5 Powerful Formative Assessment Strategies for Mathematics Classes!

For teachers to successfully deliver new common core based lessons in mathematics to their students, they will need to incorporate a variety of formative assessments to monitor student success in mastering the content or meeting the objective of the lesson.  Asking for a show of hands as to determine if enough of the content has been grasped so the teacher can move on is not efficient.  Formative assessments must go deeper, be more varied, and allow all students-especially English language learners-to fully demonstrate their grasp of lesson content.

In the article " formative assessments in math classes at all levels", the NCTM (National Council of Teachers of Mathematics) offers 5 creative approaches to conducting formative assessments in math classes. 

1.  Be sure students understand the learning goals by clarifying in student friendly language.  Be sure students know the criteria for success.  This provides them with a purpose for learning.
2.  Create a classroom environments filled with effective classroom discussions, questions, activities, and tasks which demonstrate student learning.
3.  Provide feedback that identifies what students are doing well so that they will know what to repeat.  "Good job!" means little if anything since the student doesn't know what he did well/
4.  Have students learn to take charge of their own learning.
5.  Have students support each other within the class as they grapple with ever increasing math problems.  In effect, students should be resources for each other.

The article expand on this of course.  In fact, these suggestions would work in any discipline.

Denise

ELL TEACHER PROS


   (pdf of article)

Can Math Be Fun? You Bet:)

Common Core has radically transformed the math class, at all levels, from basic computations to calculus.  The textbook no longer drives classroom instruction.  All levels of math instruction must have a direct tie-in to the real world.  Further, with thoroughly all inclusive classroom activities, all students will have multiple opportunities through multiple venues to master the material.  Standardized tests will no longer drive instruction--no more "one inch deep and one mile-wide" approaches to instruction.  How refreshing:)

My board PINTEREST FOR MATH offers a variety of new ways to view math as teachers.  Pinterest is an account that can be used for academic issues as well as cooking.  Take a look at creative ways to teach all levels of mathematics.  Delight your students in the process.  Develop a love of mathematics in all your students!

Denise

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Follow me on TWITTER @ell_teacherpros and Pinterest as dmcyberteacher.

10 Applications of Algebra in the Real World!

Not all students grasp the key concepts of algebra with ease.  The learning process becomes even more  challenging when students have gaps in their school history.  So, what can teachers do to motivate students to actually enjoy learning algebra?  Tie it to the real world.  Give students real examples of algebra beyond the textbook.  When such context is fully incorporated into the lesson, algebra becomes more accessible for all.

In the New York Times learning blog (free to join), teachers will find great strategies to turn the complex into the accessible.  The blog also supports the new Common Core Standards in all content areas (middle school and high school are the audiences here).  For this post, the teaching of algebra is addressed through 10  real world applications.  What examples are chosen?  

A favorite is comparing the speeds of 21st century athletes with those of past events.  This could also be applied to any sport for that matter.  If students are not interested in sports, then what about recipes?  Or, mortgage interest rates?   Or calculating car rates?  Tie algebra to areas of interest for them and the lesson will have meaning.

Denise

ELL TEACHER PROS

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Great Classroom Management + Accessible Quality Instruction = Academic Success for ELLs

With the demands of delivering quality instruction based on the new Common Core Standards, teachers might need to hone their classroom management skills to fully engage all students in an orderly productive fashion to master the content material.  A willingness to try new approaches in this area has the potential of motivating all to want to succeed.  Self-confidence soars in a setting where every student has multiple opportunities to interact with the content.

So how might classroom management look like in this 21st century classroom with Common Core Standards?  It is one where students have multiple opportunities to share with partners their understanding of the key points of the lesson.  These interactions are very short and the teacher maintains control throughout.  Is the classroom a little noisier than usual?  Yes, but the noise is evidence of students trying to process the content in a low stress setting.

