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Chapter 5: Task Classification

In this chapter, I analyze two assignments using the classification explained in

Chapter 4. This is intended to demonstrate how the classification can be used to

describe an assignment and compare it to other assignments. For the purposes of

classification, a questionnaire was developed that helps to determine which categories

apply and which instances of these categories apply to the assignment. This

questionnaire can be found in Appendix C. Each question corresponds to a category

or subcategory and the answer codes can be appended to the code in the right margin

to give the numbers corresponding to the instance of the category. The codes

resulting from each answer can be recorded in the corresponding box on the Coding

Results Sheet in Appendix D; the first column lists the codes found in the right margin

of the questionnaire and the second has spaces to enter the code(s) for the answer(s).

Therefore the resulting numbers correspond to instances of categories found in the

task according to the numbering in Appendix B. In the analysis, I also include

comments from the teachers that describe why certain choices were made. These

comments may suggest ways in which different choices in designing a writing task

might affect student learning.

Two assignments were chosen for analysis: Adams’ use of TIPS [Appendix A:

25.1] and Favata’s Olympic Games [Appendix A: 10]. These two assignments were

chosen because significant detail and context were collected for these assignments and

they varied in a number of ways. Also, the teachers were available and willing to

respond to questions about the analysis. TIPS is a short daily assignment for middle

school students, graded based on completion. Olympic Games is a longer assignment

within a series of assignments for AP Statistics students, graded based on correctness.

These two assignments were analyzed using the questionnaire, and additional

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information was sought from the teachers who used them in order to complete the

analysis. The Coding Results Sheets for each of these assignments can be found in

Appendix E. This analysis is explained in more depth below. The Coding Results

Sheets and the analysis below were shared with Adams and Favata to ensure accurate

reflection of the writing tasks. Any differences in understanding of the assignment

and categorization were discussed, with preference in any disagreement given to the

teacher’s perspective. After the analysis of the two tasks separately, the two tasks are

compared to show how the classification can highlight differences between

assignments.

Each analysis is organized based on the three main groupings in the categories:

Teacher Intentions and Goals, Assignment, and Response and Assessment. Each

choice of instance within the categories is explained in the context of the assignment

and tied to the classification by the number of the instance, which can be found in

parentheses in bold. These numbers refer to the numbering system found in Appendix

B. Also, each section will be summarized with a table giving the numbers and names

of the categories and applicable instances that are determined by the questionnaire.

Following the analysis and a comparison of the tasks, a few challenges in using

the classification are considered.

Olympic Games as used by Laura Favata

This writing task was given to an AP Statistics class near the middle of the

school year. The students who take this class are near the end of their high school

careers and are usually intending to attend college. The summary from Appendix A

can be found below in Figure 2. Students are given the handout found in Figure 3,

along with the “Thoughts Beforehand” page in Figure 4. The rubric used to grade the

assignment is in Figure 5.

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Figure 2: Olympic Games Assignment Summary from Appendix A

10. Olympic Games: analysis of long-jump information (Favata) This assignment is from Bock, Velleman & DeVeaux’s Stats: Modeling the

World (2004) and is handed out to students on a sheet of paper. AP Statistics students are given data on the gold medal long-jump distances in all the Olympic Games. They are asked to individually (a) do numerical and graphical analyses, (b) discuss the trend in long jumps based on a linear model, (c) explain the decisions made in creating the model with historical analysis of gaps in the data and departures from the trend, and (d) predict the distance that will win in the 2004 Games, including their faith in that prediction. This assignment was done after these topics had already been covered in lecture and in group activities. The rubric specifies what is desired, defining graphical analysis as a scatterplot, and numerical analysis as finding a linear model, defining variables, calculating r and r2, and a description of the direction, form, scatter and meaning of r2. The latter description is 5 of 12 points in this section. In terms of (c), they were expected to note gaps for the World Wars, and big jumps between the first two Olympics and in 1968, as well as their analysis of linearity. Finally, there were points for the prediction. The analysis was more than half the points. Some bonus points were available for work beyond what the project asked for; for example, some students searched for the athlete who was the outlier. The assignment was graded out of 30 points. This assignment is part of a series of assignments, so students have an understanding of the requirements for the write-up. Students do a similar project at the end of most chapters, for a total of 7-10 assignments of this type throughout the course. Projects like this make up 25% of the course grade. Students are expected to be clear and concise and answer all the questions, as well as including all the graphs and data and supporting all their conclusions. They have seen what is acceptable from previous assignments and have the opportunity to ask any questions during the week they are doing the project or after the project is graded. They also have a sample grading rubric they can use as a checklist. The writing affects the grading only as a tool for communicating. If the statistics is done accurately and in context and communicated clearly, this is all that matters. Favata reports that in this assignment, students have already had enough experience in the class so that “they are handing in projects that are well written and edited” (personal communication, July 13, 2005). Students are expected to recognize that communication is a major part of the work of statistics. Students are given freedom regarding the form in which they write the projects; for example, they can add extra graphs or write it in the form of a newspaper article. The length is determined by the information that they need to communicate. Each paper is commented on extensively in accordance with the rubric in the areas of content and clarity. The grading is intended to model an AP grader’s rubric. The comments are intended to help students correct their mistakes and misconceptions.

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Figure 3: Handout for Olympic Games task

AP Statistics Name _________________________ Project Date ___________________

Olympic Long Jumps

The modern Olympic Games, a modified revival of the ancient Greek Olympian Games, were inaugurated in 1896. Since then, the Games have been held nearly every four years at various sites around the world, and have become a major international athletic competition.

Based on the gold medal distances shown, write a report about the men’s long jump. In your report be sure to:

• Include appropriate graphical and numerical analyses • Discuss the trend in long jump performances, based on an appropriate

linear model • Explain the decisions you made in creating your model, with some

historical analysis of gaps in the data and departures from the trend • Predict the distance that will win the men’s long jump in the 2004 Games

in Greece, with comments on your faith in that prediction. Year Distance

(inches) 1896 249.75 1900 282.875 1904 289 1908 294.5 1912 299.25 1920 281.5 1924 293.125 1928 304.75 1932 300.75 1936 317.3125 1948 308 1952 298 1956 308.25 1960 319.75 1964 317.75 1968 350.5 1972 324.5 1976 328.5 1980 336.25 1984 336.25 1988 343.25 1992 342.5 1996 334.65 2000 336.6

Bock, Velleman, DeVeaux Stats: Modeling the World, 2004

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Figure 4: “Thoughts Beforehand” Handout for Olympic Games Task This handout was intended to give guidelines for what students should include in the report and how the reports would be graded.

