Central Bucks Schools Teaching Authentic Mathematics in the 21st Century

Barth, R. (1990). Improving schools from within: Teachers, parents, and principals can make the difference. San Francisco, CA: Jossey-Bass.

Dana, N.F., & Yendol-Silva, D. (2003). The reflective educator's guide to classroom research: Learning to teach and teaching to learn through practitioner inquiry. Thousand Oaks, California: Corwin Press.

Elliot, J. (1988). Educational research and outsider-insider relations. Qualitative Studies in Education, 1 (2),155 – 166.

Sammon, G. (2007). Creating and sustaining small learning communities: Strategies and tools for transforming high schools. Thousand Oaks, CA: Corwin Press.

Wiburg, K., & Brown, S. (2007). Lesson study communities: Increasing achievement with diverse students. Thousand Oaks, CA: Corwin Press.

© Copyright 2007 Learning Sciences International.
All Rights Reserved.
Prediscussion Activity: Individual Student Needs

In this activity you will reflect on your planning and delivery of instruction based on individual student needs in your classroom. While you are expected to focus on your individual students, you must keep their identities anonymous.

1. 
   Respond to the following to guide your thoughts:
   
   1. 
      Without naming actual student names, how would you describe the unique social, emotional, or academic need that you have identified of a particular student?
      

2. 
   How will you address this specific need based on what you have learned thus far about authentic instruction? Who could you ask for assistance? How will you gauge success?
   

3. 
   What role could higher order technology play in addressing this need? Are there assistive technology tools and/or strategies that could be implemented as you develop the authentic instruction?
   

4. 
   Can you involve the students in choosing higher order technology tools based on their own experience as "digital natives"?
   

2. 
   Based on what you know about your students needs, and the research question that you identified at the beginning of this unit, consider the following Web 2.0 technologies: wiki, blog, podcast, vodcast, or RSS Feed.
   
   1. 
      Choose a specific Web 2.0 technology from the list that you have not used before in a classroom setting.
      
   2. 
      Design instruction around this technology to meet the need of your research question. Use the resources provided throughout this course to guide you on how to use the technology, and also how to use the technology to elicit higher level thinking in your students. Consider consulting your instructional technology specialist for additional implementation ideas.
      
   3. 
      Deliver your instruction, using this technology to your students. Document in detail this experience.
      

3. 
   For the purpose of the online discussion, summarize your experience in using the new technology in the space provided. Please include what was challenging, but more importantly, the benefits and what you learned during the process.
   

4. 
   Fill in the "L" and "D" columns of your "Teacher Action Research K-L-D Chart."
   
5. 
   Return to the course and advance to the next screen in order to receive further instructions to share your summary online.
   

 As a result of reading the following material, the reader should be able to answer the following questions:

• 
  What is progress monitoring and post assessment?
  
• 
  Why do I monitor progress and post-assess?
  
• 
  How do I monitor progress and post-assess?
  
• 
  When do I monitor progress and post-assess?
  
• 
  How does progress monitoring and post-assessment fit into the teacher action research cycle?
  

Diagnostic assessment is the time teachers use to measure their students' background knowledge, misunderstandings, and skill mastery level. Diagnostic assessments include interest inventories, knowledge surveys, K-W-L charts, and student responses to content-specific writing prompts (McTighe and O'Connor, 2006). These assessments generally occur at the beginning of a teaching unit or cycle and are scored, but not graded.

During the course of teaching a unit of study the teacher must also assess the learning of his or her students. McTighe and O'Connor call this ongoing measurement "formative assessment." It is how the teachers check to see if what they have planned instructionally is working for their students' mastery of the content or skills. In other words, these assessments help teachers monitor the progress of their students. This is perhaps the most important time to assess and is often the most neglected by practitioners, especially at the secondary level.

Formative assessments occur throughout the teaching cycle or unit. The result of these check-ins can inform the teacher's planning, pacing, and assigning during the course of implementing a unit of study. They help the teacher make course corrections to meet the needs of his or her students as they move through the learning opportunity, not only at the end when it may be too late to correct misconceptions and misunderstandings.

Dr. Nancy Dana at the University of Florida describes four phases of teacher research: data collection, data analysis, synthesis, and action. Formative assessments or progress monitoring tools give data to analyze, synthesize, and act during a teaching episode. They give teachers information they need to direct teaching to improve student learning and increase student understanding. Formative or progress monitoring devices may be formal or informal, and graded or ungraded. They include exit slips, written responses to prompts, reflective journal entries, graded and ungraded quizzes and homework assignments, lab work, think-alouds, graphic organizers, and draft work (McTighe and O'Connor, 2006).

Once teachers have gathered the data they need to inform teaching decisions, they must determine how they will know if their choices worked. They must post-assess to determine whether their students achieved what they intended as a result of their teaching. They can also use post-assessments to gauge the effectiveness of the instructional strategies and assessment tools they used during the unit.

Post-assessments may be summative assessments which generally serve as a culminating activity, or they may serve as a formative method of checking on the effectiveness of a particular learning activity.

