# Digital Portfolios: A Richer Picture

**Essential Question**: Can we get a richer picture of student achievement and school effectiveness by developing authentic assessment tools similar to those developed by teachers in Nebraska and adding to it the reflective thought and writing provided by a portfolio system?

The Education Reform Act of 1993 signaled the onset of education reform in the state of Massachusetts. The most notable result of this Act is the Massachusetts Comprehensive Assessment System (MCAS). This high-stakes assessment is the center of the conversation on student, teacher, and school accountability in Massachusetts. This conversation rarely includes the issue of the complexity of the task of assessing what students have learned and how their public schools have nurtured that learning. Nevertheless, the 1993 Reform Act makes the following provision:

“The system shall employ a variety of assessment instruments on either a comprehensive or statistically valid sampling basis. Such instruments shall be criterion referenced, assessing whether students are meeting the academic standards described in this chapter. As much as is practicable, especially in the case of students whose performance is difficult to assess using conventional methods, such instruments shall include consideration of work samples, projects and portfolios, and shall facilitate authentic and direct gauges of student performance. Such instruments shall provide the means to compare student performance among the various school systems and communities in the commonwealth, and between students in other states and in other nations, especially those nations which compete with the commonwealth for employment and economic opportunities.”

The Massachusetts Department of Education is not currently calling for the assessment and evaluation of work samples, projects and portfolios for all students as the Ed Reform law allows. However, according to Gerald Bracey in his article, “Big Tests—What Ends Do They Serve?” (Bracey The Big Tests.pdf), “The best assessment system, but a difficult one to bring off, begins with teachers rather than with external measures that are imposed on them. The state of Nebraska developed such a system—the School-based Teacher-led Assessment and Reporting System (STARS)—based on instruction-driven measurement as opposed to the dysfunctional, measurement-driven instruction that predominates elsewhere.” In Nebraska the STARS system has generated data that indicates students learn more as a result of this teacher-led initiative.

Can we get a richer picture of student achievement and school effectiveness by developing authentic assessment tools similar to those developed by teachers in Nebraska and adding to it the reflective thought and writing provided by a portfolio system?

One challenge of such a proposal is how to convert authentic student assessments into numeric data? Look to Wiggins and McTighe’s “Understanding by Design” for a bridge between these information types. In their “Rubric for the Six Facts of Understanding”, they have created a conversion tool. Students and teachers can evaluate student work, classify it under one of the six facets, and then assign that particular work to a location along Wiggins and McTighe’s spectrum of understanding.

For example, 7th grade students simplifying math expressions in a video clip are exhibiting the facets of explanation and application. The explanation spectrum goes from sophisticated to naive; the application facet ranges from profound to literal. If teachers can modify these criteria to “kidspeak” and assign point values, then numeric data are created. And, if students’ portfolios exhibit a series of these video assessments, students and teachers can see the progress…the deeper level of understanding that develops as kids learn and grow.

This year I plan to develop such a system of portfolio assessment using all of these components: authentic student work in the form of before and after video clips, student self-evaluation using modified forms of Wiggins and McTighe’s rubric for the Six Facets of Understanding, and teacher evaluations using the original Six Facets Rubric.

As of today, October 18, 2010, students in my 7th grade Computers classes have done some brushing up on the rules for order of operations in evaluating algebraic expressions. We used puzzles in an Excel spreadsheet to do this. At the completion of these puzzles, students created short videos of themselves evaluating math expressions by hand and explaining their thinking as they went.

Open Bracey The Big Tests.pdf

### Video Clip: The Parentheses Make the Difference

Marshall, a 7th grader, is demonstrating what he knows about order of operations in mathematics. This video is a preliminary assessment of what he already knows about evaluating algebraic expressions.

Prior to this video session, Marshall worked with a partner on order of operations puzzles to refresh his memory of this common middle school math concept.

He is writing on the video worksheet form, which allows him to choose the difficulty of the problem and gives him space to work out the two versions of the problem. On page 2 of the worksheet is a rubric for him to grade his performance in the video.

