Formative 5 Assessment Strategies Using CueThink

We are honored to have been recognized in the well-respected book on formative assessment by Francis (Skip) Fennell, Beth McCord Kobett and Jon Wray titled: Formative 5: Everyday Assessment Techniques for Every Math Classroom. In discussing ways to use technology for assessment, Formative 5 named CueThink as a “comprehensive tool designed to improve critical thinking and communications skills, while also serving to capture and share student representations, models, and solutions” (p.76).

CueThink supports each of Formative 5’s assessment strategies in your classroom.

Observations

Informal observation in the classroom is common for most teachers, but Formative 5 guides teachers to be intentional and proactive about what they look for in an observation. CueThink’s four-phase structured problem-solving process guides teachers in looking at how students solve rich mathematical problems by unpacking the question, planning a strategy, executing their strategy and then reflecting on the accuracy and effectiveness of their solution process. Thus, by focusing their observation on the phase that their students are working on, teachers can quickly discern students’ understanding of mathematical concepts as well as how effectively students are using mathematical practices.

Interviews

Formative 5 explains that the purpose of a formative assessment interview is for the teacher to better understand the student’s thought process. Using CueThink, teachers can sit with students to watch and discuss a video vignette of a student’s solution, called a thinklet, together. Being able to see and hear how the problem was solved facilitates deeper conversations about how and why the student solved the problem they way they did. Additionally, because students love being able to watch peers’ work and give feedback, teachers can focus the discussion on either work created by the student being interviewed or a peer’s work. The ability to easily engage students in looking at a peer's work means that they can discuss a thinklet containing a common error or specific strategy. In summary, CueThink provides a digital portfolio of student artifacts from which teachers can structure their interviews.

Show Me

Having a student show and talk about how they solved the problem was noted in Formative 5 to be much more powerful than pencil and paper tests for improving both comprehension and instruction. Yet, teachers rarely have time to conference with individual students and discuss how he/she solved the problem. CueThink captures students’ written work and verbal explanations during the four-phase problem-solving process for teachers to view and revisit at any time. In this way, teachers are able to virtually sit beside each student to see and hear exactly how they solved the problem. The flexibility to virtually evaluate student work frees up instructional time for teachers to focus on monitoring the whole class, ask prompting questions and provide structured interventions.

Hinge Questions

The hinge question is designed for teachers to quickly assess students’ understanding of the lesson and inform their instruction based on those results. Once a teacher has a clear vision on students’ different understandings or misconceptions, they can use CueThink to personalize their instruction. CueThink’s problems can be cloned and customized to change the numbers or complexity of the problem to meet students’ varied needs. Problems can be assigned to subgroups of students. Teachers can also assign students to view and analyze an error containing thinklet to help them reflect on their own conceptual understanding.

Exit Tasks

“The exit task is a capstone problem or task that captures the major focus of the lesson for that day or perhaps the past several days and provides a sampling of student performance” (p.109). Fennell, Kobett and Wray explain that exit tasks allow students a chance to demonstrate their knowledge from which teachers can collect data to inform their instruction. Additionally, teachers can use Exit Tasks to give students specific feedback that will further their understanding. Within CueThink, teachers can choose from rich, curated tasks designed to foster the mathematical practices. Once students have demonstrated their knowledge within the four phases of problem-solving, teachers can use an embedded rubric and rubric summary page to evaluate their students’ work and identify trends. While assessing their students’ work, teachers can easily provide both public and private feedback in the form of embedded annotations. All work is digitally saved creating a virtual portfolio of both students’ learning and teachers’ feedback.   

try these assessment strategies with your students

CueThink is offering a FREE 90-day pilot program, in which a coach or administrator, 2-6 teachers, and all their students receive full access to CueThink’s structured problem-solving application and embedded CueTeach assessment and professional learning tools. Pilots include training and support provided by CueThink Implementation Specialists. Contact Donna Gardner, Director of School Partnerships, at dgardner@cuethink.com for more information.

