Evaluation, Reflection, and Assessment

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The classroom environment enables children to demonstrate what they know through a variety of authentic assessment strategies (exhibitions, demonstrations, journals, group discussions, debriefings, interviews, and conferences). Assessment is constant and ongoing so as to identify students' strengths and learning approaches as well as their needs. Teachers observe play, watch children drawing, listen to conversations and ask questions. As children explain their thinking, teachers can assess their level of understanding. "Students points of view are windows into their reasoning. Awareness of points of view helps teachers challenge students, making school experiences both contextual and meaningful. Each student's point of view is an instructional entry point that sits at the gateway of personalized education" (Brooks & Brooks 1993, p. 60).

Documentation is vital for assessment. Documentation includes narratives of child-to-child conversations, child-to-adult conversations, photo portfolios (photo narratives), wall displays, and written summaries. Documentation offers opportunities for children to evaluate their own work, for teachers to keep parents better informed (knowledge web), and for teachers to gain a better understanding of how children learn. Documenting conversations and representations at the beginning and at the end of the project for the group as a whole and for each individual child gives perspectives of growth in all dimensions including vocabulary, concepts, knowledge, skills and dispositions.

Tomlinson's "Planning Model for Academic Diversity and Talent Development" (Tomlinson, 1996, p. 162) is a useful tool for examining how children's responses showed growth. Instead of using the model to differentiate instruction, the teachers have used it to examine how responses to the activities were differentiated among students as well as how they demonstrated growth in students throughout the study. In a project-based classroom, where many activities are open-ended, using Tomlinson's indicators can show growth. Teachers can demonstrate through child portfolios how children have gone from simple to more complex responses; concrete to more abstract understandings, and less independence to more independence in work habits and dispositions.

In an environment of inquiry, teachers look for evidence of children's growth (Klein & Toren, 1998). Children's questions may evolve from general to more specific once children have more knowledge about a topic. They may transfer their learning by making links to other things that they know and with which they are familiar. They may incorporate the new vocabulary into their every day language. Teachers look for growth in fluency of ideas and in ways in which children generate questions, solutions, hypotheses and theories. Teachers look for growth or change in students' understandings by examining artifacts of learning, which include drawings, structures, writings, and conversations. Children may also become more self-directed, more engaged, and may strengthen their dispositions to inquire, to assume responsibility, to persevere, and to take on leadership roles within a group.

The evaluation of a project investigation includes teacher reflections, student self-evaluations, parent-feedback, and an examination of each child's project portfolio to assess growth and learning. Examples of children's project portfolios are included in this document.

The primary method of assessing what students have learned in project investigations is through the documentation of their experiences. Teachers observed students carefully and provided opportunities for students' thinking to become tangible in order for teachers to see growth. Teachers listened and recorded students' ideas expressed in conversations, brainstorming sessions, interviews, writings, predictions, and representations. Teachers reflected upon class growth as well as individual students' depth of understanding by examining and comparing the documentation from the beginning to the end of the project. As demonstrated by the documentation, students made extensive growth in their vocabulary, in their awareness of measurement in different fields of study, in their conceptions of the importance of measurement to the world around them, and in their basic mathematical skills of measurement.

References Related to Evaluation

Anderson, T. (1996). They're trying to tell me something: A teacher's reflection on primary children's construction of mathematical knowledge. Young Children May: 37.

Brooks, J., & Brooks, M. (1993). In search of understanding: The case for constructivist classrooms. Alexandria, VA: Association for Supervision and Curriculum Development.

Klein, M. M., & Toren, G. (1998). Evidence of learning in an inquiry based classroom. Urbana, IL: Unpublished document.

Tomlinson, C. A. (1996). Good teaching for one and all: Does gifted education have an instructional identity?” Journal for the Education of the Gifted. 20, 2, 155-174.

Wiggins, G. & Mctighe, J. (1998). Understanding by design. Alexandria, VA: Association for Supervision and Curriculum Development.

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Teacher Reflections

The topic of Who Measures What in our Neighborhood? was active and concrete with many opportunities to measure. The students studied measurement over a period of months, which allowed for in-depth inquiry and research towards understanding. The topic also allowed for complexity. Some students learned that measurement included time and money, abstract concepts that provided challenge and differentiation of instruction.

