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Should I group students based on ability or interest?

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During the primary years students either experience mathematics lessons within mixed ability classrooms or are ability grouped across or between grade levels. In mixed ability classes and to a lesser degree in ability grouped classrooms teachers often have to cater for a range of students whose previous attainment varies considerably. The gap between low and high achievers is said to increase as students progress through school, with as much difference in performance within year levels as there is between Years 5 and 9 students overall (State of Victoria Department of Education and Training, 2004). This concurs with findings by The Middle Years Numeracy Research Project (Siemon, Virgona, & Corneille, 2001) that cites teachers in the middle years can and should expect a range of up to seven school years in numeracy-related performance. Australian TIMSS and PISA reports show our middle years students, when compared to students in other countries, are not keeping up with some aspects of mathematics (Lokan, Greenwood, & Cresswell, 2001). Among the strategies teachers implement in order to cater to the diverse needs of the classroom is the use of ability grouping and the incorporation of differentiated tasks.

Although there are arguments both in favour and against the use of ability grouping, it is not uncommon for primary and secondary schools in Australia and internationally to use such grouping in mathematics classrooms. The following is an exploration of both arguments. Clarke (2003) maintains teachers need to think carefully about reasons for choosing to place students into groups according to perceived ability. Teachers need to consider the potential impact upon students' self-esteem, and the 'self-fulfilling prophecy' (Brophy 1963, as cited in Clarke, 2003), in which students perform to the level expected of them by their teacher. He concludes that ability grouping is used in mathematics for teacher convenience more than for student benefit. This is a sentiment echoed by Boaler, Wiliam and Brown (2000), who also believe ability grouping is one of the main sources of disaffection.

Ability grouping, such as that which is common in Australian secondary schools, became the focus of a study conducted in the United Kingdom (Boaler, et al., 2000). The grouping of students into ability 'sets' emerged as a significant factor that influenced students' ideas, their responses to mathematics, and their eventual achievement. The study found that students in the school that used ability grouping were significantly disadvantaged by their placement and this disadvantage was not restricted to students in the lower ability groups. Approximately one-third of students in the highest ability groups felt disadvantaged because of high expectations, fast-paced lessons and pressure to succeed. Students from a range of groups were 'severely disaffected' by the limits placed upon their attainment. Students reported that they gave up on mathematics once they discovered their teachers had been preparing them for examinations that gave access to only the lowest grades. Large numbers of students, in the study by Boaler et al., experienced difficulties working at the pace of their particular class. For some the pace was too slow, resulting in disengagement, although for others it was too fast, resulting in anxiety. Both responses led to lower levels of achievement.

In addition to the findings above, there is research that claims ability grouping causes behavioural problems for some within the mathematics classroom. Teachers in a study conducted by Ventakatakrishnan and Wiliam (2003) found behavioural problems more common in mixed ability groups than in their fast-track, higher ability group. These behavioural problems were compounded by the weak literacy skills of some individuals in these groups in addition to peer self-management skills. Interestingly, placing students in 'tracked' groups had an effect on students' perceptions of themselves as learners of mathematics. Those who were fast-tracked perceived themselves as 'doing well' while those in mixed ability groups perceived themselves as 'low' in mathematical ability. The teachers involved in the study also noted they had problems motivating the higher attaining students within the mixed-ability groups - students who had 'just' missed out on being placed in the fast tracked group. Ventakatakrishnan and Wiliam also note that mixed-ability grouping decreases the opportunities for higher-achieving students to interact constructively with peers although ability groups have the same effect on lower achieving students. The study found that advantages of grouping by ability are limited and restricted to higher achieving students while causing disadvantage to those who are the lowest attainers.

Although there are advantages and disadvantages in grouping students according to ability, it is also reasonable to expect that a result of such grouping is differences in teacher expectations and instructional techniques. There is a tendency for instruction in lower ability groups to be of a different quality to that of higher ability groups (Ireson & Hallam, 1999). There appears to be a concern that instruction in low ability groups is conceptually simplified with a higher degree of structured, written work, as in the traditional method of teaching mathematics. Higher ability classes appear to include more analytic, critical thinking tasks with pupils allowed greater independence and choice along with opportunities for discussion, reflecting a more contemporary style of mathematics lesson. Based on stereotypes and past experiences, some teachers hold low expectations for low ability groups, further decreasing students' own expectations and self-esteem, and leading to decreased levels of engagement with mathematics (Ireson & Hallam, 1999).

At the primary level classroom, research suggests students in mixed ability classrooms display more positive attitudes towards school in general (Ashton, 2008; Ofsted, 2008). However, the more common practice of ability grouping in the secondary mathematics classroom is a complex issue. Although it appears to perpetuate the inequities associated with mathematics and the notion of mathematics being an elitist subject, it is often an attempt to address the needs of all students as well as the needs of mathematics teachers.

So what is the answer? My advice is to group flexibly. There are circumstances that require children to be grouped by ability, and other circumstances where it is more appropriate and beneficial for students to work in mixed groupings, where students can learn from each other. Another reason to have flexibility is that often children may excel in one area of mathematics, but may be challenged in other areas. Those who appear to struggle, may not necessarily struggle with all concepts. The key is knowing your students and their needs across all aspects of the mathematics curriculum, and ensuring that assessment of students' ability informs teaching and the way students are grouped. And finally, have high expectations of all students!

References:

Ashton, R. (2008). Improving the transfer to secondary school: How every child's voice can matter. Support for Learning, 23(4), 176-182.

Boaler, J, Wiliam, D, & Brown, M. (2000). Students' experiences of ability grouping: Disaffection, polarisation and the construction of failure. British Educational Research Journal, 26(5), 631-649.

Clarke, D. (2003, 4-5 December). Challenging and engaging students in worthwhile mathematics in the middle years. Paper presented at the Mathematics Association of Victoria Annual Conference: Making Mathematicians, Melbourne.

Ireson, J., & Hallam, S. (1999). Raising standards: Is ability grouping the answer? Oxford Review of Education, 25(3), 343-358.

Lokan, J., Greenwood, L., & Cresswell, J. (2001). 15-up and counting, reading, writing, reasoning. How literate are Australia's students? The PISA 2000 survey of students' reading, mathematical and scientific literacy skills. Melbourne: ACER.

Ofsted. (2008). Mathematics: Understanding the score. London: Ofsted.

Siemon, D., Virgona, J., & Corneille, K. (2001). Final report of the middle years numeracy research project. Melbourne, Victoria: RMIT University and the Department of Education and Training (Victoria).

State of Victoria Department of Education and Training. (2004). Middle years of schooling overview of Victorian Research 1998-2004 Retrieved July 7, 2005, from http://www.sofweb.vic.edu.au/mys/docs/research/

Venkatakrishnan, H., & Wiliam, D. (2003). Tracking and mixed-ability grouping in secondary school mathematics classrooms: A case study. British Educational Research Journal, 29(2), 189-204.

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Ability grouping and mathematics: Who benefits?

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During the primary years students either experience mathematics lessons within mixed ability classrooms or are ability grouped across or between grade levels. In mixed ability classes and to a lesser degree in ability grouped classrooms teachers often have to cater for a range of students whose previous attainment varies considerably.