References

Fennell, Francis; Kobett, Beth McCord; Wray, Jon A.. The Formative 5: Everyday Assessment Techniques for Every Math Classroom (Corwin Mathematics Series) SAGE Publications. Kindle Edition.”

Preparing for State Tests? Use CueThink to Uncover Student Thinking

During her CueThink Pilot, eighth grade math teacher, Krista Porter from Burleson, Texas used CueThink to support her students’ mathematical reasoning while preparing for her state assessment. Porter explained that, “the flexibility of CueThink allowed me to pull questions [released from past state tests] and put them in my question bank and have the students work on them. The students were able to go through the various problem solving methods and figure out what worked best. When one student had a particularly interesting solution (right or wrong) the others could comment on it.”

This blog describes four ways in which test release questions can be used within CueThink to uncover student thinking and mathematical reasoning:

  • Solve the original multiple choice problem

  • Change the multiple choice problem into an open response question

  • Shorten the multiple choice problem into a scenario

  • Create an error containing thinklet incorrectly answering the question

For each strategy, the following example question from the Texas Education Agency document “State of Texas Assessments of Academic Readiness (STAAR®) Incorporating Process Standards” is modified to illustrate the ease of the process:

“Of the 250 sheep in a flock, 34% are white. What is the total number of white sheep in the flock?

A) 85  (correct answer)

B) 216

C) 165

D) Not here

Solve the original multiple choice problem within CueThink

Enter the question exactly as it appears in the assessment, multiple choice options and all. Even though the problem still has multiple choice answers, students will still have to analyze information, formulate a plan, determine a solution, justify their solution, and evaluate the problem-solving process and reasonableness of the solution within CueThink.

Screen Shot 2017-10-20 at 8.03.25 PM.png

They are analyzing given information in the Understand Phase as they notice and wonder about both the question and the multiple choice options. Frequently, multiple choice questions include two sets of similar answers. Noticing this pattern can help students increase the probability of solving the problem correctly. In the Plan Phase, students are prompted to formulate a plan or strategy. Taking the time to write a detailed plan prevents students from simply guessing the answer. Determining and justifying the solution are equally important skills that students practice in the Solve Phase. And instead of worrying if your students check their work, use the Review Phase questions to prompt them in evaluating the problem-solving process and reasonableness of the solution.

Once a student has solved the problem in CueThink, the learning is just beginning. Using the annotation process, peers view student work and analyze mathematical relationships by looking at the variety of possible strategies used to solve the problem.  

Even though there is only one correct answer, there are a number of possible strategies that students could use to solve the problem. Some possible strategies are:

  • To find 30% of 250 and then find 4% of 250 and add those values together.

  • To find what is 1% of 250 and then multiply that value by 34  

  • To find 35% of 250 and then subtract 1% of 250

By giving students the opportunity to view peers’ work and evaluate their strategy, students will better understand which strategy is most logical and efficient.  

Translate the original multiple choice problem into an open response question for students to solve within CueThink

Changing a question from a multiple choice to an open response is as simple as removing the answer choices. By removing the answer choices, peers and teachers are able to identify gaps in understanding. Though there is only a 25% chance for the student to randomly select the correct answer out of the four choices, it is always possible for a student to guess or deduce the correct option in a multiple choice problem. For example, in the problem above, the student might not be able to find the value of 34% of 250 because 34% is not a benchmark percentage. But the student might know that 50% of 250 is 125. This understanding allows them to disqualify answers B) 216 and C) 165 and gives them a 50/50 chance of guessing the correct answer. The greater the chance of students guessing the answer, the greater the probability that the teacher will be misinformed about students level of understanding.

By translating the multiple choice question into an open response question, students must generate the correct answer without any answer choices. By seeing students’ exact answer along with their problem-solving process, teachers are better able to determine if students fully understood the content assessed in the question. There is no longer the risk that a student guessed the correct answer even though they didn’t understand the concept.  

