## Posts Tagged ‘Bilingual’

### How to Create an Anchor Activity Using a Tic/Tac/Toe Board

Thursday, February 25th, 2016

AUTHOR: Virginia Keasler and Mary Headley, Math Specialists

How do we teach math to the wide range of diverse learners in today’s classroom? It is often difficult to match the readiness levels of every student and knowing where to start can be a challenge. Consider starting simple and celebrating successes along the way. Anchor activities can help you reach the diverse population in your classroom.

What are anchor activities? These activities are used for students to extend learning at their level. Student choice within these activities allows for students to apply and experience the learning in a variety of ways.These ongoing assignments are considered independent work and can be something students are working on for the next two weeks or something due in a few days. While some students are working on anchor activities, the teacher can utilize small group instruction to work with students who need more help.

Tic/Tac/Toe Boards: The content for this anchor activity can be modified to meet the needs of students at varied levels. Teachers may use Tic/Tac/Toe boards for extension, assessment, or as homework choices for the week. On a Tic/Tac/Toe board, the teacher can strategically place activities to enable students to get a Tic/Tac/Toe that demonstrates their learning.

Helpful Hints for creating a Tic/Tac/Toe board:

1. Determine the content/topic for the board.
2. Brainstorm activities, assignments, and products for the content/unit you have chosen.
3. Check TEKS alignment.
4. Write ideas on post-it notes.
5. Sort activities based on learning styles (verbal, auditory, kinesthetic, etc…)
6. Place post-it notes on the Tic/Tac/Toe grid.
7. Check the configuration for variety to achieve a Tic/Tac/Toe. Move as needed.
8. Type idea onto the Tic/Tac/Toe grid.

The following table gives an example of a Tic/Tac/Toe board for reviewing a math unit:

 Explain the math steps that you would use to solve a problem from this unit Solve two of the problems in the “extensions” station Using the “beat” of a popular song create your own math song. See the choice board station for rules Create two word problems that go with the concepts in this unit Student Choice Activity (with teacher approval) Define the unit’s vocabulary words with your own form of graffiti Complete one mini-project from the project board Develop a game using skills you have learned in this unit Research and write how these concepts might be used in the real world

Variations:

• Allow student to complete any three tasks–even if it does not make a Tic/Tac/Toe
• Create different choice boards based on readiness (Struggling students work with options on one choice board while more advanced students have different options.)
• Create choice board options based on learning styles or learning preferences. For example a choice board could include three kinesthetic tasks, three auditory tasks, three visual tasks.

Author Rick Wormeli offers the following Tic/Tac/Toe board based on Gardner’s (1991) multiple intelligences.

To access a blank choice board to use in your classroom click on the following link: Blank Choice Board

Reference:

Wormeli, Rick. Fair Isn’t Always Equal: Assessing & Grading in the Differentiated Classroom. Portland, ME: Stenhourse 2006, pages 65-66

### Anchor Charts: Let the Walls Teach

Thursday, February 25th, 2016

AUTHOR: Esmeralda Alday, Bilingual

One of the first things I notice when I walk into a classroom is a teacher’s use of wall space. Having always taught multiple grade levels – in some of the smallest classrooms on campus – in one school year, I had to learn how to maximize the little wall space I had available. I learned a few weeks into my first year teaching that as glossy and sleek as the content-area and motivational posters (think that ubiquitous “Hang in There” kitten) I purchased for my classroom were, or how well-decorated my classroom was the week before school was even back in session, very little of what was on my walls was actually useful for my students in reinforcing the concepts, skills, and academic vocabulary I was working so hard to teach them. Sadly, it took a few more years for me to discover the magic of anchor charts.

What I’ve learned over a decade in this profession is that when used correctly, anchor charts are one of the most effective, engaging, and student-friendly ways to support instruction through reinforcing key concepts, skills, and vocabulary. One good anchor chart can not only replace an entire word wall, it can make the connections between concepts and terms visibly come to life for students. A great anchor chart can truly be like having another teacher in the classroom. Students can review the steps of a skill, strategy, or process during guided or independent practice using cues from an anchor chart (Harmon & Marzano, 2015).