Thoughts as you prepare your clear, concise and complete statistical analysis:

Think

Create a good linear model: • Use a subset of the data • Justify modeling decisions

Show

Visual: The scatterplot . . . • Has correct explanatory/response variables • Is accurate and clearly labeled • Shows the regression line

Numerical: The analysis . . . • Has correct r-squared • Has correct slope and y-intercept • Uses the proper notation

Tell

Interprets the model: • Evaluates the model with residuals • Describes trend in distances • Interprets the slope in context • Distinguishes model from reality

Makes a prediction for 2004: • Makes correct prediction from model • Expresses caution based on r-squared • Expresses caution about extrapolation

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Figure 5: Rubric for Olympic Games Assignment

I. Graphical Analysis

______ [5] Correct scatterplot of the data

II. Numerical Analysis

______ [3] Constructed a reasonable linear model for the data

______ [2] Defined variables

______ [1] Calculated r to measure strength of association

______ [3] Commented on direction, form, and scatter (strength)

______ [1] Calculated r2

______ [2] Described r2 in the context of the problem

III. Discusses the trend in long jump performances

______ [2] Made a statement about the trend in the data in context

IV. Explanation of decisions made in creating your model

Historical analysis of gaps in the data

______ [1] Gap between 1912 and 1920 (WWI)

______ [1] Gap between 1936 and 1948 (WWII)

Mention/justification of any departures from the trend (outliers/influential points)

______ [2] Big jump from 1896 to 1900

______ [2] 1968

Linear Model

______ [1] Constructed a residuals plot

______ [1] Correct assessment of linearity

V. Prediction

______ [2] Made correct prediction from model

______ [1] Commented on faith in your prediction

VI. Bonus Points

______ ___________________________________

___________________________________

___________________________________

Score ______

30

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Teacher Intentions and Goals

This task is intended to help students apply the collection of skills that they

have learned to real-world data. This is consistent with the intention to help students

learn procedural (1.4.2) and conceptual (1.4.3) mathematical content. Part of the

culture of the class is that answers need to be communicated well, and that answers are

more than a number or picture, but need “clear, concise and complete” explanations

(personal communication, July 13, 2005). This emphasizes both the need to

communicate carefully in an acceptable mathematical style (1.6.2) and the

mathematical need to make logical arguments (1.4.5). The AP culture of the class also

emphasizes specific forms of communication, and preparation for the AP Statistics test

is part of the rationale for why the task is done and graded as it is. Therefore, the

instance of communication in preparation for standardized tests (1.6.3) should be

included in classifying the intentions. Laura Favata uses these assignments to assess

whether students understand the concepts and skills they will need for the AP test, and

does individual remediation based on them, in part through the comments made on

student work. This exemplifies the instance of using the task to individually assess

students (1.1.2). These instances and their titles are listed in Table 50.

Table 50: Olympic Games Teacher Intentions and Goals

1. Intended Area of Change/Purpose

1.1 Teacher Assessment

1.1.2Assess individual student learning

1.4 Mathematical content

1.4.2Procedural understanding

1.4.3Conceptual understanding

1.4.5Logical argument or proof

1.6 Communication ability

1.6.2 "Math-talk" - disciplinary specific standards

1.6.3Standardized test-preparation

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Assignment

I will consider the categories that describe the writing assignment itself within

the classes of the classification: Practical Product Specifications, Theoretical Product

Specifications, and Process and Context.

Practical Product Specifications

In this section I will consider the product students are to turn in and who is

involved in the completion. The instances applicable to this task from this class of

categories can be found in Table 51.

Table 51: Olympic Games Practical Product Specifications

Laura intended this assignment to mirror much of the process and challenges

of the AP Statistics exam, and therefore required that students work individually. This

implies that the individual is both the writer (2.1.1a) and the only collaborator, or

person who has direct input into the written product (2.1.2a). The teacher is the only

intended reader (2.1.4.2), and she tries to model AP standards for responses. The

2.1.1a Writer(s): Individual Student

2.1.2a Collaborators: Individual Student

2.1.3a Audience: Not specified

2.1.4.2 Reader: Teacher

2.1.5 Sources

2.1.5.2Individual learning of class content

2.1.5.4Textbook

2.2.1.1a Units of Writing: Not specified

2.2.1.2 Length Restrictions: None (N/A)

2.2.2b Grammar and SpellingRequirements: Complete sentences required

2.2.3c Breadth of Topic: Multiple concepts or a large topic

2.2.4c Use of Visuals and Graphics: Required

2.2.4c.4Mathematical content: graph, table, etc.

2.2.5a Multiplicity of Answers and Methods: One answer, one method

2.3g Level of Student Manipulation: Analyzing information from the class

2.4c Student Choice: Choice of major parameter of assignment

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audience for the written work is not specified (2.1.3a) and students have the freedom

to choose different audiences. For example, Laura had some students choose to write

the report as a newspaper article. This shows a choice that students have which can

determine a significant parameter of the assignment (2.4c). Since students are

working individually and using content they have already learned in class, their only

sources are their individual learning of the content (2.1.5.2) and their text (2.1.5.4).

The written product is intended to communicate the content clearly, which

means, given the high caliber of students in the class, that the writing is generally of

good quality and significant length. Laura reports that by this assignment students

“are handing in projects that are well written and edited” (personal communication,

July 13, 2005). However, these standards are more implicit than explicit in the

assignment itself. While students turn in reports with multiple paragraphs which

amount to three or four pages including data and graphs, the actual length of the

written report is not specified (2.2.1.1a). In this case, not specifying the length implies

more student responsibility because they have to decide when they have included

enough information. In the same way, students are given no length restrictions, so the

category of Length Restrictions (2.2.1.2) is not applicable. Students are expected to

write in complete sentences (2.2.2b) since they are writing a report, but no particular

grammar and spelling or format restrictions are made. Again, these formatting issues

are taken for granted since the students are advanced; however, these elements do not

affect the grade directly and so the task is not classified as requiring them.

Students are writing about a particular example in order to apply the methods

of statistical analysis that they have learned, so it would appear that this is how the

breadth of topic should be classified (2.2.3a). However, students are applying a

combination of methods to this example, and in this sense are integrating many

different skills. These skills are the true content of the task, not the example.

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Therefore, according to the intentions of the category, this should be classified as

multiple concepts (2.2.3c). The methods students are expected to use are standard

statistical methods on a well-defined problem, and therefore students will use one

basic method, resulting in one answer (2.2.5a). Even though the required explanation

may vary slightly in wording, it will still be directed toward the same meaning. Some

of the methods include standard graphical analyses. These graphics are required and

part of the mathematical content (2.2.4c.4). As an AP class, students are expected to

reach a high level of performance, carefully analyzing the data and working with it in

a number of ways. Therefore, there is significant student manipulation of the data

given to them, so this is classified as analyzing information from the class (2.3g).