Screen Shot 2017-10-26 at 1.46.07 PM.png

Pose a scenario based on the original multiple choice problem to extend the rigor

Changing a problem into a scenario means removing both the multiple choice answer prompts and the question. Without an explicit question, students get to pose and then solve their own question or questions. This openness lends itself to natural differentiation because students can generate increasingly more complex questions to challenge themselves.  

From the example state assessment question, “Of the 250 sheep in a flock, 34% are white. What is the total number of white sheep in the flock?” the scenario could be “Of the 250 sheep in a flock, 34% are white. Write a mathematical question you could solve using the given information.” This scenario still addresses the content goals of assessing students’ ability to solve problems involving ratios, rates, and percents but could also become much more complex based on the question the students write.

Some possible questions a student could pose are:

  • How many white sheep are there?

  • If the rest of the sheep are black, how many more black sheep than white sheep are there?

  • If there are an equal number of black and grey sheep, how many of each color sheep are there?

By increasing students’ autonomy, they are more responsible for determining their path and naturally inclined to show teachers the depth of their understanding of the content.

Create an error containing thinklet answering a state assessment question for students to analyze within CueThink

In their article, “Get the Goof," Michelle H. Pace and Enrique Ortiz cite Bray (2011) when they state, “research suggests that focusing students on analyzing and discussing mathematical errors can emphasize classroom discourse that builds on students’ thinking, promotes conceptual understanding, and mobilizes students as a community of learners” (2016). Thus, the teacher can empower students and directly address misconceptions by presenting error containing thinklets based on the state standard assessment questions. The Massachusetts DOE and other states release Sample Student Work and Scoring Guides from previous years’ assessment. In these release packets are a series of student work that align with a specific score. Select one or two pieces of work that contain errors and use them to create thinklets. Then task students to both score the thinklet using the rubric as well as create a new version of the thinklet fixing the mistakes. Read our blog to learn more about the Benefits of Error Analysis.

Results of using CueThink to prepare for state assessments

Ms. Porter was extremely pleased by the results of her students that used CueThink. “The students learned so much!” She continued that “[CueThink] helped my students visually see the problem solving. They collaborated with each other to boost confidence and skills in critical thinking and reasoning.” “[The group using CueThink] took the test and had a 94% passing rate. The one student who did not pass missed by one question.” The teacher attributed the one student who did not pass the assessment to test anxiety not lack of knowledge.

Share Your Math Stories

Let us know if you try this activity with your students! Email us, blog or tweet using the hashtag #makemathsocial. We’re always looking to share user stories on our blog, so please email sspillert@cuethink.com for a #makemathsocial blog or interview slot!

References

“Massachusetts Comprehensive Assessment System.” Massachusetts State Seal, 13 Oct. 2017, www.doe.mass.edu/mcas/student/2017/.

Pace, Michelle H., and Enrique Ortiz. “Get the Goof!” Teaching Children Mathematics, vol. 23, no. 3, 2016, p. 138., doi:10.5951/teacchilmath.23.3.0138.

State of Texas Assessments of Academic Readiness (STAAR®) Incorporating Process Standards. Texas Education Agency , Jan. 2017, tea.texas.gov/student.assessment/hb3plan/hb3-sec1ch2.pdf.

Trautz, Caryn. “Benefits of Error Analysis, CueThink Style.” CueThink, 1 June 2015, www.cuethink.com/blog/2015/5/20/error-analysis-cuethink-style.

Facilitating Deeper Learning: Weaving CueThink Into A Math Workshop

Using CueThink for Guided Math groups and independent station rotations in a Math Workshop promotes a goal-driven cycle of targeted small group instruction, independent practice, and reflection on goals to create new ones. Read on to learn how to empower students to take an active role in their learning.

