it was very demoralizing to discover just how much there is to make up which led to Fathom not being an option. To me even as an outside observer, it a downer to watch some of the classroom interactions and notice the complete lack of commitment to learning. Of special note is the return of two boys who had missed almost a month of school. They appeared to not care at all and weren't working on their homework when given the time. They weren't sitting in any group but seemed to have succeeded in reducing the general level of engagement in the work. She did say however that homework submission rate has gone up to 12-13 out of 23 from 1-2 out of 23.

There is one student who begins to standout for me. He appears to turn in all his homework - doesn't always understand everything or have the right answers but always answers in class. In some ways, he seems to be think out aloud in class and then work out what he needs to get to the answer. In the time allotted for doing homework, he made sure that his table partner was helping him with getting the work done. The table of 4 was to have worked together but in fact only teo of them were working. The girl who was workign with him seems to be better at the actual work but I have a feeling that his motivaiton to plow through all the work was what got her going. I need to watch them more and look for more interactions that tell me something.

Spots that glow:
Today's spots have more to do with my struggle with role and bias rather than with anything that happened in class.

When, Jackie didn't use Fathom to demonstrate the idea of a probability simulation, I was in a dilemma around how much I should influence what happens in this classroom. I wanted to point out the opportunity but didn't. The conflict was a result of my perception of my role in that space. I am struggling trying to reconcile whether I should bring attention to occasions where I believe technology may have been used to good effect. If I do then, I am an actor in the space not just an observer. If I don't then I am depriving the students of a learning opportunity. In the end, is it more important to antiseptically (without contamination) document what happens or intervene and help the learning situation. I don't have the answer that works for me...

Group Quiz - Probability

Today was a no Fathom day. Jackie moves the groups around each chapter, so that the students had moved from their earlier places. 19 of the students were present.

The class was taking a group quiz on Probability. The class was divided into groups of four (one group had 3). In the end, she picked one paper at random from the group too use as the group grade for the test - so they had to make sure that all of them had all their work on their papers. they were allowed to use calculators but asked to show all their work (For some this meant that they showed the addition when calculating the mean). She had a conversation about how much work is enough for the AP exam. The course is very AP exam oriented - she is always teaching them techniques for the test like attempt all questions. "If you answer a question, whatever you put down gives you a greater chance of scoring than a blank answer".

The quiz consisted of 3 questions.

1. Review question: Data in integers(100-150) about ninja turtle weights. They had to calculate the mean, variance and standard deviation. everyone knew how to do this, they "showed" their work in varying degrees of clarity. She reassured tham that AP examiners are atrained to look for the correct bits of their answer rather than the wrong bits. "They are asked to give marks for whatever is right rather than cut marks for what is wrong" In the second part, they had to calculate the 5 number summary(Q1, median, Q3, IQR, min, max) and use that to draw a box plot. 3 out of 5 groups drew a nice symmetric box plot with the right numbers but not scaled properly.


2. Card-Based Simulation: This question called for them to do a simulation of drawing 3 cards from the same suit in a five-card hand using the calculator. There were multiple parts to this question - including a review of basic information about cards. They had to assign numbers to the cards. Most groups assigned numbers from 1-52, but made an assumption that 1-13 would denote success and the rest failure. Only one group got the idea that they needed to divide the cards into four groups with equal number of cards. However, they used numbers between 00 and 99, thereby showing understanding of the probabilities involved but not simulating the underlying situation.
   

   The rest of the question was to create part of a tree diagram that reflected the solution space that captures the situation of 3 cards from the same suit in a five-card draw. The students have quite a few time management issues and noone actually finished the tree diagram.

3. This was the part hich asked them to create an entire tree diagram. But noone got to this bit in the quiz.
   

Spots that glow:

• There was a line printed at the top of the quiz in (tiny) 7 point font, saying" If you read this go get a raffle ticket from the sink counter" She had put out only 10 tickets for 19 students. Her goal was two fold -
  1. Emphasize the importance of reading everything. Part of the struggle for this class of students is language. So Read the fine print and read absolutely everything that is in front of you is a very important exam and life skill that she is teaching.
  2. The other was to show that since only ten tickets were out there, some students were going to be more luck than others. However, she emphasized that all students had an equal chance of being lucky and they made their own luck by reading everything.
     
  In the end, only six students picked up tickets. All of them were from one side of the room (three each from two groups).
  
• In the second question, she asked them to name the four suits of cards and the cards themselves because she discovered that enough of them didn't know the basic information about a pack of cards. To a person like me who grew up playing cards every afternoon in my summer vacation, it seemed strange that these children had got to senior year in school without exposure to a deck of cards.
  
• Towards the end of the class, she spent ten minutes introducing Venn diagrams as a way to think of probability. Jackie divided the class in two groups based on gender and grade level. She said that either you are a male and if you are not a male then you are a female. To which one student piped with a "...unless you are..." - I was amazed at the speed with which she quelled this by a "that is way more information that we need at this point." what was more amazing to me was the fact that no other students said another word and neither was there any side conversation. To me it is another example of how Jackie works to keep the class on task and push distractions out the door before they have even had a chance to make it in.