So what exactly is an anchor chart and what constitutes a quality anchor chart design? If an anchor is “a source of stability and security, used to hold something in place”, then an anchor chart is a sort of classroom artifact or record that provides a visual reference or cues to support students as they progress in their learning throughout the course of a unit or topic (Seger, 2009). Simply stated, anchor charts make the teacher’s instruction “clearly visible to students” (Newman, 2010). They are visual reminders of current learning for all students and are indispensable for English Language Learners who benefit immensely from visual cues for academic concepts and vocabulary.

Above: https://www.pinterest.com/pin/559 1

The following are some helpful tips for creating and maximizing the quality and effectiveness of your anchor charts. A quality anchor chart is:

• Relevant – Include only the most relevant/key information to keep from confusing students.
• Clear – Make the chart as clear, neat, and organized as possible.
• Focused – Stick to one focus per chart to avoid overwhelming students.
• Evolving – Allow the chart to evolve throughout the course of a unit by adding information learned as the unit progresses.
• Integral/Useful – Refer to the anchor chart frequently to model its use for students.
• Prominent – Display the chart where in a prominent place in the classroom where all students can see it.
• Current – Focus on  only displaying charts that deal with what is currently being learned in order to eliminate clutter.
• Vibrant – Make the anchor chart colorful and easily visible using dark colors.

Sources:

Newman, L. (2010, October). Anchor Charts: Making Thinking Visible. Retrieved from Expeditionary Learning: https://www.engageny.org/sites/default/files/resource/attachments/anchor_charts.pdf

Harmon, K., Marzano, R.J., (2015). Practicing skills, strategies, & processes: Classroom techniques to help students develop proficiency. West Palm Beach, FL: Learning Sciences International.

### Translanguaging – Normal Bilingual Discourse

Monday, December 7th, 2015

AUTHOR: Ivonne Santiago, Bilingual/ESL Specialist

Translanguaging refers to the language practices of bilingual people. Cen Williams first coined the term in 1994, referring to a pedagogical practice in which students alternated between languages for the purposes of receptive or productive use. Students may have been asked to read in English and write in Welsh and vice versa. Since then, the term and its meaning have slightly changed and yet the basic concept is the same. It is a process in which two or more people, who have comfort in the languages being spoken, are able to maneuver through an intermingling of languages without alienating any one member of the group. Bilinguals, with facility, mix all languages freely according to the situation and their current needs. It also refers to pedagogical practices that use bilingualism as a resource, rather than something that is perceived as a problem.

Translanguaging is NOT “code-switching”. It is not simply changing from one code to another. Code-switching assumes that the two languages of bilinguals are separate monolingual codes that could be used without reference to each other. Instead, translanguaging differs from that notion in that it refers not simply to a shift or a shuttle between two languages, but to the speakers’ construction and the use of original and complex interrelated discursive practices that cannot be easily assigned to one or another traditional definition of language. In addition, it makes up the speakers’ complete language repertoire (Garcia & Wei 2014).

All teaching uses dialog or discourse to communicate and to develop academic use of language. The language of instruction is similar to that of the students’ home language. There may be some slight differences, but nonetheless there is some continuity. That is usually not the case for bilingual students. In order for bilinguals to develop the language, they must practice it within an academic context. Translanguaging affords the opportunity to use home language practices, different as they may be from those of school, to practice the language of school.

Translanguaging practices are particularly effective with bilingual students because their language practices are often stigmatized. Many Latino students are told that they speak “Spanglish”. This term has a negative connotation, as it implies poor command of the language. In reality, it may have more to do with normal contact with English; it’s normal discourse for bilingual students. Translanguaging permits students and teachers to acknowledge and use the full range of linguistic practices of bilinguals, and to use these practices for improved teaching and learning. Listed below are some effective translanguaging practices:

