What is a Mathematical Circuit?

Circuit training is a popular form of exercise at the gym. A excursion is designed by an experienced trainer to meet a concrete goal (due east.m. strength, stamina, flexibility) through a set of assigned exercises, completed in a prescribed club. The intent is to keep the participant focused and engaged during the workout, without getting bored with the routine. In a gym, a circuit may include sit down-ups, lunges, jumping jacks, and push ups. Individually, each do may not exist very difficult, but put together, one gets a bang-up conditioning. My students and I take had success and fun doing mathematical circuit training
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Principles to Actions (National Council of Teachers of Mathematics, 2014) calls for teachers to "constitute mathematics goals to focus learning" (p. x). A mathematical circuit is designed by an experienced teacher to meet a mathematical goal through a gear up of assigned exercises, completed in a designated order. An AP Calculus colleague, Nancy Stephenson from Houston TX, beginning exposed me to the concept of a mathematical circuit when she forwarded a calculus review circuit she wrote. I used the circuit for several years and noticed the format kept my students engaged. In the Bound of 2013, I wrote iii algebra circuits in preparation for the Mississippi state-mandated subject field area algebra test
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Since then, I have written over lx circuits in many unlike areas of mathematics (algebra, trigonometry, calculus, etc.). With the encouragement of Academy of Mississippi professor Dr. Joel Amidon, I began creating focused circuits that did non simply serve the purpose of review, but probed the material at a deeper level as students advanced in the circuit. For example, my reaction to a PARCC assessment item in the Autumn of 2013 prompted me to write an Algebra I circuit "Finding Structure in an Equation." I thought about what my students needed to master before having success with that detail detail and those cognitive hurdles became the issues in the excursion. My use of the circuit format has allowed me to see my students accelerate toward that goal at their own pace, without fifty-fifty realizing that they are doing it! It has as well allowed me to transition from and so much direct pedagogy into the office of facilitator since students are cocky-checking their work
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I have shared these circuits and the design framework with my network of math colleagues both locally and throughout the land through give-and-take of mouth, blogging, my Teachers Pay Teachers site, and presentations. Many have reported back with their own classroom success stories, using either circuits I wrote or circuits they have crafted themselves. Their students stay engaged! Their classrooms hum with conversation! Their students master concepts and procedures!

Near circuits I design typically have between 12 and 28 problems, however, the students do not feel that they are staring at a blank paper, moving at a snail's stride through their work. Students move around on the page, similar to moving around the gym, which helps keep them engaged. Some students may need to do twenty exercises for a workout, whereas some students may need 10, regardless they are getting a mathematical conditioning. The structure of the excursion allows students to accelerate at their own pace without also much direct comparison to where other students are in the excursion. The circuit format can be used for review, for weaving 2 concepts together, or for practicing a specific skill (e.g. factoring quadratic trinomials or order of operations). Circuits can even be used to innovate new vocabulary assuasive students to apply that vocabulary during the trouble solving process.

How Can a Teacher Use Mathematical Circuits?

Independent Exercise

Students enter the mathematical circuit on an entry-level problem, solve it, and and so search for their answer to locate the side by side problem in the circuit. For example, a factoring circuit might enquire students to gene the binomial 3ab – 6b, so to accelerate in the circuit the educatee must find either 3b or a – 2. Only one factor volition be available and then that it makes working backwards from answers (a valuable strategy, but one I do not want my students using in low-cal of these new assessments) catchy. As students motility forward in the circuit, the problems go progressively more hard and challenge their previous skills and knowledge. I ensure that many of the answers are similar, so that students demand to be accurate and precise. This makes the circuit format terrific for differentiated instruction.

About every fourth problem the circuit "levels up", which means information technology becomes harder and/or incorporates students' common errors and misconceptions. If students cannot observe their answers, or if they selection the wrong respond and interruption the circuit (which would cause them to terminate with problems unworked), they know they made a error. This chemical element of self-cheque enables opportunity for questioning their ain reasoning and attending to precision of their piece of work. In addition, learning progressions can be incorporated into a excursion, see McCallum (2014), then that the assigned problems address significant cognitive hurdles in the agreement of of import mathematical content.