Theoretical Product Specifications

In this class of categories, the cognitive demands of the assignment are

classified, with a specific focus on what is required to complete the assignment

satisfactorily rather than what may result from the task. The categories and applicable

instances of this class of categories can be found in Table 52.

The function of this task is clearly to convey information. The use of the word

“report” in the assignment signals this, as do key verbs like “explain” and “predict.”

These imply specific information and an audience that wants to understand this

information. This is not an artistic performance to please the writer, as poetic writing

would be, and is not expressive of the writer’s personal thoughts and feelings, as

expressive writing would be. It is transactional (2.5c), and intended to convey the

results of the data analysis to the reader. The rhetorical demands of this specific task

include some generalization as students analyze the data for a general pattern and use

this pattern to make a prediction. Therefore, the task demands at least low-level

analogic work. This task is best classified as analogic (2.5c.e), because the nature of

the report and the methods used require that this generalization be well organized

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Table 52: Olympic Games Theoretical Product Specifications

and justified. This is a better choice than the analogic-tautologic or tautologic levels

because the result is the generalization itself rather than discussion of the

generalizations. The use of prediction might appear to confuse this; however, the

prediction required by this task is the use of the generalization – the equation for a line

modeling the length of the winning long jump – rather than prediction of further

generalizations.

When the cognitive demands of the task are determined according to Bloom’s

Taxonomy, it is evident that the processes of analysis are used as students compare the

data and determine outliers and gaps. This assignment also combines many of the

methods and concepts that students had been learning in class and therefore requires

synthesis. Since Bloom’s Taxonomy is considered a hierarchy, this task should

therefore be classified as synthesis (2.6e).

2.5c.e Function of Writing: Transactional: Analogic

2.6e Bloom's Taxonomy: Synthesis

2.7.1 Level of Language

2.7.1.1Particular procedural

2.7.1.2Particular descriptive

2.7.1.4Generalized descriptive

2.7.2 Aspects of Mathematics

2.7.2.2Logical

2.7.2.3Algorithmic

2.7.2.4Methodological

2.7.2.5Conventional

2.8 Connections

2.8.1 Concepts with procedures, symbols and objects

2.8.3 Current learning with other experiences

2.8.4cConcepts and procedures with related examples

Example(s) followed by student generalization

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The language of this task is varied and complex because many different

aspects of the concepts and the example are integrated. The category Level of

Language (2.7.1) describes the type of statements that students will need to make and

whether they are particular or general, procedural or descriptive. The rubric in Figure

5 can help determine whether some of these types of statements are required. In the

procedures required, particular procedural language (2.7.1.1) should result when

students construct a linear model, calculate r, and calculate r2 because they must use

specific language about these procedures relating to the example. As they comment

on trends found in this example, particular descriptive language (2.7.1.2) would occur

when r2 is described in the context of the problem. Students may make statements that

are generalized procedural if they discuss the procedures they are using in general, but

this is not required of the task. In order to make “a statement about the trend in the

data in context” students will have to use generalized language, since they are

discussing a trend and this language will also be descriptive (2.7.1.4) rather than

procedural. Students are also required to use a variety of Aspects of Mathematics

(2.7.2) in their writing. Again, the rubric can direct the classification through its clear

statements of what is required for successful completion of the task. In order to define

variables, students must use conventional language (2.7.5). The specific methods and

procedures they follow in finding a linear model and computing variables will require

algorithmic language (2.7.3), and the explanation of methods and conclusions will

require logical language (2.7.2). Discussion of outliers and gaps is not concerned with

a specific procedure, and therefore is methodological (2.7.4) in nature; students will

make general statements about outliers that they will also interpret within this specific

context.

There are also various connections needed in this assignment. Students must

connect the various concepts and procedures that they have been studying to each

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other (2.8.1). They also need to connect their analysis in the project to their

knowledge of history in order to understand the gaps caused by World War I & II.

This is an experience that is outside the mathematics class (2.8.3). Finally, students

need to connect the concepts and procedures they know to this specific example

(2.8.4). It is difficult to determine in this instance how the examples are sequenced

with explanation. It is the nature of statistics to work within the context of a given

example, so this can be considered a case where all explanation is related specifically

to the example and there is no general explanation (2.8.4a). On the other hand, one

could consider the nature of statistics as inherently generalizing from examples, which

results in models and future predictions. In this case, students must generalize from

the particular data they are given and explain this generalization (2.8.4c). This shows

how these cognitive categories depend on the perceptions of the subject and the task

brought by the person categorizing them. However, I believe that the argument for

generalization is stronger since students are required to make statements about trends,

which are generalizations, and therefore classify this accordingly. Laura agrees with

this, noting that students also need to distinguish the model they are working with

from reality, as noted in the “Thoughts Beforehand” handout in Figure 4.

Process and Context

In this section, the greater context of the task within the classroom is analyzed,

including issues of related activities, repetition and communication of the task, and

time, place and sequencing of the task. The categories and applicable instances of this

class of categories can be found in Table 53.

As noted above, this assignment is intended as an individual assessment and no

other groupings were used after the completion of the task, so the only grouping is that

of the individual (2.9.1.1). Therefore, the category Sequencing of Activities (2.9.2)

does not apply to this task. Since the task is individual, it is completed entirely at

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Table 53: Olympic Games Process and Context

home, or outside the classroom (2.13.1e), and therefore receives no time within the

classroom (2.13.3a) and the category of Timing Within Class Period (2.13.5) does

not apply. Similarly, no revision is required for this task, so the categories related to

revision (2.10.1) and (2.10.2) do not apply. Some students may choose to

2.9.1.1 Groupings: Individual

2.9.2 Sequencing of Activities: None (N/A)

2.10.1 Modifying Writing Within the Same Structure: None (N/A)

2.10.2 Adapting Writing into a New Structure: None (N/A)

2.11.1c Task Frequency: Once a Unit

2.11.2cImportance/Centrality of Assignment Type

Regular, high value series of assignments

2.11.3b Overlap of Material with Other Assignments

Content repeated in other activities

2.11.3b.1Lecture/class discussion

2.11.3b.3Group work

2.11.3b.5Exercises (routine)

2.11.3b.6Tests/summative evaluation

2.11.4c Placement in Learning Sequence: Follow up for introduced material

2.11.4c.bNovel context

2.11.5b Relationship Between Words and Symbols

Explaining symbolic work as it is completed

2.12.1.3 Mode of Assignment: Given in writing on a sheet of paper

2.12.2b Modeling of Assignment: Some modeling of assignment

2.12.2b.1Processes of assignment modeled

2.12.2b.3Example(s) of assignment assessed

2.13.1e Place of Completion: Entirely at home

2.13.2d Time to Complete Assignment: Until 5-9 class periods later

2.13.3a Amount of Classroom Time: No time

2.13.4d Expected Time at Home: 2-4 hours

2.13.5 Timing Within Class Period: (N/A)

2.14.5 Relevance of Task Context: Real-life setting

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do some self-modification through editing and this is encouraged, but it is not

required.