1. Create a student-centered classroom in which they are sitting in collaborative groups and work on engaging, hands-on tasks together, which will inevitably lead to translanguaging.
2. Provide many opportunities for students to discuss, reflect upon, negotiate, and debrief on content, in whatever language they choose, but to present something or collaborate on a product in English.
3. Have students present in one language and provide analysis in another.
4. Provide many opportunities for low-stakes writing in which students can use whatever language they wish (learning logs, personal dictionaries, journals, reflections). These writings can then be used as a scaffold to write something in English.
5. Structure the class so that students are asked to do frequent formal/informal presentations where there is reason to use English. You may allow them and encourage them to use whatever language they wish for reading texts, the negotiating process and ideas and discussion.
6. Purposefully group students so that home language support is available to those who need it. It is best to have students sitting in a small group with at least one other person who shares his/her home language.
7. Have students read a text in their home language before reading one on the same topic in English. This strategy can be used as basic scaffolding-reading about a topic in a language in which students are more comfortable, thus enabling them to better understand a reading on the same topic in English.
8. Encourage students to use bilingual dictionaries to ensure they are learning the “anchor concepts” in both their home language and in English.

Translanguaging is a process by which the human brain is capable of accessing two or more linguistic databases in order to formulate a tapestry of words in various languages (all bound by the rules or English grammar) in the formation of a thought (Vinson 2012). One may implement these pedagogical practices in any educational setting: bilingual, ESL, and even a monolingual class. Translanguaging can serve as a scaffold for learning English and is a powerful way for students to use their languages as an invaluable resource.

References

García, Ofelia, and Li Wei. Translanguaging: Language, Bilingualism and Education. Basinstoke, Hampshire: Palgrave Macmillian, 2014. Print.

Gunnarsson Tina. Translanguaging: A Review of Flexible Language Use on Students’ Learning of Additional Languages (n.d.): Translanguaging. Lund University, 2014. Web.

Vinson, Jenni, and Dr. Ophelia Garica. “The Deliverance of Bilingual Education: Translanguaging.” Translanguaging. NYU, 2012. Web. Nov. 2015.

Witt, Daria. “The Deliverance of Bilingual Education: Translanguaging.” Translanguaging Strategies. CUNY-NYS Initiative on Emergent Bilinguals, Mar. 2013. Web. Nov. 2015.

### Why We Filter Out: Understanding the Affective Filter

Friday, September 25th, 2015

AUTHOR: Seth Herrington, Bilingual/ESL Education Specialist

Educators spend countless hours developing engaging and interactive lessons for students. They pour over curriculum, participate in PLC’s, refine lesson plans through peer-review, and scour the internet for resources that will make the content delivery comprehensible for their students. Despite the deep level of care taken to plan a lesson, there are external factors that can hijack the learning process, rendering the countless hours of preparation useless. This is a phenomenon experienced by all learners and isn’t confined to education. It’s the basketball player that performs well during practice but freezes on the free-throw line under pressure. The business executive who fits the job description for an exciting new position perfectly, but doesn’t interview well due to social anxiety. The English Language Learner who sees themselves as intellectually inferior as a result of repeated failures in mastering academic content in English.

This imaginary barrier is called the Affective Filter. It’s a term developed by Stephen Krashen as part of his “Affective Filter Hypothesis” (Krashen, 1982). According to Krashen, there are three main sources of a raised affective filter.

• Motivation: Learners who are highly motivated tend to acquire new content more quickly. When it comes to English Language Learners (ELLs), fostering motivation to acquire English is at times a difficult task, especially when a lack of motivation stems from an incongruence in the cause/effect relationship between content mastery and personal success.
• Self-Confidence: Damaged self-confidence comes almost exclusively from repeated failures in mastering the English language for ELLs or from damaging experiences in attempting to master English.
• Anxiety: Stemming from circumstances inside the classroom or out, anxiety has an adverse effect on the acquisition of content. Students suffering from anxiety in the classroom experience triggers that render them emotionally hijacked and unable to truly process information presented, let alone demonstrate their comprehension of previously mastered material.

Students can suffer from an affective filter coming from more than one of the above sources. For example, an ELL with damaged self-confidence can also suffer from high levels of performance anxiety. Regardless of the source, a raised affective filter can diminish comprehensible input to the extent of eliminating it altogether.