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First Person

If committed educators could be easily trained to implement a low-cost intervention that boasted consistent learning gains for all students, headlines would herald the discovery of the educational holy grail.

That low-cost intervention is here and readily available. It's called ability grouping. Unfortunately, despite overwhelming evidence that the flexible and appropriate use of this intervention benefits learners at all levels, some have opted to smear it as an evil twin of tracking and to lament its resurgence in the nation's classrooms.

Flexible ability grouping, when used appropriately, works. According to a 2010 meta-analysis by Kelly Puzio and Glenn Colby, students who were grouped by ability within a class for reading were able to make up to an additional "half of a year's growth in reading." Similarly, a 2013 National Bureau of Economic Research study of students who were grouped by ability found that the performance of both high and low performing students significantly improved in math and reading, demonstrating the universal utility of this tool, particularly as our classrooms become more academically diverse.

For years, ability grouping has been unduly criticized and misconstrued. Contrary to what some may say, flexible ability grouping is not tracking, which typically sets a far more rigid and defined path for a student to traverse and where breaking out of one track and into another often requires the skills of Harry Houdini.

Flexible ability grouping could not be more different. When used properly, ability grouping does not affix permanent labels to students and does not prevent students from moving-either up or down-during their educational careers. Rather, flexible ability grouping is a tool used to match a student's readiness for learning with the instruction provided, delivering the right content to the right student at the right pace and at the right time.

Ability grouping should not be static. Rather, flexible ability grouping, as its name implies, is an ongoing process where student assignments can and do change based on performance, requiring teachers to be on the lookout for signs of improved competency and skill development in their students.

It must be based on student performance data so decisions are objective and not subject to bias, and it must be customized by subject, never assuming that because a student is either advanced or in need of remediation in one subject he or she would require that same level of instruction in all subjects.

Constant Reassessment

To understand how flexible ability grouping works, imagine the following scenario: A 2nd grader's past performance, including test scores, indicates he needs some additional support in reading. As a result, at the start of the school year, he starts off in a less-advanced reading group.

Over the course of several months, as a result of instruction aimed just above his skill level, his reading ability improves markedly. Based on daily work, his teacher notes this progress and moves him to a more advanced reading group. This same process of grouping based on data and reexamining based on performance happens constantly throughout the year for all students.

As noted above, ability grouping is not an effortless panacea for all of our education woes. Teachers must be willing and able to detect signs students are demonstrating changes-hopefully for the better-in their learning abilities and thus may be ready for movement to a different group. They must also be trained on how to differentiate their instruction to learners at different levels within the same classroom. To be effective, this requires that teachers are able to add advanced content and adjust pacing for students who are ready to move ahead. It's important to emphasize that without modified instruction, the learning gains that are possible will fail to materialize.

When flexible ability grouping is used appropriately and effectively, students win. They receive the right content at the right time from teachers better able to direct their instruction to a smaller group of students. Additionally, because the students are concentrated with others who have similar levels of knowledge and learning rates and clear learning goals, they can better challenge one another to grow further.

The latest evidence makes clear that flexible ability grouping is effective, enabling students to make the types of gains all educators should desire and expect. The time has come to dispel the myths, to stop criticizing ability grouping using disingenuous rhetoric and to redouble efforts to support teachers and others as to how to appropriately use this tool so all students can maximize their abilities and achieve their full potential.

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Setting the Record Straight on Ability Grouping

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First Person If committed educators could be easily trained to implement a low-cost intervention that boasted consistent learning gains for all students, headlines would herald the discovery of the educational holy grail. That low-cost intervention is here and readily available. It's called ability grouping.

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I plan to study 4th grade math centers, because I want to find out how to best implement them in my classroom. I would like to be able to show my colleagues how they can also use math centers in their own classroom, while still working within the district curriculum. I want to better understand how I can teach in small groups using math centers on a regular basis.

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Direct instruction vs. Student lead activities

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Direct instruction vs. Student lead activities

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I thought that would get your attention! Now just hear me out. I want you to consider that there is really very little in math that students must learn through direct instruction, that is explicit instruction from a teacher. Let me give two examples, and then I'm sure you can think of others.
Take, for example, expanded notation [eg., 234 = (2 x 100) + (3 x 10) + (4 x 1)]. Yes, students need to be directly taught the conventions for writing a number in expanded notation. They would have no way of knowing that we put parenthesis around each multiplication expression, nor could they discover it through exploration. But they can construct their own learning about what expanded notation is (describing the value of each digit using a multiplication expression) through exploration with base-ten blocks and careful questioning by the teacher. Be sure to check out this blog post for more on that.

Another great example is decimal equivalencies. Say, for example, you are trying to teach the concept that 0.4 and 0.40 are equivalent. That is a very abstract concept for students to grasp through direct teaching. Instead, have students use base-ten blocks to build 0.4 and 0.40. Note that when using base-ten blocks for decimal values, we typically use the flat to represent ones, the rod for tenths, and the unit for hundredths. If they build those two numbers, how could the not see the equivalence? Have them build a few more similar pairs (0.7 and 0.70, etc.) and then have them explain why the two numbers in each pair are equivalent.

Need decimal place value mats? Grab the ones pictured for free by clicking here.

In her book What's Math Got to Do with It?, Jo Boaler describes traditional teaching methods as passive learning. She cites years of research that underscore how ineffective the lecture-demonstrate-practice cycle of teaching is for student learning. I love this quote: "Students taught through passive approaches follow and memorize methods instead of learning to inquire, ask questions, and solve problems." If we want deeper understanding (and don't we?), we must move past stand and deliver teaching.

The idea of direct teaching vs inquiry is not really a debate about small group instruction vs whole group instruction. It's more a teaching style and philosophy. Unfortunately, direct instruction happens as often in a small group setting as in whole group instruction. The shift we need is more toward facilitating learning through thoughtful questioning and away from telling and showing students what they need to learn.

Do you notice the other common thread that is a must for learning through discovery? Students must be allowed to explore concepts with concrete materials for discovery to occur!

Can't wait to hear your thoughts on direct instruction vs discovery!

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Direct Instruction...Do We Need It? - Math Coach's Corner

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I thought that would get your attention! Now just hear me out. I want you to consider that there is really very little in math that students must learn through direct instruction, that is explicit instruction from a teacher. Let me give two examples, and then I'm sure you can think of others.

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By Kitty Rutherford, Posted April 27, 2015 -

People of all ages love to play games that are fun and motivating. Games give students opportunities to explore fundamental number concepts, such as the counting sequence, one-to-one correspondence, and computation strategies. Engaging mathematical games can also encourage students to explore number combinations, place value, patterns, and other important mathematical concepts. Further, they afford opportunities for students to deepen their mathematical understanding and reasoning. Teachers should provide repeated opportunities for students to play games, then let the mathematical ideas emerge as students notice new patterns, relationships, and strategies. Games are an important tool for learning in elementary school mathematics classrooms:

* Playing games encourages strategic mathematical thinking as students find different strategies for solving problems and deepen their understanding of numbers.