In our first blog series on the Math Workshop, we detailed how to gradually introduce CueThink to your students using the structure of a Math Workshop. Investing a bit more time in the beginning to clearly set expectations and gradually release responsibility to students results in the creation of high quality thinklets and annotations. Student learning in a #makemathsocial environment is enhanced for the majority of the year because students openly communicate questions and ideas and receive high quality, timely feedback from peers.  

The Cyclic Process of Using CueThink In Guided Math Groups and Independent Stations

Once your students are familiar with creating thinklets, incorporate CueThink in Guided Math groups and independent station rotations. Use a cyclic process of Guided Math instruction → Technology Station → Guided Math instruction to facilitate goal-driven targeted small group instruction, independent practice, and reflection during small group instruction. Use a Guided Math session to focus students on one specific goal each time they create a thinklet. The Technology Station provides students with scaffolded independent practice centered around their selected goal. Use another Guided Math session to reflect with students on their independent practice and determine the next course of action to achieve their goal, or select a new one.  

Students visit the Technology Station 3-4 times within the cycle, depending on the length of your rotations. Throughout the cycle students will complete their thinklet, view and annotate peers’ thinklets, and make revisions to their own thinklets based on  peers’ annotations. Students focus on thinklet creation in the first visit (and second if needed). Dedicate the next session to view and annotate peers’ thinklets. Use the final session to make revisions to thinklets based on peers’ feedback, to encourage math as a process of creation, reflection and revision. The goals students selected during Guided Math group are worked on in the Technology Station during the visit that correlates to the process they are working on.

Carry Out The Process

Empower students to take an active role in their learning. Work with students during Guided Math groups to identify one area for improvement to work on independently during the Technology Station. This promotes student agency and a growth mindset by encouraging students to see problem solving as a cyclic process of creation, reflection and revision.

Refine thinklets students already created during the Technology Station or begin thinklet creation during a Guided Math group that students will finish during the Technology Station. Reflect with students on their work in the Technology Station during the Guided Math group to further their growth or select a new goal. Goals can be focused on any of the Four Phases of problem solving and annotations. Listed below are 30-minute lesson plans focusing on a variety of problem solving goals that can be addressed in Guided Math groups.

  1. Unpacking the Problem by Noticing and Wondering

  2. Estimating an Answer

  3. Choosing the Best Strategy to Solve a Problem

  4. Writing a Plan to Solve the Problem

  5. Organization of a Solution to a Multistep Problem

  6. Fostering Mathematical Communication

  7. Written Feedback to Encourage Revision

 

Conclusion...Your Next Steps

Integrate CueThink into your station rotations and Guided Math groups to improve your students’ problem solving skills and math communication. Within the station rotation model, students visit 3-4 stations a cycle. At one station, students create thinklets either individually, or in pairs. In a second station students view and annotate peers’ thinklets. Use other complementary independent stations such as a Technology Station that focuses on skills practice, an Independent Work Station that provides students with differentiated work, and a Math Games station that coincides with the current unit of study’s content and skills, or spirals to review past units and prerequisite skills of upcoming units of study. Finally, station rotations allow for teachers to work with small, targeted Guided Math groups. Guided Math groups can address students’ misconceptions, missing prior knowledge or enhancing problem solving skills using the themes listed above.

Diversify Homework With CueThink: Digitally Extend Your Classroom

Vary and enhance homework to create a digital extension of classroom learning. Youki Terada (2015) asks, “How can we transform homework so that it’s engaging, relevant and supports learning?” Here are some ways that teachers use CueThink to answer that question.

At home, students can:

Preview a problem

Students can begin to create thinklets that they will work on the following day in class. Teachers can ask students to not submit their thinklet to the class gallery so they can continue working on it during class time. Or, teachers can assign students to submit their thinklet, complete or incomplete, to the gallery to receive feedback from peers. After receiving feedback, students can edit their thinklet and submit to create an updated final version. 