If a circuit is designed according to a learning progression, then information technology can exist used as a pre-assessment to see where students are lacking agreement. Similarly, it can as well be used as a mail-cess to approximate procedural fluency of the unit's concepts. Finally, if the circuit can be used as guided notes that a student completes at his or her own footstep successfully, then understanding has been achieved.

Cooperative Groups

Having students complete a circuit in a group is a nifty way to add support, in addition to those already designed into the circuit. The structure of the excursion allows for students to self-check their results, simply they may be confused on where they went incorrect or how to remedy the state of affairs. Having peers in multiple locations in the circuit allows for aid to be on hand/on demand, or, having students piece of work through the circuit together tin allow for students to meet multiple strategies and piece of work to understand multiple students' point of view. My students lean over effortlessly to hash out mathematics and explain things to each other when they are engaged in circuit training.

Circuitous Instruction

Some other style to utilize the Circuit Grooming framework with groups is in what Lotan (2003) would describe equally a "grouping-worthy" chore. This is following the design standards of Cohen (1994) in circuitous instruction. Students are handed the circuit in pieces with the included task card. Students are to work through the excursion together (distributing ownership of the bug) with the focus being to develop multiple strategies for finding the grouping-generated solution. Establishing these connections will aid students make sense of the solutions (e.chiliad. what does a tabular, graphical, or algebraic solution to a quadratic look like?) , make connections across dissimilar representations, and identify the optimum method for solving particular types of quadratic equations (run into Tools and Engineering Guiding Principle (NCTM, 2014) and CCSS-Thousand Standards for Mathematical Practice #five (Common Core State Standards Initiative, 2010)).

Professional Teaching/Learning Communities

Another swell way to apply the excursion format is for a instructor to write his or her own circuits and share them with others. 1 of the highest predictors of student accomplishment (after controlling for socioeconomic status) is teacher content knowledge. If teachers are challenging their content cognition by writing circuits and and then sharing these circuits with their section members, all of the students benefit. Several of my colleagues have written their own circuits, and I have used some of these circuits with a lot of success with my own students. In fact, 1 of my colleagues in a different state writes what he coined "Mobius Circuits" which closes with two, 3, 4, or 5 bug not completed and these remaining problems create a mini circuit. Students beloved a game, and unlike many games we play in loftier school mathematics classes, the excursion provides a written record of what they have worked on in class or at home. I have also written circuits at the middle and elementary levels and accept shared them with the teachers in our district and in other districts around the state. In addition, a challenge for students and preservice teachers could exist asking them to write a circuit toward a detail mathematical goal.

Final Remarks

Afterward didactics 25 years, many teachers are ready to retire. I feel just the opposite. I love working with my students every mean solar day. The circuit format has breathed new life into my teaching. It is not the only resource I utilise to help bring my students to better conceptual understanding and procedural fluency, but it is the one I am most excited near at this time.

Virginia Cornelius
Lafayette Loftier School
Oxford, Mississippi
April 2015

References
Cohen, Elizabeth Yard. 1994. Designing groupwork: Strategies for the heterogeneous classroom. Teachers College Press.
Mutual Core State Standards Initiative. 2010. Common Core State Standards for Mathematics. Washington, DC: National Governors Association Eye for All-time Practices and the Quango of Principal State School Officers.
Lotan, Rachel A. 2003. "Grouping-Worthy Tasks." Educational Leadership 60, (6): 72–75.
McCallum, William. Tools for the Mutual Cadre Standards. (weblog). http://commoncoretools.me/category/progressions/
National Council of Teachers of Mathematics (NCTM). 2014. Principles to actions: Ensuring mathematical success for all . Reston, VA: NCTM.