Curriculum & Instruction

A “The Big Q” is a graphic organizer to help elementary math students employ sound reasoning and develop mathematical language while completing a four-step problem-solving process.

Q What does “The Big Q” look like?

A As its name suggests, a large letter “Q” divides the page into various functional areas. Details are written within the circular portion, strategies are demonstrated in the large open region to the right, and sentences are written both above and below the tail of the “Q.” A math problem (in paragraph form—a “story” problem) may appear at the top of the page. For very young students, the paragraph may consist of only a couple of sentences.

Q What are the key components of “The Big Q”?

A This problem-solving method consists of four steps. As students work through each step, they use the “Q” to organize their ideas, provide evidence of their mathematical thinking, and show their computation.

Step 1: Question: Main Idea?

In this step, the student is a reader, a thinker, and an analyzer. First, the student reads over the problem and finds any proper nouns (capitalized words). If unusual names of people or places cause confusion, the student may substitute a familiar name and see if the question now makes sense. It may help the student to re-read the problem, summarize the problem, or visualize what is happening. When the student identifies the main idea, he or she should write it down, using words or phrases. Students need to ask themselves questions such as the ones shown below.

? “What is the main idea in the question of this problem?”
? “What do we want to know?”
? “What are we looking for?”
? “What do we want to find out?”

Step 2: Details

The student reads the problem again, sentence by sentence, slowly and carefully. The student identifies and records any details, using numbers, words, and phrases. The student looks for extra information—facts in the reading that do not figure into the answer. In this step, the student should also look for hidden numbers, which may be suggested but not clearly expressed. (example: The problem may refer to “Frank and his three friends.” For working the problem, the student needs to understand that there are actually four people, even though “four” or “4” is not mentioned in the reading.) Students ask themselves the following kinds of questions.

? “What are the details needed to answer the question?”
? “What are the important details?”
? “What is going on that can help me answer the question?”
? “What do I need?”

Step 3: Strategy

The student chooses a math strategy (or strategies) to find a solution to the problem and uses that strategy to find the answer/solve the problem. Possible strategies, as outlined in the Texas Essential Knowledge and Skills (TEKS) curriculum, include the following.

use or draw a picture

look for a pattern

write a number sentence

use actions (operations) such as add, subtract, multiply, divide

make or use a table

make or use a list

work a simpler problem

work backwards to solve a problem

act out the situation

(The preceding list is just a sampling of the strategies used in elementary mathematics.)
Students’ thinking in Step 3 relates to questions such as the following.

? “What am I going to do to solve this problem?”
? “What is my strategy?”
? “What can I do with the details from Step 2 to get the answer?”

Step 4: How?

To make sure that their answer is reasonable and that they understand the process clearly, students use words or phrases to describe how they solved the problem. Students may ask themselves questions such as the following.

? “How did I solve the problem?”
? “What strategy did I use?”
? “What were my steps?”

In this final step, students must explain the solution strategy they have selected. They must provide reasons for and offer proof of the soundness of their strategy. Step 4 gives students the opportunity to communicate their understanding of math concepts and math vocabulary represented in the problem they solved.

Responses on steps 1, 2, and 4 need not be lengthy—a list of words and numbers for step 2 and phrases for steps 1 and 4 will do.

Q Who created “The Big Q”?

A The four-step method existed previously, but the graphic organizer itself was developed in-house by curriculum experts in CFISD’s math department, including the elementary math coordinator and helping teachers, incorporating feedback from classroom teachers to refine the instrument during Summer, 2005.

Q How does “The Big Q” compare to SQ-RQ-CQ?

A The two methods are very similar, with the district’s former approach—Survey/Question, Read/Question, Choose/Question—having only three steps, as opposed to “The Big Q,” which employs four steps.

Philosophy: Reasons for Valuing “The Big Q”

Q Why did Cypress-Fairbanks change from SQ-RQ-CQ to “The Big Q”?