Some categories describe the type of writing tasks that Olympic Games

exemplifies. Most units have a similar project, so the task frequency is once a unit

(2.11.1c). Students are given about a week to complete each of these tasks (2.13.2d),

expected to spend multiple hours on it (2.13.4d), and 25% of the course grade is

devoted to projects like these. Therefore, this is a central and important part of the

course structure, constituting a regular, high value series of assignments (2.11.2c).

This task took place at the end of the unit that contained the skills used in the

assignment. Therefore the task was follow-up for material that had been introduced

(2.11.4c), allowing students to integrate the various methods and concepts and apply

them in a real-life setting (2.14.5). In particular, this task gives students a novel

context to apply their learning (2.11.4c.b). Students were to apply the skills they had

learned without any further expansion of the concepts, so this is an example of content

being repeated in other activities (2.11.3b). Students had participated in group

activities (2.11.3b.3) regarding this content; one activity required that each student

find a linear equation that goes through two points of the data and then residuals were

calculated for each of these lines to see which was the best fit to the data. The topics

had also been covered through lecture and class discussion (2.11.3b.1), homework

exercises that required application of the concepts and methods (2.11.3b.5), and were

covered in tests (2.11.3b.6). Students have already done a significant amount of

symbolic work throughout the unit, as well as related explanation. Since the course

emphasizes explaining findings in context, symbolic work is usually explained

concurrently. In this task, they are explaining symbolic work as it is being completed

(2.11.5b), although the order is not as easy to determine here since students have a

significant amount of time to do the assignment and the order may vary.

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The task is communicated by passing out a sheet of paper to each student

(2.12.1.3). The processes of the assignment have been modeled in previous

assignments of this type and throughout the unit as students have learned the content

(2.12.2b.1). Students also have their own graded work from similar tasks completed

earlier, giving them insight into how the task is assessed (2.12.2b.3).

Response and Assessment

This group of categories concerns what happens after the task is completed,

considering both response to the task in the form of grading and comments and any

use of the assignment in future learning. The categories and applicable instances of

this class of categories can be found in Table 54.

Table 54: Olympic Games Response and Assessment

3.1.1 Teacher Comments

3.1.1.1.1Form: Written

3.1.1.2.1Group: Individual

3.1.1.3Type

3.1.1.3.1 Focus: content and clarity

3.1.1.3.2 Specificity: detailed by rubric

3.1.2.1 Feedback Frequency: Every written product

3.1.3a Peer Response: None

3.1.4b.c Collection of Writing: Turned in: At due date

3.1.5b Availability to Students: Kept at discretion of student

3.2 Use of Completed Assignments

3.2.1 Source for grade

3.2.3 For assessment of individual progress

3.3.1c Standards for Grading: Graded based on correctness

3.3.1c.1a Content vs. Expression: Content mostly

3.3.1c.2e Standards for Justification: by Proof

3.3.2b Grading method: Distribution of Points

3.3.3.3 Grader: Teacher

3.3.4 Percentage of grade: 3% (75% for type)

3.3.5b Student Awareness of Assessment Parameters

Students have access to grading scheme

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After the task is completed and collected at the due date (3.1.4b.c), Laura reads

each student’s work carefully and grades it (3.3.3.3) according to a rubric that

specifies a distribution of points (3.3.2b). These grades are based on whether the

content is correct (3.3.1c) rather than on effort. Most of the grade is based on the

content (3.3.1c.1a); points may be lost if the expression obscures the content, but this

is not included in the rubric and therefore is not directly affected. Students are

expected to justify and explain their work according to statistical standards, so the

standards for justification are equivalent to those of proof or logical argument

(3.3.1c.2e). Students had the Thoughts Beforehand handout in Figure 4 that

corresponds closely to the rubric so that they knew how the task would be graded

(3.3.5b). This particular task would account for about 3% of their grade, with similar

tasks accounting for 25% of the course grade (3.3.4).

Laura makes comments on the tasks that are individual (3.1.1.2.1) and written

(3.1.1.1.1). The distribution of points in the rubric is an aid in making these comments

since they give students specific information (3.1.1.3.2) about where they lost points.

The comments focus on both content and clarity (3.1.1.3.1). Such comments are made

on every assignment of this type (3.1.2.1), and no peer response is made, so the

instance in the category of Peer Response is none (3.1.3a). These tasks are returned

to students, who keep them at their own discretion (3.1.5b). Overall, the tasks are

used both as a source for a grade (3.2.1) and for assessment of individual progress

(3.2.3) that allows for remediation.

Summary

Overall, this analysis of the assignment shows that it requires significant

independence and responsibility on the part of students to complete this assignment.

Students do the work individually, it is graded individually, and the task is intended to

help individual assessment and prepare for a test that students must take individually.

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This is understandable and expected within the culture of a college preparatory class

and the need to perform individually on the AP Statistics examination. A number of

aspects of this assignment are also implicit rather than explicit, and therefore

underemphasized by the categories. Students are to submit excellent work, but since

these are advanced students and this is the middle of the course, these expectations are

not explicit in the assignment. For example, no explicit requirements for grammar,

spelling or format are made, and no minimal length is imposed. These elements are

taken for granted in excellent assignments. Finally, this assignment makes a variety of

cognitive demands on students that are in keeping with an advanced course and the

desire to have students perform at discipline standards. There are a number of

questions that require a high level of both transactional writing and cognitive

processing as measured with Bloom’s Taxonomy. The assignment also expects many

different types of language and connections. Discipline standards can be seen in these

cognitive standards, as well as in the general expectations for writing, the requirement

of graphics, and analysis as part of student manipulation.

TIPS as used by Kimberlee Adams

This task was used as a typical Problem of the Day (POD) to begin an 8th grade

mathematics block on January 11, 2005. I observed this assignment and have

conversed with Kimberlee about her daily use of similar tasks. The task summary

from Appendix A can be found in Figure 6.

Teacher Intentions and Goals

This assignment was used to review ideas about solving linear equations that

had been learned in the previous class. Kimberlee writes that the “idea is for the kids

to understand and express their learning” (personal communication, July 13, 2005).