Growth in Vocabulary

In the first topic web in Phase 1, students remembered being measured or measuring at school. A few students brainstormed ideas that were not measurements that they had done, but they predicted that someone might have measured this way. The teacher categorized the students' responses on the web and found that they fell into categories of linear and weight measurement, with a few responses including liquids or solid quantities. No student recalled or used the terms area, volume, time, or money. Perhaps they did not consider these areas as being measurement. At the end of the project in the Student Measurement Topic Web 2, students categorized what they learned about measurement. They titled their categories: New Vocabulary, Ruler Work, Weight, Clocks and Time, Thermometers, How Much, and 1 to 10 Rating Scale.

Student Measurement Topic Web 1		Student Measurement Topic Web 2

Growth and Awareness of Measurement in Different Fields of Study

At the beginning of the project, when the students predicted what kinds of measuring they thought people were doing in and around the school (Phase 2 predictions), twenty-one predictions were related to prior experiences of the class. The students were surprised that the preschool students and the people in the offices outside the classroom were not engaged in the kind of measuring that they predicted. However this opened their minds to a broader view of measurement in the neighborhood.

A close look at the web (Student Measurement Topic Web 2) created at the end of the project, indicated that the students were influenced by their experiences. A comparison of the web created at the end of the project with the web from the beginning of the project showed students had increased their understanding of the measurement in different fields of study, the kinds of measuring tools that are used for collecting data, and the many things in their lives that can be measured.

To gather more information about what the students understood, the teachers asked parent volunteers to elicit more detail from the students about brainstormed web responses. Students dictated and embellished their original ideas as parents typed their responses on classroom computers. Many students named a fact from an expert, an experience, or a field visit from their work during the project. The text of these expanded responses are found in the Expanded Web. Some examples are listed below:

The teachers wanted to know if students had a definitional concept about measurement. On the last day of the project, teachers prepared a handout that asked, "What is measurement?" Student responses included volume, quantity, number, and time. The teachers noted that the students in the class had broadened their views of measurement. They referred to the practical applications of measuring that they had engaged in during the project investigation. These responses reflected that they had answered their original researchable question, "Who Measures What in our Neighborhood?" They also gained an operational definition of measurement through their experiences.

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Growth in Knowledge About Measurement

Teachers noticed an increase in the number of students including the units of measure in their conversation and recording sheets. In January, when asked how tall they were, students responded with a number without a unit such as 11, 5, 4, 8, 5, or 60. In most cases the number was in error. Students measured themselves and many other items throughout the project. On 2/19, one of the students shared his measuring work at a group meeting.

By the end of the project when measuring and weighing the chicks, all students included units of measure on their recording sheets. This demonstrated that they gained a better understanding of units of measure. Students also improved their abilities to manipulate measuring tools and to measure using both standard and non-standard units.

LS records the predictions and results of measuring chicks and includes in temporary spelling ounces ("os") and inches ("n").		AC (kindergartener) uses temporary spelling to write centimeters, ounces, and inches.

Growth in Representation

Teachers saw growth in student's ability to make three-dimensional representations out of boxes and junk. Teachers guided students' work by placing the digital photographs near the student and asking them to refer to it as they proceeded to make their representations. The teacher also asked questions to facilitate problem solving:

A comparison of representational structures made first semester to those made during the measurement project, showed growth in using rulers and comparing sizes and proportions to create more sophisticated three-dimensional models.

LS records the predictions and results of measuring chicks and includes in temporary spelling ounces ("os") and inches ("n").		AC (kindergartener) uses temporary spelling to write centimeters, ounces, and inches.

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Strengthened Dispositions to Cooperate and Persist at a Task

During Phase 2, students self-selected to work independently, in pairs, or in small groups to make their representations. All groups that worked together to make a common product reflected on the importance of cooperation. Most students listened to each other and shared their views about problems that needed to be solved. Teachers noticed that students became more articulate and backed up their opinions and ideas with reasons.