A Reason #1 is to increase the depth of students’ thinking.
Analysis of student work revealed that many students were not using SQ-RQ-CQ as it was intended. Instead of carefully figuring out the important parts needed to solve the problem, students merely underlined, circled, and crossed out numbers and words in problems in an unthinking, mechanical fashion. Often, the only evaluation was an answer from a multiple-choice list. (During grading, teachers could just look for the answer without making sure the students used sound logic to think through the process.) By evaluating students’ work beyond an A-B-C-D answer choice, teachers are able to find incorrect patterns of thinking. Improving students' true understanding of math would call for beefing up the three-step process by requiring a fourth step: students must describe and justify their thinking and their result.

Reason #2 is to elevate success in learning the Texas Essential Knowledge and Skills (TEKS).
Data analysis of both district and state assessments (including 2005 benchmarks and TAKS results) shows that students in CFISD experience greater difficulty with “process” objectives than with “content” objectives.

Objectives for Mathematics

Content

Number, Operations, and Quantitative Reasoning
Patterns, Relationships, and Algebraic Thinking
Geometry and Spatial Reasoning
Measurement
Probability and Statistics

Underlying Processes and Tools

Problem Solving:

Reasoning and Proof
Communication
Representation
Connections

The major portion of the TAKS test evaluating students on “Mathematical Processes and Tools” (TAKS Objective 6) appears in eight questions—about 20% of the items. (See examples here.) Many TAKS questions covering the content skills require students to think conceptually about mathematics, not just to identify the answer, so students must understand the process skills thoroughly enough to apply them when finding answers for test items that cover the content skills—a “double hit.”

When test-constructors list answer choices A, B, C, and D, they usually generate the three incorrect options by predicting the ways that students are likely to go off-track in their thinking. Final test results provided to districts, schools, teams, and even classrooms, include an “item analysis” that shows how many students chose wrong answer B, wrong answer D, etc., for each test question. By reviewing such data, educators can see which “wrong path” students took during their attempt to find the answer, enabling them to target those lessons to be taught in different ways, so that students’ weaknesses are addressed. For example, an analysis of CFISD’s third-grade results reveals that 6 of the 10-most-missed TAKS questions were answered incorrectly due to students’ lack of understanding underlying processes. District results in fourth and fifth grade are similar.

A Reason #3 is proven success experienced in CFISD. Several accomplished teachers in the district supplied insights about the way to strengthen our problem-solving process to improve student learning. They indicated that they had added a fourth step to the SQ-RQ-CQ method—prior to development of “The Big Q” graphic organizer, these teachers (at Adam, Copeland, and Hairgrove) had already been requiring students to answer "how" or "why" in the final stage of the process.

Q What are the benefits of using “The Big Q” method?

A One of the method's major benefits to students is that it forces them to operate at high levels of thinking. Teachers, using the tried-and-true Bloom’s Taxonomy to describe levels of thinking, want to bring students beyond the lower levels and help them reach the upper levels. Doing so requires students to record their thinking about three steps in the process, in addition to actually "working the problem."

A second benefit of extending the process from three steps to four is that having students think at these levels will deepen their understanding of mathematics and improve their fluency in using math language. In the short term, students' performance on assessments will improve, and confidence in their mathematical ability will grow. In the long term, this rigor in elementary school mathematics will prepare students for increased rigor in secondary mathematics, beginning particularly in grade 7.

Another benefit of using “The Big Q” is that it will increase teachers’ ability to identify specific problems students are having and provide specific corrective feedback to students.

Q Does any educational research support “The Big Q”?

A Although scholarly articles do not mention “The Big Q” by name (since it is unique to Cypress-Fairbanks and developed only recently), most educational experts do advocate the use of multi-step problem-solving methods that foster students’ performing at complex levels of thinking.

The math coordinator and helping teachers studied the work of meta-researcher Dr. Robert Marzano in depth during the 2004-2005 school year, including the book Classroom Instruction That Works (Marzano, Pickering, Pollock). Conclusions drawn from compiling numerous research studies indicate that significant improvement in student achievement occurs when teachers use these strategies.