Summative assessments "summarize what students have learned at the conclusion of an instructional segment" (McTighe and O'Connor, 2006, p. 13). These are usually graded and recorded for credit. They include tests, final exams, research papers, culminating projects, portfolios, or long-term performance tasks (McTighe and O'Connor, 2006). They evaluate student learning and the effectiveness of the teacher's instructional design. This last statement is rarely discussed when thinking about the results of summative assessments. Teachers must use the data collected to reflect on and modify instructional units or we will continue to use these data to evaluate only the students, leaving the teachers out of the accountability loop altogether.

In his book Accountability for Learning: How Teachers and School Leaders Can Take Charge, Doug Reeves states that accountability has been reduced to test scores because teachers have not told their stories well. They have not told the tales of progress and reflection they witness and plan for every day.

Historically, as educational professionals, we have placed ourselves in discreet boxes, building four walls around our teaching, administrative, professional learning and curriculum development practices. These walls have been fortified to protect us from perceived review and analysis from those outside our boxes, those who don't understand the way "we" do things. We nurtured the notion that we were all experts, or artists, in our own boxes and couldn't learn from the novices in those other boxes. Research is showing us that we need to bring down the walls and collaborate across boundaries to ensure that our students succeed. We need to open our doors to analysis, experimentation, and reflection; reporting our results to colleagues and supervisors working together toward a common goal. (Reeves, 2004)

With effective progress monitoring and post assessment teachers can tell their stories and can become researchers in their own classrooms. After all, as Doug Reeves reminds us there are no mandates preventing teachers from participating in action research and measuring the success of their instructional decisions against the success of their students. Teachers can, and should, take the lead to examine those decisions in light of their students' learning. (Reeves, 2004)

Becoming proficient at progress monitoring will take practice. Teachers can practice by starting to look at all student results through a new shared lens, one that evaluates the effect of teacher decisions on student learning. Looking at the formative and summative data as a statement on his or her teaching, as well as on the students' learning, may feel threatening to some teachers. An environment that celebrates successes publicly and regularly will recognize the power of these stories to breed collaboration and collegiality, which will lead to more successes. Teachers will begin to see the causes for student achievement instead of making excuses for the lack of progress.

Researchers have pointed to best practices that, when implemented with fidelity, have a high probability of positively affecting student achievement. These instructional strategies have been observed and documented over time and are considered research-based because of their enduring success when replicated in a variety of classroom settings. For example, we know that a time bound feedback loop is critical to student growth. We also know that having students communicate their understanding of concepts and deep content knowledge in multiple ways promotes student learning and achievement. (Reeves, 2004)

McTighe and O'Connor outline seven practices for effective learning in their article of the same title (Educational Leadership, summer 2006 (adapted)). These practices are:

1. 
   Use summative assessments to frame meaningful performance goals for students. Share the tasks and assessment criteria with the students at the beginning of the instructional unit so they know the direction they need to be going and so that they can set goals based on this information.
   
2. 
   Show criteria and models in advance. Share samples of exemplars and some samples that don't make the grade. Give the students a clear picture of what they are working toward.
   
3. 
   Assess before teaching. Using diagnostic tools helps teachers plan for content depth, differentiation, student choice, and grouping strategies.
   
4. 
   Offer appropriate choices. The word "appropriate" is important in this practice. All choices offered must collect evidence of learning on the basis of goals. Teachers must not get caught up in the number of choices, but on providing students choices that will yield evidence of student learning.
   
5. 
   Provide feedback early and often. Monitor progress and let the students in on your findings. Make the research process transparent for them so they can be active researchers alongside the teacher. Show the students the cyclical nature of the research process.
   
6. 
   Encourage self-assessment and goal setting. As the teacher is monitoring progress and post-assessing for evidence of success, students should be given the opportunity to reflect on their own progress toward their goals. This could look like filling in a graph or keeping a learning journal.
   
7. 
   Allow new evidence to replace old evidence. This challenges a robust traditional teacher behavior: keeping a cumulative grade book. Traditionally teachers have graded all assignments, added them up according to the assignment's weight and produced a "final" grade. Our traditional system rewards when students learn, not necessarily how well. The suggested practice rewards mastery, whenever it occurs. It stresses understanding and demonstration of that understanding. Once students show mastery of a concept or a skill, that evidence is recorded, but their failed attempts are not. It puts the focus on learning instead of on grades.
   

Teachers engaged in the practice of action research are, by nature, reflective practitioners who go beyond reflection to action. Customary praxis reserves this practice until the data are culminating and summative in nature. This action research model encourages ongoing reflection and action through progress monitoring, lesson revision, and post-assessment during the teaching and learning, not afterward. The sharing of final reflections and conclusions between and among colleagues is encouraged.

Teachers at a comprehensive high school held unit planning sessions over the summer in all content areas. Groups of teachers planned units together and committed to implementing them during the coming school year. The units were based on an action research model that stressed monitoring progress throughout the instructional design.