Minimizing the Affective Filter

Maintaining a friendly, comfortable environment is ultimately the single most effective way to minimize the prevalence of a raised affective filter in ELLs. However, there are a number of additional practices that can help educators ensure that the lessons, units, and/or activities they plan for students result in content and language acquisition. Here are a few:

• Elicit student performance only at the appropriate level.
• Avoid public error correction and focus on the message being communicated rather than correct grammar.
• Increase wait time and include “think time” for ELLs who are devoting an extraordinary amount of cognitive capacity to translating material delivered from English to their native language.
• Allow for ample rehearsal time before student performance.

By implementing these and other strategies, educators can foster an environment where their students can easily acquire language and content — making the countless hours spent in planning instruction worth the effort.

Krashen, S. (1982). Principles and Practice in Second Language Acquisition. Pergamon Press.

### Eight Language Program Models: Four Linguistic Roads

Sunday, March 23rd, 2014

### Author: Tracy Dennis, Bilingual/ESL Education Specialist

All students must travel down the educational super highway. However, English language learners (ELL) must be diverted down different educational roads in order to keep up with the regular population. The No Child Left Behind Act of 2001 fired up states, districts, and schools to construct and/or reconstruct alternate routes along the American highway of education.

A variety of language program models are utilized to assist ELL students, so they can shift gears and reach the same speed linguistically as other students. Eight language models being implemented today are ESL pullout, ESL class period, sheltered instruction, newcomers program, transitional bilingual education, developmental bilingual education, and dual language program.  Four specialized roads and/or routes have been built along the super highway to provide ELL students with assistance: the “pullout feeder road,” the “ELL cul-de-sac,” the “bilingual one-way street” and the “bilingualism two-lane highway.”

In Table 1, Comparison and Contrast of Language Program Models, 7 models are compared and contrasted by definition, characteristics of students served, which grade levels are offered in the program, entry grade stipulations, goals of the program, the number of years students can participate, and the qualifications of teachers (Genesee 1999).  Each language program model tries to help ELL students merge onto this busy and fast-paced education highway, but which model is better?

### Table 1

Comparison and Contrast of Language Program Models

Comparison and Contrast of Language Program Models

Some ELL students are sent down the same highway of education as regular students, but are given more rest stops along the way. Pullout ESL programs place ELL students in the slow right lane of the highway, so students can fuel up with small group or individualized ESL instruction outside of the mainstream classroom. ELL students receive personalized attention and instruction. Nevertheless, ESL pullout is the most expensive of all language program models and is the least effective model (as cited in Ovando et al. 2003). Students pull off the education highway onto the “pullout feeder road” for extra English instruction. When this happens, ELL students miss out on classroom instruction and tend to feel isolated. An alternative road currently under way is the “ESL team teach road” with the ESL and mainstream teachers working as a team. Yet, these teachers must “share equal teaching responsibilities for the whole class, have joint planning time, and collaborate well together.” (Ovando, p. 74)  ESL team teaching allows ELL students to be on the highway without having to exit frequently, yet students still get the roadside assistance they might need.

ESL programs that provide specific classes for ESL students are similar to being on a cul-de-sac surrounded by other ELL students yet still within the mainstream educational community. ESL students might have regular classes for math, science and social studies but have special ESL classes for reading and writing. Also on the “ELL cul-de-sac” is sheltered instruction where students are provided more linguistic modifications and clarifications during content instruction. “Sheltered instruction provides students with continuing English language development, access to the core curriculum, and opportunities for classroom interaction.” (Ovando et al. 2003) The newcomer program in this cul-de-sac is designed for new immigrant students, usually at the middle school or high school level. This High Intensity Language Training (HILT) uses ESL instruction in content area classes, usually incorporating sheltered instruction, and then mainstreams students into linguistically less demanding classes such as music, physical education, and art. (McKeon 1987) The “ELL cul-de-sac” nurtures students as they acquire the English language while giving students access to the super highway curriculum.