After returning from the Credit Union, four girls decided to work together to make a cash drawer. They drew their plans and chose to make their cash drawer from boxes and cardboard. Some problems stumped the group. They wanted to make partitions in the drawer to hold different sized bills. They had difficulty getting the cardboard to stand upright. The girls presented their problem at a large group meeting. CS offered to help them solve their problem. However, his solution did not influence their group. The next day, the girls brought their problem back to the large group. Another child offered to assist them. She cut a piece of cardboard and taped it to the cash drawer. (Interestingly, her suggestion was very similar to CS's idea.) For two days the girls diligently taped cardboard partitions in place and the cash drawer held separate bills.

This group also wanted to make dollar bills, coins and coin wraps that each of them had received as an artifact from the Credit Union. It was small detailed work and after a while, the group decided to donate their personal coin wraps to the representation to make it just right for the Open House. The next day, individuals changed their minds, and decided to keep their wraps at home. However, they still wanted to create representations of coin wraps.

After two weeks, all four were very pleased with the cash drawer, money, money wraps, a key, and a keyhole. They reflected on the process.

Members of the group work on the partitions of the cash drawer.		LS attempts to attach the partitions to the drawer.

The girls continue to work on the cash drawer.

PJ perfects the coin wraps.		The money drawer displayed at the Open House with the digital picture below.

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Conclusions

Teachers used students' misconceptions and misunderstandings in Phase 1, to develop instructional activities that supported conceptual growth. In a multi-age classroom not all students gain the same level of understanding about abstract and complex concepts. The discussion during the categorization of their memories showed some possible confusion between linear and weight measurement. The teacher decided to use this question to survey the class about what other children understood about types of measurement. On January 24th, the morning sign-in question asked, "Is measuring a baby's weight the same as measuring the inside of a clubhouse?" This time, two students who previously thought that it was the same answered no, along with the rest of the class. One child responded that the two types of measurements were the same. By the end of the project all students understood the difference between linear and weight measurement.

Some aspects of measurement continued to challenge students. On 4/16, some students asked questions at a large group meeting in an attempt to better understand the relationship between measurement and time.

Over a series of days, students mark time by drawing the shadow of the rod.

The relationship between measurement and money also continued to challenge students. Students going to the Credit Union asked questions about the size of money and checks and how much money the bank had. ST's questions represent those of others in the group, "How do you measure money? How big or how small is it? Why do you want to know how big the money is? How much money do you have?" At the end of the project some students in the class understood the relationship between the value of money and measurement.

At the beginning of the project, students knew there were numbers involved in measurement, but they did not have enough experiences to know the relative meanings of the number. For example, 100 degrees Fahrenheit is very hot to go outside, just right for the chicks to hatch, but not hot enough to cook the Gingerbread boy. HB wrote in her Gingerbread story that the oven was very hot at 100 degrees. She did not indicate Fahrenheit or Celsius. In a conference with the teacher, she said it was Fahrenheit. Even at the end of the project, some numbers that the students wrote, although close, were still not exact.

In conclusion, this project helped students gain an awareness of measurement in different fields of study and the importance of measurement to the world around them. Students had authentic purposes to measure, collect, analyze, and evaluate data that gave them a meaningful context for learning basic skills in mathematics. Students matured in their dispositions. They improved in their ability to collaborate and cooperate and increased their curiosity about measurement. Because the project was multi-faceted, it engaged the children for five months. The comments from student and parent reflections demonstrated that the children enjoyed the challenge of working in-depth and having the opportunities to investigate their own questions.

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Student Reflections

To gain a better understanding of what students have learned about measurement, the teachers asked them to complete a questionnaire. If students could not write their own responses, parent volunteers asked them the questions verbally and typed their responses on the computer. The questions and their responses are listed below:

1. What they would tell a friend about measurement?
2. What would you like to keep doing with measurement?
3. What are you still wondering about measurement?

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Parent Reflections

The teachers gave questionnaires to parents to determine if there was transfer of information from school to home and if students were able to generalize their newly learned concepts and apply them outside of the school context. The following are the responses from the parents:

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Continue to Part 2 of Measurement Evaluation (Student Portfolios) >>