Fasching-Varner 2013, Educational Foundations

“Uhh, You Know,” Don’t You?: White Racial Bonding in the Narrative of White Pre-Service Teachers

This article is about preparation of White (capitalization is following that in the paper) pre-service teachers to examine their racial identity and its potential impacts on students.  The author looks at attempts at White racial bonding between pre-service teachers via use of the phrase “you know”.  The term “racial bonding” is used to indicate ways White people “show affinity and alliance with each other”.

Educational landscape:
As of ~2011, ~85% of teachers are White and female.  White students were ~55% of public school students, creating a demographic disconnect.  Teachers are increasingly inexperienced, as well.

Critical race theory (CRT) — Whiteness as property:
See Ladson-Billings and Tate 1995 for CRT in education.  Four elements of the value of Whiteness are relevant: benefits (use and enjoyments), a right to exclude ‘others’, rewards for certain behaviors, and status/reputation maintenance.  Part of the value is in never needing to define itself (but

Reading Ljung.  System Identification: theory for the user.

1: Introduction.

Goal: infer a model from observations.  “Model” refers to the set of relationships between variables in the system.  System identification involves analyzing input and output signals from the system.

Example: assume a linear difference equation relates inputs to outputs.  Use least squares to find parameter values that minimize the least squares error.  This is partly an autoregression: a linear regression “where the regression vector contains old values of the variable to be explained”.

Adding noise: assume the observed data are from a deterministic process with noise.  We’re interested in two expectation values: the parameters and the covariance of the parameter error.

System identification involves: a data set, candidate models, and an assessment rule (see chapter 7).  Then use model validation to check whether the model is good enough.  This process ends up being iterative.

2: Time invariant linear systems.

Impulse response can be used to characterize the system.  If there’s an additive disturbance info is needed on that too (spectrum and pf).

3: Simulation and prediction.

4: Models of linear time-invariant systems.

5: Models for time-varying and nonlinear systems.

Linear time-varying models might be used when we linearize a nonlinear system about some trajectory.

6: Nonparametric time and frequency domain methods.

7: Parameter estimation methods.

8: Convergence and consistency.

9: Asymptotic distribution of parameter estimates.

10: Computing the estimate.

11: Recursive estimation methods.

12: Options and objectives.

 

13: Experiment Design.

14: Preprocessing data.

15: Choice of identification criterion.

16: Model structure selection and model validation.

17: System identification in practice.

 

Notes on Chapter 1 of Maybeck 1979, Stochastic Models, Estimation, and Control.

1.1: why stochastic models, estimation, and control?

A math model isn’t perfect, and parameters are not known absolutely.  Sensors don’t provide perfect data either.  Given uncertainties, you still want to be able to estimate quantities of interest and control the system.

1.2: Overview of the text

skip.

1.3: The Kalman filter: an introduction to concepts

The Kalman filter is an “optimal linear estimator”.  Given (1) knowledge of the system and the measurement device, (2) a statistical description of noise and error, and (3) initial condition info, a Kalman filter can combine the knowledge to create an estimate.  When the system is described by a linear model, and the noise is Gaussian and is white noise, the Kalman filter is the best estimator.

1.4 Basic assumptions

The model is linear, the noise is white noise, and the error is Gaussian/normally distributed.

1.5 A simple example

A static problem: Trying to determine your position, you have a single measurement (z1) and its precision/standard deviation.  This leads to a conditional probability density (conditioned on your measurement).  The best estimate is currently z1.

A friend takes a second measurement, z2, with smaller variance.

The best estimate will now be a combo of these two that takes into account the precision/variance on each.

There is a predictor-corrector structure to the way the estimate is made: we can take the previous best estimate and associated standard deviation and then “correct” it with the new data and new standard deviation.

A dynamic problem: Now add a motion model.  This evolves the pdf forward in time.  (And adds noise so will increase the standard deviation).  This creates a new estimate and variance.  Then take a measurement and use the corrector process from above.

Kohn, 1986 and 1992, “No Contest: The Case Against Competition”

Chapter 1: “The ‘Number One’ Obsession”.  American life is a succession of contests, so some people fail or lose so that others succeed or win.  There is “structural competition” (an external win/lose framework) and “intentional competition” (a competitive intention on the part of the individual).  A structurally competitive activity has “mutually exclusive goal attainment” (MEGA: a zero-sum game).  Competitive, cooperative, and independent modes are all possible.  In the competitive and cooperative cases, the success of participants is interlinked.  Structural cooperation requires coordinated effort “because I can succeed only if you succeed, and vice versa”.

“The case for competition… has been constructed on four central myths”.  (1) It’s human nature.  (2) It motivates our productivity.  (3) Contests are a good time.  (4) It builds character.

Chapter 2: “Is competition inevitable?”.

Chapter 3: “Is competition more productive?”.

Chapter 4: “Is competition more enjoyable?”.

Chapter 5: “Does competition build character?”.

Chapter 6: “Against each other”.

Chapter 7: “The logic of playing dirty”.

Chapter 8: “Women and competition”.

Chapter 9: “Beyond competition”.

Chapter 10: “Learning together”.
1. Competition promotes anxiety.  2. It contributes to extrinsic motivation.  3. Whether winning or losing, “luck or fixed ability” is often credited.  4.  The presumptive winner is often already known.  5.  Cooperation has emotional benefits.  6.  Academic work becomes a valued activity.  7.  It enhances student enthusiasm.

I’m reading Effective Grading: A Tool for Learning and Assessment in College, by Barbara Walvoord and Virginia Johnson Anderson.

To think about grading, they emphasize that building learning objectives is core to the process.  They break these into a few categories:

• the vocabulary and content and concepts that students should know,
• solving problems within the discipline,
• following the ethical guidelines of the discipline (citing sources and collaborators, as well as identifying and addressing ethical issues)
• big picture ideas – how does the content expand someone’s worldview?
• development of the habits of mind of the discipline

Because grading is quite labor intensive, Walvoord and Anderson point out that the major assignments should be constructed to match these goals.  One mis-step is that tests often check basic knowledge, rather than focusing on analysis, synthesis, and critical thinking.  In mathematics our grading systems can be focused on process rather than simply rewarding a correct final answer.  For time efficiency, it might be appropriate to use a multiple-choice test for basic content knowledge so that grading time can be focused on synthesis and evaluation skills.

The authors also suggest taking advantage of peers.  Peers are ‘the strongest single source of influence on cognitive and affective development’ (quoted from Astin 1996).  Ideally the task would be better done by a group than by individuals, often because it is complex or because it requires multiple areas of expertise.  It is a task that is hard to divide so that students work together.  One option is to incorporate individual responsibility so that grades may vary between members of the group.

To actually construct assessments, one can engage in the process of “test blueprinting”, where the learning objectives and test questions are linked.  The rubric is also part of this process.

Given a set of tests and assignments, they need to be structured into a course skeleton that generates “an assignment-centered approach”.  To set up the course structure, write summaries “of the skills and knowledge that the exam will test”.  Think about whether these fit the learning goals and create a sustainable workload for students and staff.