Instructional Strategy	Average Percentile Gain	Relationship to “The Big Q”
Summarizing and Note-taking	34 points	Steps 1, 2, and 4
Arguing (in the sense of defending or justifying one's thinking)	29 points	Step 4
Articulating generalizations and principles	29 points	Step 4
Providing feedback to students (“corrective,” timely, specific)	29 points	Grading
Using nonlinguistic representations	27 points	Step 3
Using advance (graphic) organizers	22 points	All Steps

A The National Council of Teachers of Mathematics endorses the use of such strategies as those appearing in “The Big Q”—particularly the step requiring students to explain their answers—as effective for producing students’ math competency, as described in NCTM publications such as Principles and Standards for School Mathematics. Excerpts from NCTM documents validate the district's problem-solving strategy. Some of the key ideas and teaching standards identified include the following.

Teachers need to investigate how their students arrive at answers. Correct answers don't necessarily equate to correct thinking.
Students need to explore various ways to think about math problems and their solutions.
Students need to learn to analyze and solve problems on their own.
Students' discourse in a mathematics classroom should focus on their thinking process as they solved a problem.

Q Is “The Big Q” required by the TEKS curriculum?

A Although the TEKS for elementary math do not mention a graphic organizer for problem-solving, they do require that students in grades 1-5 learn and do the following things in the area of “Underlying Processes and Mathematical Tools.”

The student applies mathematics to solve problems connected to everyday experiences and activities in and outside of school.
1. Identify the mathematics in everyday situations.
2. Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.
3. Select or develop an appropriate problem-solving strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.
4. Use tools such as real objects, manipulatives, and technology to solve problems.
The student communicates about mathematics using informal language.
1. Explain and record observations using objects, words, pictures, numbers, and technology.
2. Relate informal language to mathematical language and symbols.
The student uses logical reasoning to make sense of his or her world. (grades 3-5 only)
1. Make generalizations from patterns or sets of examples and nonexamples.
2. Justify why an answer is reasonable and explain the solution process.

Pedagogy: Instructional Methods Behind “The Big Q”

Q How do teachers help students learn to use “The Big Q”?

A Teachers will use a variety of techniques as they instruct students regarding “The Big Q.” They will

model use of the “Big Q” graphic organizer as they guide students through the four-step problem-solving process;
use a think-aloud method to share their reasoning with students;
employ questioning strategies that provoke students to higher levels of thinking; and
foster rich dialogue, both in whole-class discussions and for partner/table activities.

For success with “The Big Q,” talking must occur prior to writing. Students will be shown how to bridge the span between math and language to express their reasoning in a way that uses logical sequences and proper math vocabulary terms. Once students have mastered the ability to communicate out loud with the teacher and with peers, they can transition to developing the skill of conducting an “internal dialogue” for solving problems independently.

Q How can parents help students complete homework assignments that use “The Big Q”?

A To support the teacher-focused methods described above, parents can do the following.

Tasks Specific to “The Big Q”

As your student works on a “Big Q” homework problem, be a “discussion partner” as you listen to the ideas that he or she expresses while thinking through the parts, weighing options, and making decisions during the steps of the problem-solving process.
After your student has completed a “Big Q” problem, check for understanding by having the child explain Step 4 to you.

Overall Daily Habits

Model positive qualities such as curiosity, patience, self-confidence, willingness to try again, etc.
Get in the habit of “thinking aloud” as you accomplish tasks in daily life, allowing your child to observe the logic you’re using when you make decisions and solve problems.
Ask questions that go beyond “yes/no” answers. Ask “Why?” and “How?” questions that require your child to imagine a new answer—then challenge your child’s answer so that he or she has to defend the response. (Ask, “Are you sure?” “How do you know that?” “What made you decide that?”)