SEE THE POWER OF SOLID CLASSROOM MANAGEMENT AND QUALITY INSTRUCTION--This 6 minute clip is just one example of how highly effective classroom management permits a teacher to deliver lessons.  The teacher use of all three learning styles in her lesson leaves no one out of the instructional process.  Her unique tools fully prep students for the focus of the lesson which is how to solve algebraic equations. 

Weave in some fun approaches in the class routines and see the grades improve:)

Denise

ELL TEACHER PROS

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Texas Instruments TI-1795-SV Desktop Calculator TI-1795SV (Google Affiliate Ad)

SEE HOW BLENDED LEARNING MOTIVATES HIGH SCHOOL STUDENTS IN ALGEBRA CLASS

Khan Academy is making inroads in slowly reversing the failure rate of ELLs in algebra.  Since computers have infinite patience, ELLs may revisit a problem they are struggling with multiple times until they finally understand it.  Further, students may progress at a rate that works for them.  Trying to keep up in the traditional high school setting often led to tuning out which led to giving up.

Well, with the flipped classroom using KA, students see a video on the math problem the teacher has designated for the class to solve.  With the task, students have several options to tackle the problem:  watch a video from the KA, check out the hint KA supplies in helping a student solve a problem, ask a peer for assistance, and last--raise one's hand for assistance.

How can the teacher use KA to fully support a student's efforts at learning?  There is the teacher mode which lets the teacher access student progress reports, perform quick checks which allow them to hone in on specific weaknesses and all the steps the students tried on his own in attempting to find the answer on his/her own.  This type of feedback makes the teacher's feedback even more productive since the teacher knows exactly where to step in to support the student in arriving at the solution.

Scores of students in this high school have gone up.  Students have a greater well-founded confidence in tackling algebra.  In fact, at this site, the pass rate went up 40%!

BLENDED LEARNING ENERGIZES HIGH SCHOOL STUDENTS

Try the site out.  It works for all levels of math though the above video was set in high school.

Denise

ELL TEACHER PROS

Algebra Games Offer a Fun Approach to Prepare ELLs and EOs for Final Examinations

With final examinations only a few weeks away, teachers are trying their best to liven up review sessions so that students will be in a stronger position to take and do well in their examinations.  So how does a teacher liven up the review process in algebra, a subject that many ELLs struggle in (due to language and not intellectual ability)? Games with academic objectives address this goal with ease. 

ALGEBRA GAMES offers a fairly wide range of non-traditional approaches to tackling math.  The activities offered could be done with a partner, in a small structured cooperative group, or individually.  As students attempt to win the game or solve the puzzle, they will be honing their algebra skills without knowing it:)

Denise

ELL TEACHER PROS

ENGAGING ELLS PRODUCTIVELY IN MATH CLASSES

All too often, ELLs struggle with math content language.  They may get the concept, but they have a difficult time navigating the language of the problem.  Imagine a very simple addition problem for elementary school such as the following:

14 boys and 13 girls went on a fieldtrip to a museum.  How many children went on the trip altogether? 

Problems here for the ELLs are several.  First, the problem talks about boys and girls.  Adding -s to a noun often times makes it plural.  However, the problem now puts in the word CHILDREN.  If the student is an ELL, s/he might be confused on where the word CHILDREN came from.  Then, the ELL sees the word FIELDTRIP.  S/he knows what the words FIELD (open area where games are played) and TRIP (going somewhere to visit someone or a special place) mean individually, but together presents a meaning that may be totally new for her/him.  Last, the word ALTOGETHER is another way of telling the reader to add, but it might not be a vocabulary word the student is familiar with.  So, the bottom line is that teachers may wish to rewrite problems or explain with visuals, cognate dictionaries, etc. words that may be new for ELLs.  How can a teacher know what is new for the student?  Have him/her try to explain what is expected of him/her to do in the problem.  It is at that moment the student will either stumble through it due to language issues or arrive at the correct interpretation on his/her own.