The first goal of understanding is related to students learning mathematical content

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Figure 6: TIPS Assignment Summary from Appendix A

(1.4), while the second goal of expression refers to helping students to communicate

about mathematics (1.6). The content is procedural by nature and therefore the

improvement of procedural understanding (1.4.2) was central in Kimberlee’s

intentions. The task also included elements of conceptual understanding in the larger

context of solving equations and the various properties of operations. Therefore,

conceptual understanding (1.4.3) was also a goal of this task. This task is intended to

improve students communication ability (1.6) for a variety of reasons. The school

25. TIPS (Spriggs, Adams) In the Think-Ink-Pair-Share (TIPS) process, students are asked to think about a problem, write about it, share it with a partner and then share with the whole group. This is a pattern that fits into the school emphasis on writing and the use of the Collins Writing Process (see Note 3 after [34]). 25.1: (Adams) Problem Of the Day (POD)

Students are regularly given a problem of the day that is done using the TIPS process. On the day observed, students were asked to solve a problem based on the previous day’s lesson: “Solve: 7N + 4 = 32. Using words, explain how you would solve this equation.” They are reminded that they need to write in complete sentences for their explanations - using words, not numbers - and should write 3-4 sentences. Students are asked to write as if they were writing an E-mail or letter to a friend explaining how to do the problem. Students are given about 30 seconds to think, 2 minutes to write, 1-2 minutes to share with a partner, and then each table of four students was asked to have one person read exactly what they wrote. While students are working, Adams would read what they were writing and ask questions to help them answer the problem. More time can be given or steps repeated if students have difficulty. Students were asked to write in such a way that it would be a good explanation for someone else in the class. After some students read to the class, all were given a short period of time to Re-Ink, that is, revise what they had written. Adams goes over the POD after students have written and shared about it, asking questions until they reach the answer. This type of task was recorded in their class notebooks. At this point in the course, students have already done a number of hands on activities related to linear equations, as well lecture and class discussion and homework exercises. This assignment is usually used to check understanding on the most recent lesson or to introduce a new lesson. It could be used for individual assessment, in which case Adams would draw a line after what students had written individually and then allow them to write below the line after interaction with peers and the class.

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district is emphasizing the Collins Writing Process [Appendix A, Note 3 after [34]]

and therefore the Writing Across the Curriculum (1.6.4) movement is a significant part

of the motivation for this task. Also, Kimberlee notes that these questions were

intended to prepare them for tests (personal communication, July 13, 2005), including

standardized tests (1.6.3). Finally, at the time of observation, Kimberlee noted that

she wanted students to use this task as a way to gather their thoughts for the class

period and use their own words to express their learning rather than having the teacher

telling them how to do it. This shows how she wants students to use their own words

and everyday normal speech to explain their work (1.6.1). These instances of Teacher

Intentions and Goals are found in Table 55.

Table 55: TIPS Teacher Intentions and Goals

Assignment: Practical Product Specifications

In this section I will consider the writing product students complete in this task

and who is involved in the completion. The categories and applicable instances of this

class of categories can be found in Table 56.

Since this task was an opportunity for students to express their personal

understandings and to struggle with the work, the individual was central in the actual

production of the original written work. The individual student was both the writer

(2.1.1a) and the only collaborator (2.1.2a), and they draw only on their individual

learning of class content as a source (2.1.5.2). The written product was intended to

communicate to a peer how to solve the equation, so the audience is that of a peer

1. Intended Area of Change/Purpose1.4 Mathematical content

1.4.2Procedural understanding1.4.3Conceptual understanding

1.6 Communication ability1.6.1 "People-talk" - normal speech1.6.3Standardized test-preparation1.6.4Writing Across the Curriculum

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Table 56: TIPS Practical Product Specifications

(2.1.3c). More people serve as readers of the written product. The work is read by the

teacher (2.1.4.2) as she observes student work and helps them answer the question, by

the students (2.1.4.3) as they read their paragraph aloud to another student in the

pairing process, and by peers through this same process (2.1.4.4). Therefore, there is a

match between the intended audience and the reader, which may make this assignment

more authentic for students.

Students are asked to write a paragraph with 3-4 complete sentences using

words rather than numbers. Therefore, students are expected to write a paragraph as

the unit of writing (2.2.1.1d) and are given a minimum length (2.2.1.2.1). The

direction of 3-4 complete sentences could also be considered a maximum length, but

this is not how it was intended. The grammar and spelling requirements do ask

students to use complete sentences (2.2.2b), but grammar and spelling are not checked

and no format is specified. This task asks students to consider a particular example of

2.1 Contributors2.1.1a Writer(s): Individual student2.1.2a Collaborators: Individual student2.1.3c Audience: Peer/Class2.1.4 Reader

2.1.4.2Teacher2.1.4.3Self2.1.4.4Peer(s)

2.1.5.2 Sources: Individual learning of class content2.2.1.1d Units of Writing: Paragraph2.2.1.2.1 Length Restrictions: Minimum length

2.2.2b Grammar and Spelling RequirementsComplete sentences required

2.2.3a Breadth of Topic: A particular example2.2.4a Use of Visuals and Graphics: None expected2.2.5a Multiplicity of Answers and Methods

One answer, one method2.3c Level of Student Manipulation

Applying modeled skills to a new example2.4a Student Choice: None

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solving a linear equation, which determines the breadth of topic (2.2.3a). No graphics

are expected for this particular task (2.2.4a), and correct student work is expected to

use one method to determine one answer (2.2.5a). This may not always occur as

students make mistakes or discover other ways to solve the equation, but it is expected

that students will follow the same method they had learned the previous day. Since

this is a short classroom task, students are given no choices (2.4a); this also allows the

whole class to discuss the work together at the end of the TIPS process.

The student manipulation required for this task involves more than copying.

They are faced with a new example and must do it independently, so they are at least

at the level of applying modeled skills to a new example (2.3c). Since they are only

explaining this example, the task cannot be classified at the higher level of

manipulation. This higher level would require a general explanation of how to solve a

linear equation. Some students may include this, but it is not required by the task.

Assignment: Theoretical Product Specifications

In this class of categories, the cognitive demands of the assignment are

classified, with a specific focus on what is required to complete the assignment

satisfactorily rather than what written work actually results from the task. The

categories in this class and the instances that apply to this task can be found in Table

57.