* When played repeatedly, games support students' development of computational fluency.

* Games present opportunities for practice, often without the need for teachers to provide the problems. Teachers can then observe or assess students and work with individuals or small groups of students.

* Games have the potential to allow students to develop familiarity with the number system and with "benchmark numbers" (such as 10s, 100s, and 1000s) and engage in computation practice, building a deeper understanding of operations.

* Games support a school-to-home connection. Parents can learn about their children's mathematical thinking by playing games with them at home.

This game is on p. 65 of the downloadablePDF. Building Fluency
Fluency requires a balance and connection between conceptual understanding and computational proficiency. Computational methods that are over-practiced without understanding are forgotten or remembered incorrectly. Conceptual understanding without fluency can inhibit the problem-solving process (NCTM 2000, Principles and Standards for School Mathematics, p. 35).

Developing computational fluency is an expectation of the Common Core State Standards for Mathematics. Games provide opportunity for meaningful practice. The research about how students develop fact mastery indicates that drill techniques and timed tests do not have the power that mathematical games and other experiences have. Appropriate mathematical activities are essential building blocks to develop mathematically proficient students who demonstrate computational fluency (Van de Walle and Lovin, Teaching Student-Centered Mathematics Grades K-3, p. 94). Remember, computational fluency includes efficiency, accuracy, and flexibility with strategies (Russell 2000).

The kinds of experiences that teachers offer their students clearly play a major role in determining the extent and quality of students' learning. Students can build understanding by actively engaging in tasks and experiences designed to deepen and connect their knowledge. Procedural fluency and conceptual understanding can be developed through problem solving, reasoning, and argumentation (NCTM 2000, Principles and Standards for School Mathematics, p. 21). Meaningful practice is necessary to develop fluency with basic number combinations and strategies with multidigit numbers. Practice should be purposeful and should focus on developing thinking strategies and a knowledge of number relationships rather than on drilling isolated facts (NCTM 2000, Principles and Standards for School Mathematics, p. 87). Do not subject any student to computation drills unless the student has developed an efficient strategy for the facts included in the drill (Van de Walle and Lovin 2006, Teaching Student-Centered Mathematics Grades K-3, p. 117). Drills can strengthen strategies with which students feel comfortable-those they "own"-and will help make these strategies increasingly automatic. Therefore, strategy drills will allow students increasing efficiency, even to the point of recalling a fact without being conscious of using a strategy. Drills without an efficient strategy offer no assistance (Van de Walle and Lovin 2006, Teaching Student-Centered Mathematics Grades K-3, p. 117).

This game is on p. 5 of the downloadable PDF.

Cautions

Sometimes teachers use games solely to practice number facts. These games usually do not engage children for long because they are based on students' recall or memorization of facts. Some students are quick to memorize; others need a few moments to compute a related fact. When students are placed in situations in which recall speed determines success, they may infer that being "smart" in mathematics means getting the correct answer quickly instead of valuing the process of thinking. Consequently, students may feel incompetent when they use number patterns or related facts to arrive at a solution and may begin to dislike mathematics because they are not fast enough.

Introduce a game
This game is on p. 67 of the downloadable PDF.

A good way to introduce a game to the class is for the teacher to play the game against the class. After briefly explaining the rules, ask students to make the class's next move. Teachers may also want to model their strategy by talking aloud for students to hear his or her thinking. "I placed my game marker on the six because that would give me the largest number."

Games are fun and can create a context for developing students' mathematical reasoning. Through playing and analyzing games, students also develop their computational fluency by examining strategies that are more efficient and by discussing relationships among numbers. Teachers can create opportunities for students to explore mathematical ideas by planning questions that prompt students to reflect about their reasoning and make predictions. Remember to always vary or modify the game to meet the needs of your leaners. Encourage the use of the Common Core's Standards for Mathematical Practice.

Holding Students Accountable

While playing games, have students record mathematical equations or representations of the mathematical tasks. This yields data for students and teachers to revisit to examine their mathematical understanding.

After playing a game, have students reflect on the game by asking them to discuss questions orally or write about them in a mathematics notebook or journal:

* What skill did you review and practice?

* Which strategies did you use while playing the game?

* If you were to play the games a second time, what different strategies would you use to be more successful?

* How could you tweak or modify the game to make it more challenging?

This game is on p. 42 of the downloadable PDF.

K-Grade 5 Math Games were created by North Carolina teachers and can be accessed on the North Carolina Department of Public Instruction, under Kindergarten Instructional Resources/Games.

For students to become fluent in arithmetic computation, "they must have efficient and accurate methods that are supported by an under-standing of numbers and operations. 'Standard' algorithms for arithmetic computation are one means of achieving this fluency" (NCTM 2000, Principles and Standards for School Mathematics, p. 35).

"Overemphasizing fast fact recall at the expense of problem solving and conceptual experiences gives students a distorted idea of the nature of mathematics and of their ability to do mathematics" (Seeley 2009, Faster Isn't Smarter: Messages about Math, Teaching, and Learning in the 21st Century, p. 95).

" Fluency refers to having efficient, accurate, and generalizable methods (algorithms) for computing that are based on well-understood properties and number relationships" [emphasis mine] (NCTM 2000, Principles and Standards for School Mathematics, p. 144).

" Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently" [emphasis mine] (NCTM 2000, Principles and Standards for School Mathematics, p. 152).

Kitty Rutherford serves as the North Carolina Elementary Mathematics Consultant for the Department of Public Instruction in Raleigh. She is an experienced leader, collaborator, and licensed educator with a Master's Degree in Elementary Education coupled with over twenty-seven years' experience teaching elementary school students, training educators, collaborating with multiple stake-holders, and implementing effective programs. She has received such honors as the Presidential Award for Excellence in Mathematics and Science Teaching, NCCTM Outstanding Elementary Mathematic Teacher, Alpha Delta Kappa State Excellence in Education Award, and Teacher of the Year Finalist. She currently serves as the State Coordinator for the NC Presidential Award for Excellence in Mathematics Teaching and on the board of the North Carolina Council of Teachers of Mathematics.

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By Kitty Rutherford, Posted April 27, 2015 - People of all ages love to play games that are fun and motivating. Games give students opportunities to explore fundamental number concepts, such as the counting sequence, one-to-one correspondence, and computation strategies. Engaging mathematical games can also encourage students to explore number combinations, place value, patterns, and other important mathematical concepts.

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The 4 elements of differentiation and how it relates to math centers.

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The 4 elements of differentiation and how it relates to math centers.

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Really Good Teachers™ Blog and Forum | A Really Good Stuff® Community

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Differentiation is the process through which teachers are meeting the needs of all students. Instruction is organized and flexible to maximize growth of the learner by addressing the variety of learning styles, students' readiness, and interest levels. Providing different modalities of learning allows students the opportunities to experience, conceptualize, analyze and apply meaning to their learning experience. Varying modalities, as defined by Howard Gardner, include linguistic, logical, musical, spatial, kinesthetic, interpersonal, and intrapersonal.

Four Elements of Differentiation

There are four elements for successful differentiation in my classroom. These elements include behavior management, time management, tiered activities with a variety of strategies, and flexible groupings.