How does a teacher build math (algebra, geometry, trigonometry) vocabulary for ELLs?  Graphic organizers can be quite productive here:  Venn-diagrams to show similarities and differences, charts where terms with like meanings are grouped together (see example on site where under ADDITION, four different terms for the action are listed), concept maps, word walls, math journals where students can keep running records of what they learned in class on any given day,  etc.  For ELLs to make connections to math terminology, they need to be surrounded by it in meaningful formats. 

CONNECTED MATHEMATICS PROJECT offers some very effective, practical, and easy to implement approaches to demystify math language for ELLs. It is a good starting point:)

Denise

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Great Strategies to Support ELLs in Accessing Geometry

As most teachers already know, geometry has quite a bit of challenging specific subject vocabulary in it.  Though many students have a difficult time with it, English language learners struggle the most since they are tackling unfamiliar content being taught through a language which they are not yet proficient in. 

To support geometry teachers of English language learners, here are some fresh ideas in making the complex understandable.  In GEOMETRY PROJECT WITH ALGEBRA CONNECTIONS, students in London explore geometric figures used in local buildings.  Imagine the impact of seeing geometry in the real world.  This experience breathes life into any geometry textbook.  Those figures really do have meaning.  It is as though the math takes on an ordered life of its own:)  Note the observations the students make in studying these beautiful geometrical figures in their classes.  Then there is the fun project of origami.  Japanese paper art is full of geometry.  Many cultures enjoy it and include it in math classes.  Students of all ages enjoy it and they are working with both algebra and geometry in creating their paper art.

MATH OPEN RESOURCE SITE  Everything math related is included in this open resource site.  It is a good tool to have on class computers for students to refer to as needed.  Homework centers might like it as well just in case the textbook is not enough.  

The U.S. is number 27 in the industrialized world in mathematics.  Common Core offers the potential to reverse this sliding trend:)

Denise

ELL TEACHER PROS

P.S.  Our website was just listed one of the top 25 websites for English Buffs! 

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FREE Math Worksheet Generators for All Levels of Mathematics:)

Math teachers are always looking for practice work for their students beyond the textbook.  Here are three sites that will allow a teacher to design and print out activity sheets for their students with just a few clicks.  Each one is FREE! 

What math is covered?  CREATE MATH WORKSHEETS covers basic math facts, telling time, working with money, word scrambles, and mazes.  Though this is more in line with elementary school, older ELL/ESL students with limited school experience from their home countries would benefit from it as part of their English language development/ESL classes.

FUN MATH addresses high school math:  basic math, algebra, geometry, trigonometry, and statistics.  There are also lots of math games (math logic) and puzzles.  Last, take a look at FUN STUFF.  See math application problems tied to the real world.

MATHSHEET GENERATOR allows algebra to generate worksheets with ease.  Two clicks covering the topic of the day and the teacher will have a worksheet! 

Hope these sites meet your needs:)

Denise

ELL TEACHER PROS 

Texas Instruments TI-84 Plus Graphing Calculator TI-84PLUS (Google Affiliate Ad)
LEARNING RESOURCES LER0053 CALCULATOR CADDY (Google Affiliate Ad)

TAKING THE "FEAR" OUT OF MIXTURE PROBLEMS IN ALGEBRA FOR ELLS AND OTHERS

Algebra is a course that many ELLs, as well as English only students, struggle with in both middle school and high school.  The language of algebra word problems is new, the concepts are unknown, the execution of the steps to solve the problems lead to confusion, etc. 

For ELLs to fully grasp the material and feel confident in applying newly acquired knowledge beyond the classroom,  they need the materials to be accessible in both language and content.  To accomplish this, teachers need to establish solid connections to student lives.  This is done by finding "props" that are common to students outside the classroom (see video).  With this information, teachers must build bridges or connections for students.  Teachers move from the known to the new.  Once the foundation is laid out for students, teachers need only tie the new concepts to that foundation.  Students will find it easier to relate to the lesson with such connections firmly established.