Table 57: TIPS Theoretical Product Specifications

The function of writing of this task is transactional (2.5c). This can be

recognized from the instruction that students write as if they were explaining to a peer:

2.5c.b Function of Writing: Transactional: Report2.6c Bloom's Taxonomy: Application

2.7.1.1Level of Language: Particular procedural2.7.2.3Aspects of Mathematics: Algorithmic

2.8.4Connections: Concepts and procedures with related examples2.8.4aExample only

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they are writing to convey how to solve this particular linear equation. It is not

expressive in focus, since students are not writing about their personal thoughts and

feelings related to this task, although some expressive elements may be found as

students express their difficulty or ease as they explain the procedure. Neither is the

writing poetic, in that the finished product is not performed for the audience or

intended to give pleasure to the writer and creator. This task does not require

generalization, and therefore, students are expected to write at one of the three lower

levels of transactional writing: record, report or generalized narrative. The latter is

also eliminated since students are dealing with one example rather than a group of

examples. Therefore, the transactional level is either record or report. It is possible to

think of this work as a record (2.5c.a) as students record what they are doing as they

are doing it. However, students are making some determination of the steps they are

using rather than just observing the steps and recording them. This element of choice

as to what to include is consistent with a report (2.5c.b), so this is the most accurate

classification.

The cognitive level required in this task, as meausured by Bloom’s Taxonomy

is application (2.6c). Students are being asked to apply their knowledge of how to

solve linear equations to this particular example. This also requires significant

Comprehension, the immediately lower level of the Taxonomy, as students understand

the process that they have to use. If students wrote about a similar example that they

had first solved as a class, this would be the level of cognition required by the task.

However, the task is classified according to the highest level of Bloom’s Taxonomy

required, since this is a hierarchy where each level requires the lower levels, resulting

in the determination of application.

Since this task asks students to solve a specific problem using a standard

procedure, most student language will be specific to this problem and procedural in

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nature. Specifically, the expected student language would be classified as particular

procedural (2.7.1.1). No other levels of language are expected; there is no requirement

to discuss any general setting and no elements of the task require descriptive language

rather than procedural. Of course, these may occur in a few students’ work if they talk

about the procedure in general (generalized procedural) or mention that this is a linear

equation that they have to solve (particular descriptive). The procedural nature of the

task also influences the aspects of mathematics that students need to use in their

writing. Students need to use the algorithmic aspect (2.7.2.3) in order to discuss the

solution, but are not likely to use any of the other forms. Again, the few who discuss

linear equations in general may use other aspects, like methodological aspects that

deal with more general elements (e.g. ‘we undo operations in the opposite order they

were done to the x’) or logical aspects that explain why they make certain steps.

However, these are not required by the task. Theoretical and conventional aspects

seem irrelevant to the example in this task.

The only connection students need to make in this task is the connection

between what they know about solving linear equations with this particular example of

a linear equation (2.8.4). There is no need to draw on outside experience, make new

connections with prior mathematical learning, or connect concepts to procedures or

symbols in a new way. Students are working on a particular example, and no general

explanation of the process is required, so within this instance, this is classified as an

example only (2.8.4a).

Assignment: Process and Context

In this section the greater context of the task within the classroom is

considered, including issues of related activities, repetition and communication of the

task, and time, place and sequencing of the task. The categories within this class and

the instances that apply to TIPS can be found in Table 58.

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Table 58: TIPS Process and Context

2.9.1 Groupings2.9.1.1Individual2.9.1.2Pairs2.9.1.4Class

2.9.2.2 Sequencing of Activities: Grouping after writing2.10.1 Modifying Writing Within the Same Structure

2.10.1.1Self-modification2.10.1.2Responding to peer comments2.10.1.3Responding to teacher comments

2.10.2 Adapting Writing into a New Structure: None (N/A)2.11.1f Task Frequency: Daily2.11.2d Importance/Centrality of Assignment Type

Regular, low value series of assignment2.11.3b Overlap of Material with Other Assignments

Content repeated in other activities2.11.3b.1Lecture/class discussion2.11.3b.2Activity/exploration2.11.3b.3Group work2.11.3b.5Exercises (routine)2.11.3b.6Tests/summative evaluation2.11.3b.7Other writing activities

2.11.4c Placement in Learning Sequence2.11.4c.bFollow-up for introduced material: Novel context

2.11.5b Relationship Between Words and SymbolsExplaining symbolic work as it is completed

2.12.1 Mode of Assignment2.12.1.1Given verbally2.12.1.2Given in writing to class as a whole

2.12.2b Modeling of Assignment: Some modeling of assignment2.12.2b.1Processes of assignment modeled2.12.2b.2Example(s) of assignment given

2.13.1a Place of Completion: Entirely in class2.13.2a Time to Complete Assignment

Task given and done in same class period2.13.3c Amount of Classroom Time: 5-20 minutes2.13.4a Expected Time at Home: No time2.13.5a Timing Within Class Period: Beginning of Class Period2.14.2 Relevance of Task Context: Pure mathematical work

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Although this task is written individually, a significant amount of work is done

in the class to process the written product that results. Students share their written

work in pairs, and then about a quarter of the students read their work to the whole

class. Therefore, a number of groupings are involved: the individual (2.9.1.1), pairs

(2.9.1.2) and the class (2.9.1.4). All of these groupings, other than the individual

student, occur after students have written their answers (2.9.2.2). Revision is part of

this structured processing of the written work. Kimberlee gave them the opportunity

to Re-Ink on this particular day, allowing them to make changes to their work. This

revision did not change the form of the written product, so the category Modifying

Writing Within the Same Structure (2.10.1) applies, while the alternate category of

Adapting Writing into a New Structure (2.10.2) does not. Each student revised

their own work, and the theory of Collins Writing views this self-modification

(2.10.1.1) a response to reading the written product aloud. Since they had read to a

peer, there was a structured opportunity for peer comments which could affect the

revision (2.10.1.2), and they also were responding to teacher comments (2.10.1.3),

given both to individual students as Kimberlee circulated throughout the classroom

and to the class as a whole as she reviewed what she had heard when students read

their work to the class.

This type of task, the Problem of the Day (POD), occurred daily (2.11.1f), and

Kimberlee had been using the TIPS process as part of the POD for about a month.

These paragraphs were required regularly, but did not have a high value, forming only

a few points in the notebook check that occurred every four to six weeks. The low

grade value combined with the time spent on this task every class, signifies that this

type of task is important, but not very important. Therefore it is classified as a regular,

low value series of assignments (2.11.2d). The content in this task applies content

addressed in other activities of the class in the same form, and therefore is repeated

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(2.11.3b) rather than expanded in these activities. The variety of activities that

address this content is wide and varied, and is supported by a curriculum that involves

many different activities. Students had learned about solving linear equations the

previous day through lecture and class discussion (2.11.3b.1) and hands-on

explorations in the curriculum (2.11.3b.2). These activities are done in the context of

groups (2.11.3b.3) and reinforced through routine homework exercises (2.11.3b.5). In

Kimberlee’s class structure, students will have written a class summary [Appendix A:

31] about this learning the previous day, so the content has been addressed through

other writing activities (2.11.3b.7). After this task, solving linear equations will be

part of a test or other summative evaluation (2.11.3b.6). From this description, it is

clear that this task is placed near the end of the learning sequence for this content, as

follow-up for the introduced material in the novel context of a new linear equation to

solve (2.11.4c). In this particular task, students are explaining their symbolic work as

they are completing it (2.11.5b). Some students may break out of this pattern and

solve the equation symbolically and then write the paragraph, but this is not the

intention of the task. In contrast, in the previous class students completed similar

symbolic work and then wrote a class summary about this topic, so the writing task

clearly followed symbolic work. Although there is explanation involved, this is

standard algebraic manipulation and not connected to any context, so the relevance of

the task would be classified as pure mathematical work (2.14.2).