The one-way street language program consists of students with the same first language traveling together to gain knowledge. This street has a fork in the road, where some ELL students are driven down the “transitional bilingual street,” or “early exit,” and others take the “developmental bilingual street,” or “late exit.” Transitional bilingual education uses students’ first language to develop English skills needed to quickly move onto the super highway of education. Bilingualism is used to transition students to all English instruction. (Genesee 1999) “The highest priority of most transitional bilingual programs is teaching English, with the goal of mainstreaming students into grade level classes as soon as possible.” (Ovando et al. 2003)  Developmental bilingual education seeks to obtain fluency in both languages before releasing students. Students are mainstreamed based on English proficiency that is sufficient for sustaining academic achievement in an all-English classroom (McKeon 1987). Another route constructed is the One-Way Dual Language, which supports “one language” groups of students to become bilingual, bicultural, and biliterate. Curriculum is separated 50/50 into two languages for instruction, consisting of no translation and no repeated lessons in the other language. The language of instruction is dependent on the content area. The goal of the One-Way Dual Language is to develop students’ English proficiency while maintaining their native language proficiency.

The bilingualism two-lane highway offers native English speakers and limited English speakers the ability to develop fluency in two languages. This highway may soon be the route of choice for helping all students to have the extra edge of being bilingual. On this highway, bilingual education is for all, not just for ELL. “Two-way bilingual programs integrate language minority and language majority students in a school setting that promotes full bilingual proficiency and high academic achievement for both groups of students.” (Ovando et al. 2003)  Dual language programs, originally developed in Canada in the 1960’s, allow for students to learn from each other and develop a sense of community and appreciation of different cultures. (Ovando et al. 2003) In order to construct this two-lane highway of bilingual education, there must be a common second language and a group of native English speakers willing to participate.

Currently, choosing the best language program model is often not centered on what is best for each individual child. The road students are given depends on the district’s and school’s demographics and available resources, as well as the ethnic relations within school and community and the national, state and local political climate. (Mora n.d.) In fact, principals’ and administrators’ knowledge of second language acquisition and attitudes towards ELL affects the services provided. (Mora n.d.)

Districts may implement a model because of the ELL population, lack of available teachers, and/or the district’s priorities. “The design of any ESL program must take so many factors into account that it is difficult to decide which program organization is best for a given set of circumstances.” (McKeon 1987) A district may choose pullout because of the variety of languages spoken by the populations of their ELL students. Or they may choose bilingual education because so many ELL students speak the same first language. If a student is a new immigrant at the middle school or high school level, then they might choose ESL classes, sheltered instruction and/or the newcomer program. All of these language models help students become successful. In a perfect world, though, schools would employ all language models to meet the needs of each individual student.

Advancing into the 21st century will require the rebuilding of America’s educational super highway. The United States is one of the few countries that only teach their children one language. Dual language programs should be promoted to ensure that all of our children are able to compete with the global market because “the 32 million Americans who speak languages in addition to English are at a competitive advantage.” (Jackson-Lee 1996).

References

Crandall, J. 1994. Content-centered language learning. Retrieved Nov. 20, 2005, from www.eric.ed.gov

Echevarria, J., & Short, D. n.d. The sheltered instruction observation protocol (SIOP).

Retrieved November 17, 2005. http://www.siopinstitute.net/pdf/sioppaper.pdf

Genesee, F. 1999. Program alternatives for the linguistically diverse students. Center for Research on Education, Diversity & Excellence, 1-49. Retrieved Nov. 19, 2005 from CREDE Publications and Products database.

Jackson-Lee, S. 1996. Debate on English only legislation. Message posted to U.S. House of Representatives archived at http://www.humnet.ucla.edu/humnet/linguistics/people/grads/macswan/debate.htm

McKeon, D. 1987. Different types of ESL programs. Retrieved Nov. 20, 2005 from www.eric.ed.gov

Mora, J. n.d. Sheltered immersion. Retrieved Nov. 20, 2005 from http://coe.sdsu.edu/people/jmora/Pages/SEIvCanadian.htm

NCLB Action Briefs. Programs of English language learners (n.d.). Retrieved on Nov. 13, 2005, from http://www.ncpie.org/nclbaction/english_language_learners.html

Ovando, C.J., V.P. Collier, and M.C. Combs. 2003. Bilingual and ESL Classrooms: Teaching in multicultural contexts (3rd ed.).Boston: McGraw-Hill.