ALGEBRA MIXTURE WORD PROBLEMS DEMYSTIFIED  National Board Certified teacher Marlo Warburton does an incredible job in demystifying algebra mixture word problems.  Through her use of realia (cups of liquids), visuals (seesaw), laughter, and highly interactive activities, she involves every student in the lesson.  She convinces each one that there is no mystery to solving those dreaded word problems:)  In interviews with students after the class, they all felt that she was an awesome teacher who really loved her subject area and they felt confident in their new abilities to solve mixture problems with ease.

If only such a teacher had been around when I was suffering through mixture problems. 

Denise

ELL TEACHER PROS

Liven Up Math Classes With These Videos--Great Additional Support for Struggling Learners

Math language can cause problems for many English language learners.  Math word problems are especially difficult because the language around the word problem can often times be a challenge.  As a very basic example, look at the many synonyms for "DECREASE":  subtract, take away from, lowered by, reduce, minus, etc.  Then there are the NON-MATH words in the problems.  Look at this basic math problem for elementary school:

Five boys and three girls went on a field trip.  How many children went on the field trip all together?

First problem--the problem starts off with BOYS and GIRLS and then combines the two to make CHILDREN.  An ELL will wonder where that word came from (unless the teacher has addressed it).  Then there is the word "FIELD TRIP."  FIELD TRIP to many ELLs would mean a school yard or big open area with trees and lots of room to run and play.  Again, unless the teacher explains that there is not connection between a field and a field trip, the student will be confused.  Last, the words "all together."  To an English speaking student, that means ADD.  That will be a new word for the ELL.   So math teachers will also need to be English language teachers no matter what level of math they teach:)

Since math becomes increasingly more difficult as ELLs move on to middle school and high school, the same problem still faces them---the language of math.  Teachers need to develop the math language before the ELL can undertake solving the problem.

The video sites below offer more support for struggling students both ELLs and EOs.  Since it is visually presented in simple formats, it should be comprehensible for the majority of students.  Students hear the problem, see it drawn out, and watch it being solved as the teacher carefully covers each step of the process slowly and accurately (with a dose of humor throughout).  Further, these are sites that they can access at home, school library, on smart phones, iPads, tablets, etc.  For such students to know that they can revisit a math activity as often as they like until they finally understand it eases some of the stress of trying to learn English and content at the same time. 

Both sites are free of course though they do want students and teachers to register.  If students don't feel comfortable doing this, the teacher can just load these sites on class computers for students to use as needed.

Please note that though I am not a math teacher, I am an instructional coach who looks for practical ways to support all teachers with ELLs in their classes.  So what I share with you here, I pass on to colleagues:)


MATH VIDEOS FOR ALL GRADE LEVELS

HIGH SCHOOL MATH AND BEYOND!

Denise

ELL TEACHER PROS

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DEMYSTIFY MATH PROBLEM SOLVING PROCESSES FOR STUDENTS

For many students, math classes consist of textbook activities and regular assessments.  Due to the pressures of state assessments, high school exit exams, PSAT, SAT, etc., teachers are under a great deal of pressure to stick with the text.  This type of instructional delivery will be changing over the next two years in that now students will be able to SEE how, for example, quadratic equations are used in the real world outside of the math class.  Relevance will be a major component of the new math class.  Teachers might be able to share with kids what they really love about math, what inspired them to pursue studies here and not in another discipline, etc.  Hopefully their love of the subject will catch fire in their classrooms:)