This assignment was communicated and modeled for students in a number of

ways. The prompt was written on the overhead projector for the whole class

(2.12.1.2) and the parameters of the assignment, such as length and audience, were

given verbally (2.12.1.1). There was some modeling of the assignment (2.12.2b), both

through previous uses and through explanation at the time. The processes of the task,

both of the task structure and content, have been modeled some for students

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(2.12.2b.1). Students had already used the TIPS process, and the content of the task

was taught on the previous day and therefore the content processes have been modeled

as well. Since students have used this process over time, they have also seen examples

of similar completed tasks (2.12.2b.2). In fact, the very structure of the task requires

that students read examples to each other.

The task is given about 10-15 minutes (2.13.3c) at the beginning of the class

period (2.13.5a). These tasks are entirely within the class period (2.13.1a), both given

and completed within the class (2.13.2a). Therefore, students are not expected to

spend any time at home (2.13.4a).

Response and Assessment

This group of categories concerns what happens after the task is completed,

considering both responses to the task in the form of grading and comments and any

use of the assignment in future learning. The categories and the instances that apply to

this use of TIPS can be found in Table 59.

Since this was a daily assignment, Kimberlee did not comment on student

work in writing because of time constraints. Instead she comments verbally to

students (3.1.1.1.2). These comments are made to students individually (3.1.1.2.1) as

she circulated around the classroom as students were working and to the class as a

whole (3.1.1.2.2) after the students have shared with each other and before they

revised their work. These comments usually took the form of questions intended to

help the students understand the content of the task. This means that students get

verbal responses as a class to every written product (3.1.2.1) and will get individual

responses occasionally (3.1.2.2). These PODs are compiled in one section of student

notebooks, which also receive the feedback of a grade (3.1.2.3). Therefore, the

assignment are both compiled (3.1.4b.2) and turned in after the day they are

completed (3.1.4b.1b). Since this compilation is done by students (3.1.5c.a) in their

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Table 59: TIPS Response and Assessment

class notebook, it will be available to students at any time. Peers also responded to

student writing verbally through pairings (3.1.3b.1.1). This particular use of TIPS did

not include class discussion of the student work, even though students shared written

work with the whole class, since the students were getting the main ideas, and the

teacher only had to summarize these ideas.

After the whole task has been completed, the written products are used

primarily as a source for a grade (3.2.1). These tasks are graded based on effort and

completion (3.3.1b), so the categories of Content vs. Expression (3.3.1c.1) and

Standards for Justification (3.3.1c.2) do not apply. With this in mind, the tasks are

graded holistically (3.3.2a), with only 5 points given for all the PODs each time

notebooks are collected. Other class activities recorded in the notebook are given

3.1.1 Teacher Comments3.1.1.1.2Form: Verbal

3.1.1.2Group3.1.1.2.1Individual3.1.1.2.2Class

3.1.2.3 Feedback Frequency3.1.2.1Every written product3.1.2.2Occasional response3.1.2.3Compilations of writing

3.1.3b.1.1 Peer Response: Verbal feedback: Pairs or small groups3.1.4b Collection of Writing

3.1.4b.bTurned in: Later3.1.5c.a Availability to Students: Compiled: By student

3.2.1 Use of Completed Assignments: Source for grade3.3.1b Standards for Grading: Graded on effort and completion

3.3.1c.1 Content vs. Expression: (N/A)3.3.1c.2 Standards for Justification: (N/A)

3.3.2a Grading method: Holistically3.3.3.3 Grader: Teacher

3.3.4 Percentage of grade: very small (1-2% for type)3.3.5b Student Awareness of Assessment Parameters

3.3.5.bStudents have access to grading scheme

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more credit, so these PODs account for only 1 or 2% of the course grade (3.3.4). The

teacher assigns these grades (3.3.3.3). Students are aware of these grading parameters,

since they have had their notebooks graded in the past, so students have access to the

grading scheme (3.3.5b).

Summary

Some of the elements that are most unique about this assignment include the

specific process of writing and the structure with which this writing is processed.

Students are given time intended only for thinking before they begin to write and then

are given opportunities to share their writing with another student and the class. There

are a large variety of opportunities for students to receive feedback from other students

and the teacher, despite time restrictions that make written comments impossible.

Students are also given the opportunity to modify their writing and, thereby, their

thinking about this content. The content covered by this task is also repeated in many

other activities, allowing students to learn it in many different ways.

Comparison of Tasks

Both of these tasks require the student to work individually for different

reasons: Olympic Games recreates the challenges that students will have to face on the

AP examination and holds students individually accountable for their knowledge

while this use of TIPS asks students to work on their individual understanding of

solving linear equations and their personal expression of this understanding.

The communication of the requirements for length and grammar and spelling

vary between the tasks although they have similar classifications in this area, because

Kimberlee is much more explicit in her instructions to students than Laura is. This

reflects the difference in the basic expectations between a general 8th grade

mathematics class and an AP Statistics class. The concepts and required cognition of

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the two tasks also reflect the different students and content levels of the classes: AP

Statistics requires students to integrate a number of concepts from a unit and analyze

them using higher levels of cognition and functions of writing, while an 8th grade

mathematics class is working on a specific example of a process and requires

relatively lower levels of cognition and functions of writing. These differences are

increased because of the different focuses on the assignments: Olympic Games occurs

at the end of a unit while this use of TIPS occurs in the midst of a unit as a short

assignment to begin the class period and review material specific to the previous

lesson. The different parameters of the tasks match the respective goals and

placement in the learning cycle, and also account for different lengths of time being

allotted to the different tasks. This also corresponds to the TIPS task’s completion

within the classroom and the Olympic Games task’s completion at home.

Both tasks occur in a sequence of writing tasks, so students have basic

expectations of the nature of the task and how it will be assessed. The greater

frequency of the TIPS assignment also motivates the difference in comments, since

there is no time for Kimberlee to make the extensive written comments on each POD

that Laura makes on each end of unit project. This is also consistent with the fact that

Olympic Games and each similar task was graded based on correctness according to a

distribution of points, while TIPS was graded holistically in a compilation based on

completion.