Rennie, J. 1993. ESL and bilingual program models. Retrieved Nov. 20, 2005 from www.eric.ed.gov

### Designing a Campus Task Force to Increase Parental Involvement Among Latino Families

Friday, March 29th, 2013

### Author:  Trish Flores, Bilingual/ESL Specialist

It is evident that our schools are becoming increasingly diverse with students from different nationalities and language backgrounds represented.  Of these groups, Latinos account for the highest growth rate in the last 40 years.  Latinos are the second largest minority group in the United States and it is projected that in the next 40 years the U.S. Latino population will reach 102.6 million. (Tomas Rivera Policy Institute, 2004) There are an estimated 9.8 million Spanish bilingual students ages 5 to 17 residing in Arizona, California, Florida, New Jersey, New Mexico, New York and Texas.  This data indicates that much thought and consideration needs to be given to the instruction and language development of Latino students who are second language learners.  Authors David Campos, Rocio Delgado and Mary Esther Soto Huerta have researched and explored this subject in their book, Reaching Out to Latino Families of English Language Learners. (2011)  In this book they outline a comprehensive plan on how to best meet the needs of this population of students through the increased involvement of Latino parents.

Change needs to occur at all levels of the culture and environment of our schools in order to positively impact Latino students to achieve high levels of academic success.  If schools fail to identify and support the crucial areas of need of these students they will be more likely to drop out of school, not enroll in rigorous academic courses, and not pursue a college education.   Implementing change requires that schools establish goals and desired outcomes to specifically target areas of needed improvement.  For many of today’s educational communities, this change begins with increased parental involvement.

The phrase “it takes a village” resounds especially true in the educational community of today.  Schools cannot reach all of their educational goals alone.  It has become increasingly apparent that schools need parental support to sustain the academic progress of their students.  When parents are actively involved, students are more likely to attend school and master challenging curricula and graduate from school.  This type of partnership requires systematic planning on the part of the district, especially at the campus level.  Campus leadership is charged with forming a plan to welcome parents and involve them to meet the goals of the campus and the needs of their students.  One way to accomplish this is through the creation of a campus task force.

The first step in creating a campus task force is to identify key individuals who can organize and lead this initiative. These staff members should have high interest in promoting a partnership with Latino parents and establishing goals for increased student performance.  Once the task force has been established, there are several steps that need to be accomplished.  To start, the task force should assess the existing perceptions of Latino families at the campus level by conducting a survey or questionnaire of some type.  Some questions to consider include:

• How is Latino parental involvement perceived by the school staff (inclusive of all staff members) and students?
• Are there Latino parental involvement initiatives at the district level and, if so, how do they impact involvement at the campus level?
• Should Latino parental involvement be improved?  Why or why not?
• What are the desired goals for the campus?
• What hinders parental involvement?

It will be crucial for the task force leader to hold scheduled meetings with the team to determine who will be collecting the data, who will be interviewed, and how the collected information will be analyzed.  The team leader is responsible for generating a plan for aligning the collected feedback with the predetermined goals and objectives set by the team. Careful consideration needs to be given to the different groups of people who will be interviewed and how the interviews will be conducted.  For example, teachers might answer the questions on written forms or on the computer whereas parents might need to be interviewed in person.   It would also be essential to have documents translated into Spanish so that the written language is not a hindrance to parental participation.

Collected data is read and categorized by the team.  Members of the task force will share their findings and look for common threads to be examined, assets, differences, and potential barriers to parental involvement.  Analyzed responses can be shared with the interviewed groups to confirm the accuracy of the interpretations.

Organizing the Campus

After the Latino parent data is assessed and analyzed, the next step is to assess the organization of your school.  This assessment will enable the task force to make decisions about how to structure a plan to increase parental involvement.  Under the guidance of the principal, the team reflects on the level of change needed for each initiative.  For example, if the goal is to increase parental involvement in the PTA, the team would follow a protocol to determine the key participants and their responsibilities.  A chart can be used to track the changes being implemented and their success.

Deciding on Campus Goals and Action Plans

Campus wide decisions about outcomes should guide the goal setting process.   Key questions to consider when making these goals might include the following:

Is it the goal to have Latino parents:

• Learn the behaviors/values of the school?
• Participate in seeking solutions to problems?
• Become active in voicing their concerns for change?

