Archive for the ‘Math’ Category

Assessment for Learning: Technology Supported Formative Assessment

Wednesday, October 12th, 2011

Every day in classrooms across Texas, technology tools are infused with quality instruction to boost engagement, simplify learning task management, differentiate for diverse learning needs and increase learning through exposure to content with multiple modalities.  Educators have who embrace the transformative power of learning with technology can also take advantage of the opportunities available for assessment for learning, a.k.a – Formative Assessment.

Technology-rich, authentic assessments and automated quick-checks for understanding can provide feedback to inform teachers on how to design instruction and students on how to continuously improve. In the publication “Meaningful Measurement”, author Lyndsay M. Pinkus points out:

Many formative assessment strategies address the teacher’s information needs, helping to answer questions critical to good instruction:

• Who is and who is not understanding the lesson?

• What are this student’s strengths and needs?

• What misconceptions do I need to address?

• What feedback should I give students?

• What adjustments should I make to instruction?

• How should I group students?

• What differentiation do I need to prepare? (Pinkus, 2009)

I encourage you to download and read the full publication “Meaningful Measurement”, specifically chapter 3 concerning formative assessments.


When you get a chance, passively observe K-12 students as they interact with the technology around them.  Watch as they courageously explore the buttons and features they encounter.  They risk getting stuck or lost. They risk creating a “mess” of the tool.  They risk having to ask for help, or look up answers.  Observe as they test a solution, evaluate its effectiveness and determine the next action based on the information they gather.  Or, more simply stated, click a button and see what happens.  You can literally watch learning happen, in real time.  Each action is a moment of self-teaching, learning, and formative assessment for the student.  A popular label for this type of learning is “Problem Based Learning” or in some more structured cases “Project Based Learning”.  Both are a form of “Performance Assessment” and work as your guidance system as you lead each learner down the path to understanding and demonstration.   Check out “Sources of Performance Assessment Tasks, Rubrics, and Samples of Student Work” for excellent examples, rubrics, tasks and more for each content area and general topics.


Here are a few notable technology tools that are simple to integrate and get powerful results when it comes to student quickly taking the “pulse” of learning to formatively assess student progress.

  • is “a smart student response system that empowers teachers to engage their classrooms through a series of educational exercises and games via smartphones, laptops, and tablets.” In short, it allows teachers to create a variety of short assessments, such as quizzes and exit tickets, that can be taken from any web enabled device.  The interface is extremely kid-friendly, even for young students.  Best of all, it does not require student accounts, but still provides somewhat detailed student performance data by name via secure e-mailed excel file directly to the teacher.  Visit for a preview.  The site says it is in beta as of this writing, but you can go to (teacher tool) and (student interface) and grab an account and start assessing right away.  Easy to learn… easy to use.


Use to quickly and easily set up an online place for students to post comments, questions, and answer your prompts.  Again, this does site does not require students to have accounts, and the posts expire after a time you decide, allowing for “easy cleanup” while still giving access to absent students.  You simply set up the room (one click) and share the URL.  Try this site for your next “exit ticket”.

  • Epsilen – Project Share Texas

You’ve heard the buzz, and perhaps had some professional work experience in Project Share as a Texas educator, but in case you are unaware, the project is now open for student enrollment and you are encouraged to use the learning management system with your students.  (Note: talk to your district and your Education Service Center about student accounts).  With the Epsilen platform (Project Share’s engine) you and your students can interact in a robust virtual learning environment that allows you to share files, use forums for discussion, real time chats for, full featured test/quiz making suite (and associated grade tools), wikis for collaborative writing, blogs for student publishing, electronic portfolios with interactive assessment rubrics and much more.  Having all of these tools in one, safe, uniform and free platform opens up a treasure trove of formative assessment opportunities.  For more information, feel free to check out our blog at or the State’s official page at  Also, feel free to contact Region XIII’s Project Share team at for more information and to inquire about training.

L. M. Pinkus, ed., Meaningful Measurement: The Role of Assessments in Improving High School Education in the Twenty-First Century (Washington, DC: Alliance for Excellent Education, 2009).

RtI: An InFORMed Framework

Monday, October 10th, 2011

How Formative Assessments Fit into the Response to Intervention Framework

Response to Intervention (RtI) is a tiered model of intervention that can be defined as the practice of providing high quality instruction and interventions matched to student need, monitoring progress frequently to make changes in instruction or goals, and applying student response data to important educational decisions. (

Formative Assessement

This model is built on the idea that we, as educators, are making data-based decisions regarding both the instruction and the interventions that we provide our students. Within the RtI framework universal screening and progress monitoring are two types of formative assessments that serve as key sources of these data.