Math instruction can be differentiated to allow students to practice skills appropriate to their readiness levels. I've changed my approach to differentiating math instruction through work stations. Debbie Diller, author of Math Work Stations, does a magnificent job at helping teachers understand how to organize, manage, maintain, differentiate, and assess various math concepts.

Math work stations are strategically designed areas set up around the room where students discuss their mathematical thinking. Unlike math centers which rotate each week with a new topic, math work stations often remain for multiple weeks as students reinforce or extend prior instruction and develop their understanding through problem solving.

Concepts are often introduced whole group and modeled multiple times. Working with concepts during small group instruction helps reinforce practice. Once a concept has been reinforced with the teacher facilitating, the materials can be placed in work stations allowing the teacher to observe and interact with students working on mathematical topics.

Allowing students a choice is an important component to ensure success during math work stations. As topics are developed during instruction, adding the new activity to the station will provide a "controlled choice". Providing a limited number of resources will keep the students from becoming overwhelmed.

Patience and perseverance are required to differentiate effectively. All students deserve appropriate differentiated instruction in math so to demonstrate their strengths and talents. This challenging process needs time to adapt and grow as the classroom community matures in content knowledge.
About the Author
Cheryl Saoud is a second grade teacher from Jacksonville, Florida. She would like to invite you to visit www.primarygraffiti.blogspot.com for additional teaching resources.

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Maximizing Growth of a Math Learner - ReallyGoodTeachers.com

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Differentiation is the process through which teachers are meeting the needs of all students. Instruction is organized and flexible to maximize growth of the learner by addressing the variety of learning styles, students' readiness, and interest levels. Providing different modalities of learning allows students the opportunities to experience, conceptualize, analyze and apply meaning to their learning experience.

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How will behavior problems interfere with the groupings of students?

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How often should I assess and regroup students

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Great article on how mindset affects math comprehension

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Great article on how mindset affects math comprehension

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Neuroscientists now know that the brain has the ability to grow and shrink. This was demonstrated in a study of taxi drivers in London who must memorize all the streets and landmarks in downtown London to earn a license. On average it takes people 12 tries to pass the test. Researchers found that the hippocampus of drivers studying for the test grew tremendously. But when those drivers retired, the brain shrank. Before this, no one knew the brain could grow and shrink like that.

"We now know that when you make a mistake in math, your brain grows," Boaler said. Neuroscientists did MRI scans of students taking math tests and saw that when a student made a mistake a synapse fired, even if the student wasn't aware of the mistake. "Your brain grows when you make a mistake, even if you're not aware of it, because it's a time when your brain is struggling," Boaler said. "It's the most important time for our brains."

A second synapse fires if the student recognizes his mistake. If that thought is revisited, the initial synapse firing can become a brain pathway, which is good for learning. If the thought isn't revisited, that synapse will wash away.

A recent study of students with math learning disabilities found in a scan that their brains did behave differently from kids without the disability. "What they saw was the brain lighting up in lots of different areas while working on math," Boaler said. The children were recruiting parts of the brain not normally involved in math reasoning.

The researchers tutored the group of students with math disabilities for eight weeks using the methods Boaler recommends like visualizing math, discussing problems and writing about math. At the end of the eight weeks, they scanned their brains again and found that the brains of the test group looked just like the kids who did not have math disabilities. This study shows that all kids can learn math when taught effectively. Boaler estimates that only 2 to 3 percent of people have such significant learning disabilities that they can't learn math at the highest levels.

People who learned math the traditional way often push back against visual representations of math. That kind of thinking represents a deep misunderstanding of how the brain works. "When you think visually about anything, different brain pathways light up than when we think numerically," Boaler said. The more brain pathways a student engages on the same problem, the stronger the learning.
GROWTH MINDSET AND MATH
Increasingly, educators are buying into the compelling research showing that what students believe about themselves affects how their brains approach learning. Growth mindset is probably the best known aspect of this research, and many school leaders are trying to figure out how to implement growth mindset programs in their classrooms.

"More kids have a fixed mindset about math than anything else," Boaler said. And it's no coincidence that they feel this way. Teachers often believe their students can't achieve at the highest levels, and in turn, students believe that about themselves. Plus, the tasks themselves communicate a fixed mindset.

"It is very difficult to have a growth mindset and to believe that you can grow or learn if you are constantly given short, closed questions with a right or wrong answer," Boaler said. Instead, she recommends giving visual problems that provoke discussion and have multiple ways they could be solved.

She also says kids should not be grouped by ability or tracked into "advanced" or "remedial" groups. That common practice sends fixed mindset messages to students, both the "advanced" ones and the "low-performing" ones. Kids considered to be "gifted" suffer from ability grouping the most because they develop the ultimate fixed mindset. They become terrified that if they struggle they'll no longer be considered smart.

Instead, mixed ability grouping can work if the tasks are open-ended and what Boaler calls "low-floor/high-ceiling" tasks that allow every student to participate, while allowing lots of space within the task for students to grow in their thinking.

Boaler has lots of example tasks on her website, YouCubed, and on the NRICH website.
PUTTING IT INTO PRACTICE
During the summer of 2015, Boaler invited 81 seventh- and eighth-graders from a low-income district near Stanford to come to a summer math camp focused on algebra concepts. She gave the students a pre-test and found that their abilities ranged from very low (getting 0 answers correct) to fairly high. Then, for 18 days she taught them math well.

The instructional program focused on mindset messages, was full of inquiry-based, low-floor/high-ceiling tasks, was visual and used mixed achievement groups. At the end of 18 days, when Boaler gave them another test they had improved on average by 50 percent.

"They improved because they changed their beliefs that they were not a math person to believing they were a math person," Boaler said. After the course, students said they looked forward to math and saw math as a creative subject.

Administrators from the district came to observe partway through the camp and couldn't tell who was a low achiever and who was a high achiever in the class. Boaler also makes it clear to the students in the workshop what she expects from them, and speed is not something she's evaluating. Instead, they do norm building so that everyone knows how to appropriately work in groups, help one another and be supportive.

"If we don't pay attention to those kinds of interactions, and kids are dominating, or thinking they're smarter, then we're really in trouble," Boaler said.

Removing the time pressure from math is another important issue for Boaler. Neuroscience research out of Sian Beilock's lab at the University of Chicago has shown that time pressure often blocks the brain's working memory from functioning. This is particularly bad for kids with test anxiety.

"The irony of this is mathematicians are not fast with numbers," Boaler said. "We value speed in math classrooms, but I've talked with lots of mathematicians who say they're not fast at all." But it is common for math teachers to call on the kids who get the answer quickly, reinforcing the idea for all students that rapidity is what matters.
COMMON PUSHBACK
Math education experts have been making the same case as Boaler for decades, and yet math education in the U.S. has not shifted much. Teachers often say they have to cover all the topics in the curriculum to prepare students for the tests they will be expected to pass, leaving them with no time for the kinds of open-ended, discussion-based math that Boaler advocates.

'It is very difficult to have a growth mindset and to believe that you can grow or learn if you are constantly given short, closed questions with a right or wrong answer.'