Development of a generic unit planning frame was an outcome of this work. It was cooperatively developed to inspire teachers to become action researchers in their professional practice. Use of the frame is intended to guide teachers' thinking, not tie their hands. It provides prompts that encourage inclusion of all the stages of action research.

Opening the Unit: Use a diagnostic assessment measure to check on students readiness for content, skill level mastery, and grouping possibilities. Consider the results in terms of your plan. Make adjustments to the unit plan if necessary.

Week One: Content input and formative assessment. Provide students with opportunities to make meaning of the content and to show their level of understanding. Make adjustments to the unit plan as indicated by the data.

Week Two: Content input and formative assessment. Provide students with opportunities to make meaning of content. Provide formative assessments that let the students apply their knowledge. Make adjustments to the unit plan as indicated by the data.

Week Three: Content synthesis and formative assessment that helps students begin to tie content to relevant contexts. Make adjustments to your unit plan as indicated by the data.

Week Four: Evaluating of understanding. Provide culminating performance tasks and/or summative tests to students. Share data with the planning team. Make adjustments based on cumulative database.

Teacher planning teams came together after the administration of the first common, summative assessment. Not surprisingly, the data were consistent for those teachers who followed the plan faithfully. The team was able to think about their implementation plan and make some changes to that unit plan and the upcoming unit plan based on their data.

Action research, especially the progress monitoring and post-assessing pieces, are at the heart of reflective practice and the focus on teaching for learning. Thinking about measuring students' progress along the way, making some detours as necessary, and assessing the effectiveness of the new route help teachers provide a clear map for student achievement.

Let's revisit the opening questions.

• 
  What is progress monitoring and post assessment? Progress monitoring is a way to collect data about student learning during the process of teaching. It allows teachers and their students to check for understanding and to make adjustments to their plan if the data suggest a gap. Post assessment is the method by which the teacher tests his or her adjustment's success.
  
• 
  Why do I monitor progress and post-assess? Teachers monitor progress and assess their decisions to maximize the opportunity for student understanding in a given content area. They also use this process to answer questions that arise during the teaching and learning process. The process ensures that misunderstanding and misconceptions are cleared up before they can prevent future learning.
  
• 
  How do I monitor progress and post-assess? Teachers monitor progress and post-assess by using three types of assessments: diagnostic assessments help teachers determine their students' background knowledge and skill level; formative assessments determine distance traveled through the content and the effect of their instructional decisions; and summative assessments evaluate student learning and teacher design.
  
• 
  When do I monitor progress and post-assess? Teachers monitor progress and post-assess throughout the teaching and learning opportunity. This gives them ongoing data on their students' understanding and depth of knowledge. Testing hypotheses should occur whenever an adjustment to an existing unit plan is made and implemented.
  
• 
  How does progress monitoring and post-assessment fit into the teacher action research process? Progress monitoring and post-assessment are at the heart of teacher action research. Once a teacher has a question to research, he or she must collect data, analyze and synthesize that data and then act upon them. Progress monitoring gives teachers the data to analyze, synthesize, and act upon. Pos-assessment evaluates our actions.
  

Dana, N. (2005). Presentation for Learning Sciences International. University of Florida.

Marzano, Pickering, Pollock. (2001) Classroom instruction that works: Research based strategies to improve student achievement. ASCD. Alexandria, VA. (In Reeves' Accountability for learning: How teachers and school leaders can take charge.)

McTighe, J. & O'Connor, K. (2006). Seven practices for effective learning. Educational Leadership 63, 13-19.

Reeves, D. Accountability for learning: How teachers and school leaders can take charge. ASCD. Alexandria, VA.

© Copyright 2007 Learning Sciences International.

In this activity you will identify key progress monitoring and post assessment points, and provide rationale for their selection. Then you will design and implement your own progress monitoring and post assessment system.

1. 
   Based upon the "Guide to Progress Monitoring and Post Assessment" answer the questions found below the guide, design a system to progress monitor and post assess.
   

1. 
   What types of diagnostic tools will you utilize to identify where students are academically?
   

2. 
   What types of formative or progress monitoring assessment will be incorporated? Will these formative types be formal, informal, or both, and will they be graded or un-graded?
   
3. 
   It is important for the students to become partners in their own education. What techniques or strategies will encourage and maintain student involvement in order to keep students informed and actively engaged in improving their academic achievement?
   

4. 
   Students can use self-reflection to gain insight into their own learning and to foster awareness and change. What do you propose as methods for students to reflect upon their work? How will you guide students to move beyond the reflection step?
   

5. 
   What types of post assessment will be incorporated? How will you gauge the success of the instruction based upon the student results?
   

6. 
   How do you see higher order technology used during the progress monitoring and post assessment process?
   

7. 
   Have you created any applications that involve your students in analysis and assessment that can be viewed from home or from school?
   

2. 
   Summarize your responses in the space provided. Be prepared to add the summary to your Learning Log.
   

3. 
   Enter your summary in your Learning Log by clicking on "Resources" and then "Learning Log." (Label your entry "Progress Monitoring and Post Assessment")
   
4. 
   Close the Learning Log window to return to the course.
   
5. 
   Return to the course.