Formative Assessment at Tier I

At Tier I (the core instruction that all students receive), RtI makes use of universal screening measures to help guide our decision making in multiple ways.  For example:

  • Universal screening or benchmarking of all students throughout the year (beginning, middle and end of the school year at a minimum) allows for us to determine whether or not the general curriculum and instruction is meeting the needs of the majority of our students.
  • Universal screening scores can also be used as one data source to help flag students at Tier I who may be in need of supplemental supports.
  • Formative Assessment at Tiers II and III

    At Tiers II and III (the provision of targeted interventions for students determined to need supplemental supports), progress monitoring tools such as curriculum-based measures or curriculum-based assessments help provide invaluable data to inform decision making such as:

    • Whether or not a student is responding to the provided intervention
    • If the type, intensity, frequency or duration of an intervention needs to be adjusted

    Whether or not students are responding at a rate appropriate enough to close achievement or behavioral gaps in learning.

  • Universal Screening: Universal screening is conducted, usually as a first stage within a screening process, to identify or predict students who may be at risk for poor learning outcomes. Universal screening tests are typically brief, conducted with all students at a grade level, and followed by additional testing or short‐term progress monitoring to corroborate students’ risk status.
  • Progress Monitoring: Progress monitoring is used to assess students’ academic performance, to quantify a student rate of improvement or responsiveness to instruction, and to evaluate the effectiveness of instruction.

For a full glossary of RtI terms see:

It’s Math, Why Journal?

Sunday, August 21st, 2011

It’s Math, Why Journal?

Communication is an essential part of mathematics and mathematics education. Mathematics is so often conveyed in symbols that oral and written communication about mathematical ideas is not always recognized as important.

Students do not necessarily write or talk about mathematics naturally; teachers need to help them learn how to do so (Cobb, Wood, and Yackel 1994).

Journals provide a way of sharing ideas and clarifying understanding. Through written and oral communication, ideas become objects of reflection, refinement, discussion, and amendment. The communication process also helps build meaning and permanence for ideas. When students are challenged to think and reason about mathematics and to communicate the results of their thinking to others orally or in writing, they learn to be clear and convincing.

Journaling in the Math Classroom supports the NCTM Process  Standards for School Mathematics. These Process Standards highlight ways of acquiring content knowledge and include:

  • Problem Solving
  • Communication
  • Connections
  • Reasoning and Proof
  • Representations

Journal Uses

The ways you use math journals will depend on your purposes, preferences, and the particular age and needs of your students. Some ideas for journal use include:

  • Assessment: Formative and Summative
  • Warm Ups, Starters, Spiral Review
  • Class Notes
  • Problem Solving and Justification
  • Projects
  • Class Assignments/Math Lab Investigations
  • Vocabulary Strategies and Activities
  • Reflection/Learning Log: What did you learn? What are you not sure about? What questions do you have?
  • Models/Foldables

Journals have the potential to grow to be motivational tools for students. Not only do they supply evidence of student learning over time, they also become a useful reference in student discussion, class review, and as a study guide. When students are given the opportunity to record information in a way that is meaningful for them, the learning is “owned” and solidified.

To get students started in their writing it is often helpful to provide a sentence starter or stem.  For ELL students this strategy is also helpful in learning the English language.

Question Prompts and Sentence Starters

  • Explain what is most important to understand about ___________.
  • Find something that you learned today that is similar to something

you already knew. Write about these similarities.

  • How would you use what you learned today in your life?
  • What questions are still unanswered at the end of this week?
  • This is how I used math this week (outside of school):
  • Describe any discoveries you made about mathematics today, this week, month, or year.
  • What patterns do you notice in ____________.
  • Make a list of objects or figures in the room which have _____.

How can you tell?

  • Write a letter to your teacher explaining what you understand about

________, and what is still giving you trouble.

  • Describe practical uses for ____________.

Prompts to use for Problem-Solving

  • When I see a word problem, the first thing I do is ____. Then I ____.
  • The most important part of solving a problem is____________.
  • Describe the process you undertook to solve this problem.
  • I knew I was right when____________.
  • Tips I would give a friend to solve this problem are ___, ___, ___…
  • Could you have found the answer by doing something different? What?
  • What strategy did you use to solve this problem and why?
  • What would happen if you missed a step? Why?
  • What other strategies could you use to solve this problem?

Responding to What Students Write

Don’t feel you have to give individual comments on all entries!  Try to learn more about individual students by focusing on the mathematics in the task. Indicate your interest in how they think and reason, and offer suggestions for further consideration. Here are some things to take into account as you read:

  • Is the answer correct?
  • Does the student include reasoning that supports the solution?
  • If computation is required, does the student use an efficient method and/or mental math?
  • Does the solution indicate the use of estimation and reasonableness?
  • What would you still like to know about the child’s thinking or response, even after evaluating the entry?
  • How will you follow up?

Students who have opportunities, encouragement, and support for speaking, writing, reading, and listening in mathematics classes reap dual benefits: they communicate to learn mathematics, and they learn to communicate mathematically.


student work  Student Work  Student Work  Student Work  Student Work