A When teachers design homework assignments, they should make sure students understand what to do and possess the ability to complete the assignments on their own. Teachers should give clear directions and discuss what is to be done on the assignment. Homework assignments should reinforce and encourage practice of previously-taught skills. Parent involvement, therefore, can consist of providing a supportive environment with supervision.

Q Has CFISD abandoned “the basics” of mathematics?

A Absolutely not. The “Third R” is alive and well in Cypress-Fairbanks. One common reason behind this myth seems to be related to parents’ expectations being based on their own experiences as students. When they observe their children learning other things, or learning things in a different sequence, parents are concerned that something has been left out. The Texas Essential Knowledge and Skills curriculum includes all the foundational ‘rithmetic that elementary students have been learning for decades—along with many other skills. Compared to elementary math of the past, some knowledge and skills expectations may be assigned to a different grade level, or taught in another context, or introduced with a strategy (including technology) that is unlike parents’ experience, but basic math is indeed still a requirement.

Pupils: Students Who Use “The Big Q”

Q Do all CFISD elementary schools use “The Big Q”?

A Use of a common graphic organizer at all schools would greatly benefit our ever-shifting population of students—not only those whose families move often, but also those affected by boundary changes we continue to experience as we grow. Districtwide staff development has occurred to acquaint all elementary math teaching staff with “The Big Q,” outlining expectations for students’ problem-solving knowledge and skills outlined in the TEKS at each grade-level.

Because it is the steps in the problem that are important, not the “Big Q” graphic organizer itself, principals (working with their teachers) have been given the option of selecting or designing another graphic organizer, as long as it fulfills the four-step approach. Alternatives to “The Big Q” include a four-pane “window pane” or a simple list of the four steps. Another scheme adopted by certain schools is being called SQ-RQ-CQ-HQ, which uses the old three steps plus a new fourth step—the “HQ” is the "how" step.

Q Is “The Big Q” geared toward certain groups of students?

A No, all elementary students in grades 1-5 are expected to use “The Big Q”. This graphic organizer is appropriate for all ability-levels—at-risk, to on-level, to gifted.

Q Do middle school students use “The Big Q”?

A Although middle school students do employ a multi-step problem-solving process that requires students to explain and justify their process and their answer, they do not (yet) use “The Big Q” as a graphic organizer. The “Problem-solving Board” used currently by CFISD middle school students actually has seven components. See completed examples of the “Problem-solving Board” here .

Q Does anyone besides Cypress-Fairbanks use “The Big Q”?

A No, unless others have adopted the idea from CFISD. Although “The Big Q” graphic organizer originated here, the idea to use a multi-step method for teaching problem-solving has existed for quite some time. School districts throughout the Houston area use four-step problem-solving processes. See examples of some others from across the U.S. that advocate similar multi-step problem-solving techniques.

Practice: Putting “The Big Q” into Action

Q What are students expected to do with “The Big Q” during class time?

A In class, students will use “The Big Q” in a variety of circumstances.

Students will participate in whole-class discussion and completion of “Big Q” pages as the teacher explains math problems to the group. To guide students through the steps, teachers may place a “Big Q” transparency on the overhead, affix a “Big Q” visual aid to the white board, use a “Big Q” poster, or simply draw a “Big Q” on the board to fill in the areas of the graphic organizer so that students observe how to solve the problems.
Students will work in pairs to complete “Big Q” daily work with a partner. Having a partner allows the students to discuss aspects of the problem-solving process, which helps them develop the language skills needed for completing the steps of the problem-solving process.
Students will complete “Big Q” assignments on their own, allowing teachers to gauge the students’ ability to master the steps needed to complete the problem-solving process.

Q What are students expected to do with “The Big Q” for homework assignments?

A Homework should reinforce skills already learned in class, and it should provide the practice and repetition of the problem-solving process, which will help students establish long-term memory of the concepts learned.

Q What are students expected to do with “The Big Q” on quizzes and tests?