This comparison is easier to make after having analyzed the assignments using

the classification. The different elements are juxtaposed within the categories so

differences and similarities are more apparent. Also, general trends within the

analysis of a writing task can be determined and connections made between the

intentions and the actual paraments.

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Challenges of Classification

A number of challenges are inherent in using this classification. I believe there

are four major challenges: determination of intention by someone other than the

teacher, the difficulty of predicting the theoretical problem parameters, differentiation

between issues of individual writing tasks and those of types of writing tasks and

decisions about whether some requirements are implicit or explicit within the task.

These four areas will be discussed below in light of the foregoing analyses.

Teacher Intentions

It is difficult for any person to determine someone else’s intentions. Therefore,

for the first category of Intended Area of Change/Purpose (1), observation and

documentation of the assignment cannot determine the teacher’s intentions although it

may hint at them. Therefore, personal interaction with the teacher is necessary to

determine which instances of this category apply to any given task. This is important

when studying this category’s effect on learning. This is also a variable that may be

impossible to control in multi-teacher studies of the effects of writing tasks, because

the same task may be used by the different teachers for different reasons. When

students complete assignments, they may have the same difficulty determining why

the teacher wants them to do a certain writing task, and this may affect their focus as

they do the writing task. Gottschalk & Hjortshoj (2004, p. 31) recommend that the

purpose of an assignment be communicated to students as part of the assignment.

Theoretical Product Specifications

The five categories of theoretical product specifications, Function of Writing

(2.5), Bloom’s Taxonomy (2.6), Level of Language (2.7.1), Aspects of

Mathematics (2.7.2), and Connections (2.8), may be difficult to determine before the

task is given. To determine the instances within these categories requires some

identification with students at their current level of learning, since different levels of

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cognition are required to do the same task when starting with different levels of

knowledge and understanding. An 8th grade student may be using application-level

cognition skills in Bloom’s Taxonomy (2.6) to solve a linear equation while the same

task may be at the knowledge level for an AP Statistics student since this is very

routine for them. The same difficulties occur when classifying the Level of Student

Maniplation (2.3). Since these tasks are given to classrooms that are never entirely

homogeneous, the required levels may vary from student to student and the

classification is difficult to make as a whole. This difficulty is exacerbated by the fact

that these categories may require more expertise to understand and use, especially the

Function of Writing (2.5). This category draws on composition research, an area of

expertise that mathematics teachers and mathematics education researchers do not

usually share. Meeting these challenges requires careful attention to the intentions of

these various categories in differentiating between the rhetorical demands of the

writing task (2.5), the cognitive demands (2.6), particular and generalized, procedural

and descriptive language (2.7.1), the mathematical roles of the language (2.7.2),

required connections within and beyond the classroom (2.8), and the manipulation of

information required (2.3). In comparing writing tasks, these differences will

frequently be easier to judge relative to each other, as it is clear above that Olympic

Games requires more demanding rhetorical roles (2.5), a higher cognitive level (2.6), a

wider variety of language in the length and breadth of the task (2.7), and greater

student manipulation (2.3). This comparison may be more important than the actual

determination of the instance when trying to determine how learning depends on

change in these categories. However, with a large collection of tasks it is impossible

to compare every pair of tasks and the different instances should be used. In this case,

consistent classification with the central principles of the variation at the heart of the

choice should be sufficient. Still, more attention to classification in these categories

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and communication of how these categories are determined for a given study is

important.

Individual Writing Task and Type of Task

Since the classification is sorted by the sequence of the assignment, it may be

difficult to determine whether a category applies to the individual task or the type of

task. Therefore, two tables are included below which list categories that describe

types of tasks rather than individual tasks (Table 60) and categories that contain

instances that may only occur if the task is part of a larger series of tasks (Table 61).

Table 60: Categories that Classify Types of Tasks

The categories of Task Frequency (2.11.1), Importance/Centrality of

Assignment Type (2.11.2), and Feedback Frequency (3.1.2) all measure variables of

the type of task rather than the individual task. With assignments that are isolated and

do not fit into a continuing type of task, only certain instances of each category can

apply so the variation is limited.

Table 61: Categories with Instances that Occur for Types of Tasks

Other categories contain instances that are affected by repetition of the type of

task or will only occur if the task is part of a larger series of tasks. Two of these

categories include instances that discuss the compilation of student work (3.1.4, 3.1.5),

and this is much more likely if the assignment type is repeated. Such a compilation

also makes it more likely that the student will use the completed assignment as a

2.11.1 Task Frequency2.11.2 Importance/Centrality of Assignment Type3.1.2 Feedback Frequency

2.12.2 Modeling of Assignment3.1.4 Collection of Writing3.1.5 Availability to Students

3.2 Use of Completed Assignments3.3.4 Percentage of Grade3.3.5 Student Awareness of Assessment Parameters

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reference (3.2e). If the assignment type is repeated, it is also much easier to model the

assignment (2.12.2) and students will be more aware of how the tasks is assessed

(3.3.5). Finally, the portion of the grade devoted to the task (3.3.4) may be measured

either by the type of task or by the individual task, as discussed in the description of

this category.

Explicitness of Task and Expected Tasks

A number of times in the task analyses above, choices had to be made about

whether an aspect of the task was implicit or explicit in order to determine which

instance of a category applied to the task. For example, in determining the grammar

and spelling requirements (2.2.2) of the Olympic Games task, no specific mention was

made of the need for complete sentences, but the decision was made that a “report”

implied this directly. However, even though students were expected to write well, it

was not classified as a task either requiring a specific format or correct grammar and

spelling because these factors did not directly affect the grade and were not likely to

make a difference in whether the information of the task was communicated clearly.

Certain categories, such as the Intended Area of Change/Purpose (1)

specifically deal with parts of the task that may not be explicit in what is

communicated to students. This category judges something implicit by its nature.

However, all the other categories classify the ways the expected task actually differs,

and should be based on more explicit elements of the task. In the example given

above, good student work will have complete sentences, but may or may not have

perfect grammar and spelling. Likewise, the theoretical product specifications classify

the expected task – what will be included in a written product that meets the standards

of the assignment. These directions may not, and probably will not, be specified in the

writing task, but these differences can be judged by what is expected. Students may

go beyond these standards, and some may fail to meet them, so I have chosen to define

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the classification in all but the first category by the expected task in order to provide a

benchmark to judge by. Sometimes this will be easier to judge than others, as is the

case in determining who the writer is or what unit of writing is expected. Other times,

as is the case with the theoretical product specifications, determining what is expected

of the task will be more difficult. In either case, the expected task is what needs to be

judged.