The action plan needs to be implemented over time and be practical, manageable, and involve school staff at every level.  Additional considerations for the development of an action plan might include seeking grants to fund activities, documenting outreach efforts as a part of the campus improvement plan, using Title 1 funds to add key staff to the campus, ensuring that school practitioners can translate for parents, and hiring certified language support teachers who have the credentials to support students.

Latino students are an ever increasing population in our schools today.  If they are to be successful in their educational careers schools must strive to create partnerships with parents to ensure success.  School staff must perceive this relationship to be an asset and design structures within their campuses to promote positive change.  It is the act of valuing home-to-school relationships that will act as the catalyst for this change and make the difference for all students.

Source

Campos, D., Delgado, R., & Soto Huerta, M. E. (2011).  Reaching Out to Latino Families of English Language Learners.  Alexandria, VA:  ASCD.

### Math with Mary!

Friday, August 24th, 2012

### Author: Mary Headley – Elementary Math Specialist

The introduction of new math concepts can be described using three stages:

I. Concrete (the “doing” stage) – This stage involves both teacher and student modeling.

II. Pictorial (the “seeing” stage) – This stage transitions the concrete model into a representational level such as  drawing pictures or using dots or tallies, etc.

III. Abstract (the “symbolic” stage) – This stage uses numbers and mathematical symbols.

Using concrete models is the first step in building the meaning behind mathematical concepts.  These models include a variety of math manipulatives, measuring tools, and other objects that students can handle during a lesson. Research-based studies show that students who use concrete materials develop more precise and more comprehensive mental representations, often show more motivation and on-task behavior, understand mathematical ideas and better apply these ideas to life situations.  (Harrison & Harrison, 1986; Suydam & Higgins, 1977)

Pictorial representations help teachers provide the perfect bridge between concrete representations and abstract algorithms. Pictorial representations include drawings, diagrams, charts and graphs that are drawn by the student or provided for the students to read and interpret. Pictured relationships show visual representations of the concrete manipulatives and help students visualize the mathematical operations. It is imperative that teachers explain how the pictorial examples relate to the concrete examples.

“Up the Hill” Manipulatives stmichaelschool.us

Connecting the dots between the concrete, pictorial, and abstract is the glue that cements the learning for students. This connection provides the understanding that students need to demonstrate a problem or operation using symbolic representations such as numbers. The meaning of symbols and numbers must be rooted in experiences with real objects (concrete) and pictorial representations. Otherwise the symbolic operations (abstract) become rote repetitions of memorized procedures with no understanding.

The gradual movement from concrete to pictorial to abstract benefits all students and helps to prevent the frustration that some students feel when instructed only with abstract processes and procedures.

Perhaps this article has caused you to think about exploring multiple ways to teach math.  Would you like to observe and experience the conceptual development of content? Do you want to give students multiple strategies for success? Would it help you to see how manipulatives can be used to build the meaning behind math concepts?

If the answer to these questions is yes, you may be interested in Math with Mary, an online resource tool that offers professional learning modules designed to build teacher content knowledge and teacher confidence with the use of manipulatives. These modules are hosted by Mary Headley, Education Specialist for K-5 Mathematics at Education Service Center Region XIII, and will walk participants through the use of a specific manipulative which will allow students to explore and develop a variety of math concepts. Using the strategies presented, students will be able to visualize the math while engaging in strategies that build conceptual understanding.

The first course module, Math with Mary: Multiplication with Base Ten Blocks (FA1224478), is appropriate for grades 3-6 and is currently available on E-Campus. This course lays the foundation for understanding multiplication of 2 digit numbers and beyond. Student expectations related to Number and Operations emphasize the use of concrete models and visual representation of numbers and operations. The Multiplication with Base Ten Blocks course supports student expectations outlined in the TEKS and will help teachers build the bridge between concrete models, pictorial representations and the abstract multiplication algorithm. (2 hours CE credit)

Sources

Harrison , M., & Harrison, B., “Developing Numeration Concepts and Skills,”  Arithmetic Teacher 33 (1986): 1–21.

Suydam, M. N.; & J. L. Higgins,  Activity-based Learning in Elementary School Mathematics: Recommendations from Research. Columbus, OH: ERIC Center for Science, Mathematics, and Environmental Education, 1977.