A Students can expect to see “The Big Q” used in all phases of math instruction, including assessments. Depending on students’ level of experience with the skill, the teacher may provide “Big Q” sheets or may ask the students to construct their own “Big Q” diagrams on a blank piece of paper.

Q Is “The Big Q” appropriate to use for any math problem, or just certain ones?

A The district’s expectation is that students will ultimately use “The Big Q” for all story problems, unless directed otherwise. Improved student achievement comes in classrooms that routinely and consistently use the process.

Q How does using “The Big Q” affect the number of problems a student is expected to do?

A Using this approach should reduce the number of problems students are assigned. Completing a “Big Q” problem should take only a few minutes. As students become familiar with this graphic organizer, they will be able to increase the pace of their work. Students can save time by writing only the main idea in Step 1 (instead of copying the entire problem) and by using words or phrases in Step 4 (instead of complete sentences).

For years, researchers of results on the National Assessment of Educational Progress ( NAEP ) and the Trends in International Mathematics and Science Study ( TIMSS ) have cited curricular and instructional differences between U.S. schools and schools in countries that outperform us in mathematics. For example, Japanese students study fewer concepts and work fewer problems than American students do. In Japan, students spend their time in exploring multiple approaches to solving a problem, thereby deepening their understanding of mathematics. Depth of understanding is our goal for students, too, and we believe that the four-step problem-solving strategy will help us achieve this goal.

Q Can I view some examples of completed “Big Q” problems?

A Sample work using “The Big Q” is provided here.

Q Can I print out a blank “Big Q” page from the CFISD Web site?

A Two versions of “The Big Q” graphic organizer are provided here.

For beginners, a “Big Q” with prompts is helpful, because students are reminded where to write the four different parts of their response.
As a next step, students who have mastered the use of this graphic organizer may transition to a blank version of “The Big Q” (without prompts).

The ultimate goal is that students learn to draw their own “Q” instead of using a pre-printed form. This ability becomes necessary on assessments such as TAKS, since security rules prohibit the teacher from distributing any materials. In 2007, when students may first be expected to take TAKS online, students will need a strategy for problem-solving on blank paper—they can’t underline, highlight, and circle on the computer monitor’s glass.

Points: Assessment and Grading with “The Big Q”

Q How does “The Big Q” affect students’ grades?

A Assignments using “The Big Q” may include daily work, homework, quizzes, and tests (including district-developed benchmarks). CFISD’s grade-averaging software includes options for all these categories. As with other assignments, grades may be taken for individuals or for partnerships/groups. Experienced teachers are already familiar with all these grading scenarios.

Q How do teachers grade “The Big Q”?

A One component of CFISD’s teacher training on “The Big Q” was to introduce a rubric for evaluating student work. The instrument describes expectations for students’ responses and guides teachers in giving feedback. Rubrics may be used in many subjects in school, especially for reviewing students’ written compositions in language arts.

A range of “partial credit” options is possible with the “Big Q” rubric, depending on the teacher’s judgment regarding the student’s reasoning and thoroughness. Students may be asked to redo incomplete portions to earn back points.

Knowledge of students’ thinking will help the teacher to provide the feedback and/or the re-teaching that will get a struggling student back on track or it will allow the teacher to identify students who have advanced understanding in mathematics so that their curriculum can be adjusted. Looking at students' work and giving feedback may require additional time because the teacher is examining each student's thought processes, not just checking for a correct numeric answer.

Because students’ success in communicating their understanding of a math concept does not require that they use formal language mechanics (complete sentences, perfect spelling, etc.) when completing “The Big Q,” the rubric does not address these skills, leading math teachers to focus and assign grades that represent the students’ mastery of math concepts.

Q How does “The Big Q” relate to TAKS testing?

A Since TAKS has no items that are straight computation, a method such as “The Big Q” is highly applicable to such a testing situation. Click here to see a sampling of problems—actual TAKS items from Spring, 2003, and Spring, 2004—on which students had to demonstrate their understanding of math concepts.

If you have additional questions regarding “The Big Q,” please contact your child’s math teacher.