Annotate peers’ thinklets

Annotations helps students with CCSS.MATH.PRACTICE.MP3: Construct viable arguments and critique the reasoning of others. Assigning students to write annotations for homework allows students to independently practice giving effective feedback. Introduce the homework assignment with a classroom discussion on what is kind, specific and helpful feedback. Use an exemplar thinklet from the gallery to generate examples of annotations that fit your class criterium. Continued practice with Annotations will support students in learning the importance of digital citizenry and virtual collaboration.

Watch two thinklets that model different strategies

Dr. Matthew Beyranevand wrote “the more strategies and approaches that students are exposed to, the deeper their conceptual understanding of the topic becomes.” Comparing multiple strategies support students in learning how to plan their solution as well as evaluating the effectiveness of a strategy in relationship to a specific skill. Assign a problem for students to review or let students choose from the gallery. After watching both thinklets, students compare and explain which strategy is most effective and why. Comparisons of the two unique strategies can be written as an annotation or on paper.  

Revise a thinklet based on peers’ feedback

In an article, Educating the World said, “Good formative assessment celebrates the student’s successes but also offers strategies for improvement and advice on how to develop a greater depth of knowledge and understanding.” The annotations process provides peer-based formative assessment that students should use to improve their work.  After students receive peer feedback, give students time at the end of class to review annotations and ask clarifying questions. Then for homework, students create a new version of their thinklet that addresses peers’ feedback.

REFERENCES

"Assessment for Learning: “Formative Assessment Is a Verb Not a Noun.” International Education Today. N.p., 26 Aug. 2015. Web. 14 July 2016.

Beyranevand, Matthew. "6 Ways to Help Students Understand Math." Edutopia. N.p., 22 Apr. 2016. Web. 14 July 2016.

Gordon, Norma. "Annotations Tic-Tac-Toe." RSS. CueThink, 4 Aug. 2015. Web. 14 July 2016.


Terada, Youki. "Research Trends: Why Homework Should Be Balanced." Edutopia. Edutopia, 31 July 2015. Web. 06 July 2016.

Introducing CueThink Using a Math Workshop Session 6: Your Next Steps

Session 5 teaches the importance of students checking their work and what appropriate, effective written feedback looks like.

The Session 6: Your Next Steps objective is to integrate CueThink on a regular basis into your independent station rotations and Guided Math groups for the rest of the year. Watch your students’ problem solving skills and math communication blossom over the course of the year with consistent practice.

Use CueThink in one or more independent stations, where students visit the station 3-4 times a cycle, depending on the length of your station rotations. In one independent station, students focus on thinklet creation either individually, or in pairs. It may take students two visits to this station to complete their thinklets. In a second independent station, students view and annotate peers’ thinklets in pairs or small groups to purposely promote student discourse around problem solving. In a second visit to this station, students view the annotations they received and make revisions to promote a growth mindset.

Use other independent stations that complement CueThink, such as another technology station that focuses on skills practice, an independent workstation that provides students with differentiated work, and a math games station that coincides with the current unit of study’s content and skills, or spirals to review past units and prerequisite skills of upcoming units of study. Read Strategies and Activities for Independent Learning (SAIL) by The Meadows Center for classroom management tips and student-led learning centers and stations ideas for K-2 students.

Use CueThink as a tool during Guided Math lessons, to help facilitate mini-lessons on specific areas students need improvement in with the four phases of problem solving and making annotations. Create different levels of problems to better differentiate your instruction during Guided Math groups.

View a Math Workshop follow-up blog on how to use CueThink to connect your Guided Math lessons with independent station practice using a goal driven cyclic process. Empower students to take an active role in their learning!

 

References

"Strategies and Activities for Independent Learning (SAIL)." University of Texas System/Texas Education Agency(2010): n. pag. 2010.  Web. 29 Aug. 2016.
Whirledge, Rebekah. "Digital Citizenship | Oregon Davis." Oregon Davis. N.p., 1 Sept. 2016. Web. 10 Oct. 2016.