Boaler agrees with teachers that there is way too much to cover in the curriculum, especially because she finds much of it to be obsolete (don't get her started on the textbooks themselves). "The most important thing we can give kids is to think quantitatively about the world and apply a mathematical lens to different situations," she said.

In addition to teaching students, Boaler trains teachers in her methods. Often they go back to their classrooms and apply these theories, which means they aren't covering every topic in the textbook, and yet their students do better on the standardized tests anyway. Boaler is not a fan of all the tests American students must take, but she says teaching math the right way deepens kids' understanding of math in real ways that show up on tests, too.

Teachers and parents often push back against this kind of math. They wonder where memorization of math facts fits into the model, given the belief that kids must know their times tables to succeed in higher-level math. Boaler says that's unnecessary. She is a math education teacher and has risen to high levels of math learning without ever learning her math facts. She has number fluency, knows how to manipulate numbers and understands concepts, but she doesn't have her math facts memorized.

The Programme for International Student Assessment test (PISA), which is often used to compare achievement across countries, has a section about attitudes and beliefs. Those surveys show that kids who approach math as memorization are the lowest achievers in the world. "America has more memorizers than almost any country in the world," Boaler said. The highest achievers are those who think about the big ideas and make connections.

Likewise, repetition of math tasks is not helpful to deep learning. The same kind of problem with different numbers does not improve understanding, Boaler said. What students really need is "productive practice," approaching the problem from different directions, applying the ideas and explaining reasoning.

Boaler is on a mission to "revolutionize" how math is taught in the U.S. She has written several books to help teachers learn to teach with her methods, offers a free online course, and even gives away curriculum for teachers, students and parents on her YouCubed website. During one week at the start of the 2015 school year Boaler gave away five free math lessons, encouraging teachers to try this approach. She's pleased that 100,000 schools tried the lessons, and teachers could see the difference in their students. A survey of students found that after the lessons and the growth mindset videos, 96 percent believed they should keep trying after making a mistake in math.

Boaler said a big problem is that math teachers themselves are math-traumatized. They came through a system very similar to the one in which they work. Elementary school teachers in particular often feel insecure about math.

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'Not a Math Person': How to Remove Obstacles to Learning Math | KQED

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Neuroscientists now know that the brain has the ability to grow and shrink. This was demonstrated in a study of taxi drivers in London who must memorize all the streets and landmarks in downtown London to earn a license. On average it takes people 12 tries to pass the test.

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"Unfortunately, as children begin school and use formal mathematics, they often begin to view math as a set of rules and procedures rather than as a way of solving everyday problems.

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Math education in the United States is a subject of constant anxiety. Our country's future feels imperiled when our students land in the middle of the pack on international standardized tests, behind many Asian countries, most of Western Europe, and the likes of Slovenia and Latvia. There's also personal angst, each time a kid throws down his pencil and concludes he's just not meant for arithmetic.

A wholesale revision of the way we teach math is a tempting idea, either in the form of a fully rebooted curriculum or in dramatic changes to teacher training. This explains some of the recent popularity in the United States of Singapore math, for instance. But maybe there's another way.

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Over the last decade, researchers in cognitive psychology have found that better math education comes from surprisingly simple changes in the way numerical concepts are presented. These insights have the potential to shake up the way math is taught in the classroom, and even move the country up in those international rankings.

Consider something as elementary as patterns. In a paper published in the most recent issue of Child Development, Nicole McNeil of the University of Notre Dame and Emily Fyfe, a graduate student at Vanderbilt University, ran an experiment in which preschool-age children were taught patterns using one of two methods.

In the first method, the researchers told kids to think of patterns in concrete terms, as in "red block, blue block, red block, blue block." In the second, they taught students to describe the same pattern with abstract labels, "a, b, a, b." McNeil and Fyfe found that students who learned with abstract labels had an easier time seeing the general rules behind what they were learning. They were also better able to transfer the skills to other patterning problems, suggesting that teaching a concept correctly upfront improves math achievement down the line. "Some relatively small changes that we may not think about can cascade to have bigger effects on the way children think about different math concepts," McNeil says.

Despite the promise and the hype, there isn't solid evidence that improving executive function leads to better grades.

Adjusting traditional English syntax also offers interesting possibilities. In 2003, cognitive psychologists at Indiana University found that elementary school students understand fractions better when, for example, ¼ is described as "of four parts, one," which is how fractions are spoken of in South Korea, rather than as "one-fourth." Another study found that students grasp the concept of cardinality - the total number of objects in a set - more effectively when the teacher names the objects first, as in "cars, there are three," rather than, "there are three cars." The reason is that when "cars" is the last thing small children hear, they fixate on the objects themselves at the expense of what they're supposed to be learning.

In previous research, McNeil had found that similarly small adjustments in the way students are introduced to the equal sign can make a difference later on. When students in the United States learn about equations, it's usually with an operation on the left side of the equal sign and a blank on the right (12+7=__). This leads kids to misconstrue the equal sign as meaning something like "fill in the blank," rather than as a symbol that indicates equality between two sides. The misconception causes problems years later when students learn algebra and need to start performing operations on both sides of the equal sign. McNeil found that a simple way to solve this is to vary the placement of the blank, so that in some problems children fill in the answer on the left side and in others they fill it in on the right.

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The idea that an understanding of children's thinking should influence the way math is taught is not new. Informally, classroom teachers are always making on-the-fly adjustments in search of an approach that makes a concept click with pupils. Researchers have also been doing this kind of work for a long time, though the application of cognitive psychology to math instruction intensified with the creation of the Institute for Education Sciences in 2002. The organization operates out of the Department of Education and was created in conjunction with the No Child Left Behind Act. It funds research that attempts to determine which teaching practices work best, and it has placed a particular emphasis on funding cognitive experiments.

The institute "attracted a lot of psychologists by making this money available. I think it's a success story," says Bethany Rittle-Johnson, a psychologist at Vanderbilt University who studies math pedagogy.

As a tool for improving math teaching, cognitive psychology has a lot of appeal. Math concepts are deep and subtle, and build on each other, such that slight misunderstandings early on can cause bigger problems later when students need to use basic ideas to learn more complicated material. Give that, it makes sense that we'd want to figure out just the right way to present concepts to a young child's brain.

Some researchers worry, though, that while small adjustments can generate encouraging results in lab experiments, they're not enough to alter the trajectory of a child's math education or to fix a system of math education widely seen as in need of major improvement. Drew Bailey, a psychologist at the University of California Irvine School of Education, has written about what he calls "fade out," or the tendency of math interventions to generate temporary bumps in achievement, which disappear over time. Rittle-Johnson is also skeptical that small adjustments in preschool and elementary school math instruction are enough to produce significant downstream benefits.

"This idea that it's an inoculation, that if we fix the problems early we won't have problems later, we were hoping it was going to be true and some people like to think it's true, but I don't know a single piece of evidence that bears that out," she says.