By solving both versions of his example, Marshall is able to explain the nuances of order of operations and thus demonstrate his knowledge.

His references at the end to the effects of the parentheses leave us hanging and wanting more details from him as to exactly why and how the parentheses affect the outcome.

Click here to view the video worksheet form:

video worksheet.pdf

Open Video worksheet.pdf

### Order of Operations Activities

The unit in the 7th grade Computers course is called Combining Practice. These activities involve solving math puzzles in an Excel spreadsheet, collaborative writing on what you know about the rules for order of operations, and a quick self-grading activity to indicate students’ current level of understanding of order of operations.

The Combining Practice puzzles introduce students to writing formulas and functions in Excel. The challenge is to combine the numbers, like 1, 2, and 3, in such a way as to make the result come to each of the values of zero to ten. For example, in Excel, to make the value come to zero, the formula is “= 1 + 2 – 3”.

Students work with a partner on this puzzle. This activity is easy to explain to students and it’s easy for them to start solving. But to complete all the entries is difficult. All parts of this puzzle have a solution, but some parts require complex formulas which include built-in Excel functions. For example, to get 8 using only 3, 6, and 9, Angela and Sabina entered:

=ROUNDDOWN(SQRT(AVERAGE(9, 3)), 0) +6.

Here are the puzzle solutions submitted by two different partnerships:

(Note: Click on the link, choose Save. After saving, click Open.)

Prewriting occurred when students were asked to submit a Word document containing two paragraphs. Paragraph one was to explain what the rules of order of operations are, and paragraph two was to explain why we need these rules in the first place. The purpose of this activity is to get students writing in detail about the process and to step back and consider why mathematicians worldwide accept these rules for simplifying expressions.

Here is the writing sample of one partnership:

The final activity leading up to making the video was to have each student rate their own knowledge of order of operations. This was done simply by checking the option that best fit each student’s situation.

Click on the link below to view how Marshall rated his understanding of order of operations.

marshallsrating.pdf

Open AngelaSabinapuzzle.xls

Open marshalldannypuzzle.xls

Open marshallsrating.pdf

### Video Clip: A Careful Explanation

In this clip, Angela gives a careful and detailed explanation of the rules for order of operation in evaluating algebraic expressions. She then uses these rules to successfully solve both versions of her example.

She prepared for this by solving some puzzles with her partner and then writing about the process.

Angela used the video worksheet form, which allows her to choose the level of difficulty of her problems and gives her room to work out both versions of the problem. On page 2 of the worksheet, she can fill out a rubric to help her evaluate her performance.

Click the link below to view the video worksheet:

Video worksheet.pdf

Open Video worksheet_0.pdf

### Next Step: Build an Artifact

**Build an Artifact**

Our next step will occur after students have formally covered order of operations in their math classes. At that point we will again create short videos of students working out problems and explaining their work.

Next, they will create an artifact of understanding around order of operations. First, students use the Wiggins and McTighe rubrics, in modified form, to rate their own change in understanding of the rules as evidenced in the two videos.

The artifact’s second step is to write reflectively about their knowledge and understanding of order of operations. The two videos, the rubric and the reflective writing will then be published by students in their digital portfolios.

In addition, the math teachers will be asked to evaluate students work from their videos using the original Six Facets rubrics. They will assign a level of understanding, from sophisticated to naïve, which will carry a value from five to one, to each set of student videos and write a paragraph to support their rating.

It will be necessary to balance the information we glean from both the student’s artifacts and their teacher’s evaluations. This graphic from the work of Dr. Helen Barrett depicts both assessment cycles and the differing interests of students and their teachers. Resolving these differences will be necessary, and challenging.

Excerpts of this work will appear here in the Digital Is site to document the progress of this effort. Next semester, beginning in January of 2011, the other half of the current 7th grade class will be in the Computers course. Those students will be asked to do a similar task based on the distributive property rather than order of operations.

Open Balanced Assessment.pdf