Yet despite these concerns, Rittle-Johnson and others continue to look to cognitive psychology as an answer to the country's math education woes. This is partly because other avenues for reform are so hard to implement. Reworking the way American math teachers are trained is a generational problem, and broad curricular changes often look good coming off the presses, but end up proving hard to implement. By comparison, asking teachers to adjust the way they describe fractions or to tweak the way they present addition problems, is something that could start happening tomorrow.

"The hope is that you teach this a little better, teach that a little better, we reach enough teachers, and you get some sustained [improvement]," says Rittle-Johnson. Indeed, it's these little additions to the field that hopefully will generate exponential learning results, which can compound over time.

Kevin Hartnett writes the Brainiac blog for Ideas. He can be reached at kshartnett18@gmail.com.

Related:

* Executive function not a panacea for education ills

* The poor neglected gifted child

* Tara Holm: The real reason why the US is falling behind in math

* Editorial: A long-overdue first in mathematics

* Taking notes? Bring a pen, skip the computer

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Could small tweaks reap big rewards in math education? - The Boston Globe

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Math education in the United States is a subject of constant anxiety. Our country's future feels imperiled when our students land in the middle of the pack on international standardized tests, behind many Asian countries, most of Western Europe, and the likes of Slovenia and Latvia.

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Differentiated Instruction Strategies: Learning Stations - TeachHUB

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It's difficult to reach every student with the same teaching strategies. Learn how to differentiate your instruction using learning stations.

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Learning centers are an amazing way to get your students to take a more active role in their learning. If designed effectively, math centers can provide much-needed review, practice, and enrichment for students that is differentiated to meet students' needs and interests. When I first began to use math centers, I had no idea what an amazing impact they could have.
Here are just some of the benefits:

I'd be willing to bet that you like it when your principal involves you in making important decisions at work, instead of simply telling you, "This is what we are doing and that's that." Kids feel the same way. Students who have a choice of learning activities feel empowered and tend to show much more interest and persistence in completing work. I am often amazed by how much center work gets completed in my classes. As a traveling math teacher, I occasionally walk into a classroom to teach the day's lesson, and I find a student or two already working on math centers before class even begins. When kids are assigning Increased student motivation. themselves work and having fun doing so, that's a pretty exciting thing to see.

Meaningful learning opportunities. Students are working on skills they genuinely need to practice or that they are personally interested in exploring further. This is provided that your center activities target students' real learning needs, which requires a degree of planning on your part, as well as an understanding of your students' strengths and weaknesses, instructional levels, and your curriculum. Future posts will address this topic in more detail. Also, it bears mentioning that after my first full year of using centers, I had a significant increase in the number of students scoring " advanced" on their state testing.

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Learning centers are an amazing way to get your students to take a more active role in their learning. If designed effectively, math centers can provide much-needed review, practice, and enrichment for students that is differentiated to meet students' needs and interests.

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If designed effectively, math centers can provide much-needed review, practice, and enrichment for students that is differentiated to meet students' needs and interests.

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"To me, “student-centered teaching” relates to lessons where I offer students experiences to figure things out for themselves. “Traditional teaching” is when I present information to students that I’d like them to learn. I use both approaches in my teaching all the time, but I’m mindful about when I choose each."

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Thursday, November 10th, 2016

I'd like to reframe the divide that seems to exist when we talk about "student-centered teaching" and "traditional teaching." Instead, I suggest that we use these labels to describe, without blanket judgment, two different kinds of teaching decisions, each with its own purpose and value. To me, "student-centered teaching" relates to lessons where I offer students experiences to figure things out for themselves. "Traditional teaching" is when I present information to students that I'd like them to learn. I use both approaches in my teaching all the time, but I'm mindful about when I choose each.

As an example, the other day I was teaching at the school in San Francisco I visit regularly. A third-grade teacher in the building brought a copy for me to sign of the Third Edition of About Teaching Mathematics. It's the one with the cover below. Vanessa is a first-year teacher, and she had used ATM in one of her teacher preparation classes.

When I looked at the cover photo, I recalled the lesson I was teaching when it was taken. It was about polygons. To prepare, I had drawn a dozen or so shapes, each on a separate sheet of paper. (For the papers, I had folded and cut copy paper into fourths to have smaller rectangles, each 4 ¼" by 5 ½".)

Some of the shapes I drew were polygons and some weren't polygons, but I didn't use the terminology of polygon with the class or present a definition of what a polygon is. Rather, I planned to tape the shapes on the board in two separate groups, one group of shapes that were polygons and one of shapes that weren't polygons. I'd have the students examine the attributes of the shapes in each group and figure out the rule I had used to sort them.

I could have begun the lesson by explaining what a polygon was, discussing with the class whether several of my shapes were or weren't polygons, and then asking students to decide which of the other shapes I had drawn fit my definition. That would be an example of what I think of as "traditional teaching." (Sometime I've heard this teaching approach described as "I do, we do, you do.") In contrast, setting up an experience where the students are asked to figure something out for themselves, confer with their classmates, and then later hear a mathematical explanation from me, is what I think of as "student-centered teaching." (This is more of "You do, we do, I do.")

Sorting the Shapes
I began the lesson by posting these two shapes:

Then I held up another shape:

I asked the students to think about which of the first two shapes it belonged with. I had them turn and talk to a partner. Then I asked students to report, asking them to explain their decisions.

Students sometimes had differing opinions about a shape, especially for the first several shapes. After students offered their opinions and explanations for each shape, I taped the shape in the group where it belonged. (See the photo of the book cover for the shapes that I used with this class.) As we proceeded, I still didn't give the students any additional information, but followed this process for all of the shapes I had prepared.

What I especially like about this experience is that it gives students the opportunity to think about the attributes of shapes, make conjectures, and try out their ideas by deciding where shapes belong. When I posted a shape in the correct group, students received feedback that either confirmed their idea or contradicted it, which is information they could use for thinking about the next shape. The students did more talking than I did in this lesson, and that's one of the characteristics I ascribe to "student-centered teaching."

Students Produce More Shapes
After we sorted all of my shapes, I gave each pair of students a piece of paper the same size as I had used for my shapes. I asked them to work together, draw a shape, and decide in which group it belonged. (I gave pairs that finished more quickly an additional piece of paper for another shape.) Then each pair came up and showed their shape (or shapes), and the others predicted where it belonged. Again, I pasted the shape in the correct place.

In this way, the students contributed to the lesson by creating shapes for the rest of the class to discuss. They were producers contributing to the experience, not only consumers of what I had prepared. This active involvement is another characteristic I ascribe to "student-centered teaching."

Describing the Attributes
I next engaged students in sharing their ideas about the shapes' attributes. One way that I've found to be successful for this discussion is to ask students to describe one thing they notice about the shapes in one of the groups, and I record their ideas for all to see. For the polygon group (still not yet labeled), students offered: no curved sides, they all have a space inside, no crossover lines, and more. For the non-polygon group, students offered: curved sides, weird shapes, curved and straight sides, sometimes not all lines touching, and more.

Again, this is to me an example of "student-centered teaching," because my focus was on eliciting students' thinking, still not yet imparting information.

Introducing Polygons
After I recorded the students' ideas (waiting until after is a key part of my teaching decision), I revealed my rule. I labeled one group Polygons and the other group Not Polygons, telling them (and here telling them is a key part of my teaching decision) that these are mathematical terms that label the shapes in each group. I described the attributes of polygons, starting with the students' language and finally moving to a mathematical definition of a polygon that I wrote on the board: A polygon is a two-dimensional shape with straight sides that enclose a space but do not cross each other.

A confession: I honestly can't recall the exact definition I wrote that time. I've taught the lesson to different classes and have always presented a definition that I thought the particular students could relate to. The definition I recall learning was something like: A polygon is a simple closed plane figure bound by three or more straight line segments. With students, sometimes I use "figure" instead of "shape," sometimes "plane" for "two-dimensional," sometimes "do not intersect" instead of "do not cross each other."

Presenting mathematical definitions to students, as I did here by defining a polygon, has long been a part of "traditional teaching," where we impart information, introduce terminology, and, when appropriate, show representations. Here I presented information―the terminology of polygon that's the conventional mathematical language. What's important here to me is that I presented this information (in the "traditional teaching" mode) after the students had done some thinking on their own and had a context to connect to, telling them information that they couldn't figure out or discover without some outside source.

So, it's not "student-centered teaching" vs "traditional teaching" that I think about, but more about knowing when each approach is appropriate. My litmus test: If the knowledge I want students to learn is something that they can figure out (like thinking about the attributes of shapes) by relying on their own thinking, I try and think of an experience that engages them in sense making. However, if the knowledge is information that students couldn't discover without information from another person, a book, or some other source (like the terminology we use to label shapes), then imparting information is not only appropriate but necessary.

Variations on the Lesson
Sometimes I've taught the lesson as a Silent Math lesson where no one talks (not even me) as we sort the shapes. Instead of having students talk in pairs about shapes, I signal individual students to come up and tape a shape in one group or the other, and then I either nod in agreement or move the shape to the other group. I like doing this when I want to provide students as much opportunity as possible to think for themselves without hearing from others. Sometimes, after we've sorted shapes, instead of leading a class discussion about how the shapes were sorted, I ask students to write what they think my rule is. As with most lessons, there's no one best way to teach it.

An Extension
The Greedy Triangle is a children's book that I wrote for the purpose of introducing polygons through the context of a story that can engage children's interest and stimulate their imaginations. It's useful as a follow-up or introduction to this lesson. A section at the end of the story provides mathematical information and ideas for involving students in thinking about shapes.

A Note about About Teaching Mathematics
About Teaching Mathematics is now available in its Fourth Edition, a new (and improved) version of the book pictured above, with a new cover.

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Thursday, November 10th, 2016 I'd like to reframe the divide that seems to exist when we talk about "student-centered teaching" and "traditional teaching." Instead, I suggest that we use these labels to describe, without blanket judgment, two different kinds of teaching decisions, each with its own purpose and value.

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Math Centers and Child  Brain Development

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Math Centers and Child  Brain Development

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Education.com | #1 Educational Site for Pre-K through 5

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As kids head back to school, our crew of trusted teachers are here for you. Our Pre-K - 5th Grade resources support children in all the different ways they learn, so parents and teachers always have what they need to boost each kid's unique potential.

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Designing Effective Activity Centers for Diverse Learners

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Designing Effective Activity Centers for Diverse Learners

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Minds in Bloom is thrilled to welcome Sara from Sara J Creations to the blog today! She's sharing five tips for setting up math workshop, which can be a challenge on its own. Enjoy!

Do you use math workshop in your classroom? A few years ago, I was just venturing out into the world of math workshop after successfully using the workshop format for reading and writing. At the time there was very little written about it, and most of what I knew I had learned from other teachers in my school district.

At the most basic level, math workshop involves a mini-lesson, independent practice, and a share time. The independent practice part goes by many different names: centers, rotations, math tubs, stations, guided math, etc. No matter what you call it, small groups rotate through a variety of activities to reinforce the concepts you are covering. During this time, the teacher can work with small groups in order to better meet the needs of each student.

Setting up a math workshop format can be overwhelming if you have never done it before. I simply did not know where to start and had very few resources to help except for my friends and trial and error. I adjusted and reworked my set-up multiple times until I finally found something that not only worked for me but worked for my students, as well. They were loving math in a way I had never seen with past classes. The format that I used went a little something like this:

Monday - longer math lesson; teach games and activities that students will use during math centers that week

Tuesday - longer math lesson; teach games and activities that students will use during math centers that week

Wednesday - math workshop - students rotate to two of the six stations

Thursday - math workshop - students rotate to two more of the six stations

Friday - math workshop - students rotate to their final two stations

My students were divided into five groups (not always equal in size but usually divided by ability level based on a pre-assessment for the unit), and they rotated through different stations during the course of a week. Now that you have an idea of the math workshop format that I used, here are my top five tips for setting up math workshop in your classroom.

If the way you have math workshop set up in your classroom isn't working, give yourself permission to change it. I know your gut instinct is to wait until next school year, because your students are already used to the routine, and you don't want to throw them for a loop. I promise...your students will figure it out and rise to the occasion. There is no point in continuing on with something that isn't working for you or your students. I completely changed how many groups and rotations I had in the middle of the year. I am not even talking about after we returned from a break. I am talking on Friday it was not working, and I was miserable, so on Monday we changed it all up.

Between math workshop becoming more popular, and the explosion of teacher ideas on blogs and Pinterest, I have seen a lot of different ways to set up math workshop. There are many ideas out there, but every idea isn't for you. When I first tried math workshop, I did what I had seen a few other people do - divide the class into three groups (high, medium, low) and have them rotate through three stations (teacher, practice, game) every day. It just didn't work for me. AT ALL. I loved that I saw every student every day, but it was crazy. It was overwhelming to plan that many activities daily. My other issue was that dividing 28 students into three groups didn't really give me "small groups." There wasn't a table that we could all fit at comfortably, and I really wasn't giving each child the attention they needed. Don't get me wrong: This format works for some teachers. Just don't feel like you have to make it work if it doesn't fit you and your students' needs.

I also tried doing workshop/centers five days a week. I just assumed you were supposed to, but I was having problems fitting all of my instruction into a mini-lesson, not to mention the amount I had to prep to have new centers every single day. That is why I finally settled on the format that I did. Monday and Tuesday gave me the chance to teach longer lessons in more detail and to have time to teach any games or activities that the students would use later that week. That way I wasn't spending our workshop days explaining each station. They already knew what to do and could get right to work.

I think a key to the success of math workshop is planning and having everything prepped ahead of time. Before, when I was just teaching a lesson and giving them a worksheet, I could easily wing it and change if something wasn't copied or ready. With math workshop, it caused me to be better at planning in advance. Here is how I prepped:

Plan out the unit roughly - what you want to cover, how long it will last, etc.

Plan one week at a time - I found that if I planned too far in advance, my students would throw me for a loop and need extra time on a concept, or they'd catch onto a concept really quickly, and then my plans would be off for several weeks.

An example of one week's worth of math workshop plans

Copy ahead of time - I planned on Thursday nights and had a copy mom copy for me on Friday. Then, I had Friday afternoon and the weekend to pull and prep anything needed for the following week.

Set up on Monday - on Monday I would put all of the activities into the bins for the week, down to the manipulatives or supplies that they might need. That way, I wasn't scrambling for anything on Wednesday when we started our rotations.

This might be a good time to mention that you do not need to plan six new activities every week. That is overwhelming. Get the most out of your activities and games. Students can use them more than once. I also usually had a review station where we practiced a concept we'd already learned to keep it fresh for them. Use what you have over and over again. Math workshop is a great way to spiral the curriculum and make sure students are practicing topics all year long.

Also, being organized does not mean it has to be a lot of extra work. It has to be functional, and that is exactly what my math bins were. Of course, I now drool over the cute color-coordinated math bins with matching labels that I see online, but that was not what my bins looked like at all. I needed something that worked for me, so I grabbed whatever bins I had on hand, wrote out labels (I know...gasp...they weren't typed and cute), and taped them on. But you know what? It worked! The bins were organized with any papers, supplies, and manipulatives they would need. I even included little laminated signs to remind them what to do with their finished product from that station. Then the next week, I would just trade out what was in the bin for the new activities for the week. Functional! It needs to work for you!

When I would be looking ahead and planning out the following week, I would check to see how many interruptions we had coming up - assemblies, field trips, testing, meetings for me, substitute teacher, etc. If they fell during math workshop time, I would first try to see if we could do math workshop at a different time during the day. If that was not possible, we would cancel math workshop for the week. Instead, all five days would look like a normal Monday or Tuesday - a lesson and activity, then some math games. If you skip a day of math workshop with the way that I did my rotations, each student would miss out on two stations, and you would miss out on seeing two small groups. That DID NOT work for me. Each rotation was too important for the students to just skip, so it was all or nothing. Now, I only had to do this a few times during the year. Usually, I could figure out a way to move things around and make it work because my kiddos LOVED math workshop days and did not like if I changed things up.

I think one of the biggest reasons math workshop was a success in my class was all of the practice we did when we first started. When we first started, we would spend several weeks just practicing what rotations would look like - where to go, how to act, how it should sound, what they should do, when they could go to the bathroom, if they needed help, where they got supplies, if they finish early, etc. At the beginning of the year, I taught them six easy games, and these were our six rotations. We would practice and practice and practice, and at each station they would play a game with which they were already familiar. It was not smooth sailing. I wanted to hit my head against the wall on multiple occasions, but the more we practiced, the better it got, and the smoother the rest of the year went. Even if you are making changes in the middle of the year, I still suggest practicing and having math workshop boot camp before you release the responsibility and let them try it on their own. I also found it helpful to create anchor charts so that the expectations were written in black and white (or whatever color Mr. Sketch I happened to grab).

An anchor chart of the expectations for everyone, teacher included!

If you need more information about setting up math workshop in your classroom, I have blogged about it HERE and also have created a product with my tried and true tips, as well as organization and planning sheets for math workshop. You can find that by searching in my TpT store, linked in my bio.

I created a free sample to help you get started with planning math workshop. It includes three planning sheets (weekly plan, unit plan, and small group plan) to get you started. Click the picture below to download your free copy.

Sara is a former second grade teacher turned stay-at-home mom to two little girls. She creates activities (many for math workshop) that she did not have time to create while in the classroom to sell in her TpT store, Sara J Creations. She also blogs about teaching, parenthood, and crafting on her blog. You can connect with Sara on Pinterest, Instagram, or Twitter.

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5 Tips for Setting Up Math Workshop - Minds in Bloom

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Minds in Bloom is thrilled to welcome Sara from Sara J Creations to the blog today! She's sharing five tips for setting up math workshop, which can be a challenge on its own. Enjoy! Do you use math workshop in your classroom?

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https://www.ixl.com/math/

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Discover thousands of math skills covering pre-K to 12th grade, from counting to calculus, with infinite questions that adapt to each student’s level.

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https://thecornerstoneforteachers.com/math-games-center-ideas/

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Learn how to create and implement math games quickly and inexpensively! On this page, you'll find photos of math games and free printable directions for several of them. You can see how to store and organize these math partner games and introduce them to your class on the Starting Math Game Routines page.

Teacher-made math games for grades 2-4

Remember, even if you don't use math partner games, you can still use the activities below as centers, in small groups, or as whole class games! Click on any picture to enlarge it and read the directions.

Division Memory

Facto: Basic Math Fact Practice

Pass Out (Multiplication Practice)

Speed (basic fact practice, any operations students know)

Three In A Row (A game of logic and strategy)

Battle (basic fact practice, any operations)

Add 'Em Up (multiplication/division facts)

Dice 1000 (3 digit addition and 3 digit multiplication)

Division Go Fish (division fact practice)

Timed 5 Card Operations (all math operations students know/ fact families)
There is also an untimed version.

Printable math partner games for Common Core

I am in the process of creating printable directions for the games above and many, many more! If you don't have the time and energy to make your own centers, just purchase and print these out-they're ready to use!

So far, I've made math games for every Common Core domain for grades 1-5 (Operations and Algebraic Thinking, Number and Operations in Base Ten, Fractions, and Geometry) with the exception of Measurement and Data. Info on each is below.

After numerous requests, I have finally made a printable set of multiplication KITs and addition KITs! Each download is 171 total pages and is available for $4.50. They include the recording sheets with directions for each KIT, instructions for making the KITs, game boards and game cards, and more. You can download a free preview to see everything that's included before you buy. I really appreciate your support!

Commercially-bought games

Below are commercially-bought games that took a very short time to turn into math tub activities/partner games.

Clever Catch Ball: Students toss this beach ball gently back and forth; whatever math problem their left thumb lands on, they have to solve. I have one for each of the four math operations. You can also buy plain beach balls at the dollar store and write on them yourself with permanent marker. You can program the balls with parts of speech, countries/capitals, vocabulary words, spelling words (read the word aloud to the partner and they must spell it correctly)... the possibilities are endless! Be sure to have students model how to toss and how not to toss the ball, and don't be afraid to put away this activity if students get too wild with it.

Many teachers have math bingo games, either store bought or handmade. Pull a few bingo cards from your supply, along with extra chips/ place holders and photocopies of the fact problem cards and you're ready to go! Students put the fact problem cards in a face-down stack and flip them over one at a time, covering the numbers on their boards as corresponding math problems are shown. The first one with a completely full board wins.

Turn a worksheet into a hands-on game!

Even worksheets can make great centers and math tubs! The only problem is you must keep a supply of photocopies. About once a month, put a center helper in charge of checking worksheet centers and math tubs to be sure they have enough copies. The student can pull one copy of the sheets that are running low and place it in your file or basket of papers to take to the photocopier. Also, some worksheets are simple enough that older students can copy the graphic organizer or framework onto their own paper. This worksheet is an example of one simple enough that some students could make themselves, especially if you did not require that they copy the pictures of the die.

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Learn how to create and implement math games quickly and inexpensively! On this page, you'll find photos of math games and free printable directions for several of them. You can see how to store and organize these math partner games and introduce them to your class on the Starting Math Game Routines page.