So, how does a teacher bring in project based learning projects into a math class?  Here are some good examples to start with:  statistics, geometry, algebra, and trigonometry.  PROJECT-students are to design a shopping mall.  Notice that for each activity, students are going from known (ex. the structure of a shopping mall) to the unknown (how to use prior knowledge with newly acquired math tools to construct a totally new version of a mall). They will be taking on roles of architects who must design different store sizes to accommodate the needs of prospective merchants, restrooms that allow for minimal care, landscaping within the mall for customers to sit and relax in, an original layout that will draw shoppers, etc.  Math is naturally woven throughout the project.   Since this would be a team effort, each member in the small group could focus on one component of the mall with the understanding that individuals must report out to the group and reach a consensus on the final design.  Students should keep detailed notes on their results and how they arrived at their project contributions.  (ELLs especially would benefit from this since they would be actively acquiring academic vocabulary within context.)  Such skills would easily transfer to the global workforce these students will be a part of when they finish their formal studies.  See the link for some additional ideas.PROJECT BASED LEARNING ACTIVITIES IN MATH CLASSROOMS

One suggestion I would offer is that if this approach is new, start out small.  Make notes on what worked and what didn't.  Move on to next project and keep a little journal on how it worked out.  Hang in there.  I guarantee that students will never forget the experience.  Who knows?  There may be some future astronauts, astronomers, architects, engineers, etc. in the class. 

Denise
ELL TEACHER PROS

Lenovo G570 Notebook 4334DBU (Google Affiliate Ad)
Acer A200 Iconia Tablet, 16 GB, Titanium Gray XE.H8QPN.001 (Google Affiliate Ad)

More on Khan Academy--An Outstanding Academic Resource for ALL Students Including ELLs!

Imagine the possibility of students doing the "classwork" at home and the "homework" in school:)  In some schools, this already being done through Khan Academy!  Students work on assignments at home through Khan Tutorials.  These videos are typically about 15 minutes long and are followed by practice.  The system keeps track of progress so the teacher can monitor quality of student work with ease.  Such insight permits the teacher to quickly discern who needs more coaching the next day in class and how much.  For students who seem to have mastered the assigned skill, the teacher can send them on to more complex projects or concepts.  Again, everything the students do, the teacher can track on her/his computer.  Some schools are even keeping their computer labs open late so that ALL children can work with the system.  The passing rates for academically struggling students has improved dramatically for these schools.

Would you like to know more about Sal Khan and how Khan Academy came into existence?  See his interview on 60 Minutes.  60 MINUTES INTERVIEW WITH SAL KHAN  He lives in the Silicon Valley and records his lessons right from his home.  For subject areas he hasn't seen in quite a while, he gets a few textbooks to brush up on the content before he does the videos.  His voice is easy to listen to and his notes on the black screen are in color and easy to follow.

For information on the layout of Khan Academy, see this link:   INFORMATION ABOUT KHAN ACADEMY  Here teachers are provided guidance in setting up assignments and monitoring student progress.  Students earn badges as they successfully complete lessons.  In fact, teachers can even add smiley faces if they like:)  It is amazing how much things as simple as badges can motivate students. 

KHAN DASHBOARD Explores KNOWLEDGE MAPS and how they keep track of progress.  Teachers or students select the area they wish to study (go to SEARCH and enter the subject to be studied).  As students answer questions correctly in the practice, they earn badges.  If they enter the wrong answers, they can watch a video tutorial on how to find the answer.  Imagine how powerful it is for students to have access to immediate tutoring as they encounter problems as opposed to waiting for the next day to see the teacher.


LIBRARY OF OVER 3000 INSTRUCTIONAL VIDEOS
Here is the current list of all instructional videos on file.  More are being added in new content areas regularly.

Sign up!  It is free.  If you have computers in your classroom, have your students sign up.  They will develop a new self-confidence in their abilities to do math (at any level):)

Denise

ELL TEACHER PROS

Model FX-300MS Scientific Calculator, 10x2 Display - Calculators
Asus TF300T-B1-BL Tablet PC

FREE Multimedia Approach to Supporting ELLs in ALL Levels of Mathematics

With the new common core standards in mathematics, teachers will need to have students address ongoing problem solving in all areas of math.  The book alone will no longer drive instruction.  High stakes tests will soon take a back seat as students apply all areas of math to life beyond the classroom.  In such a learning environment where students are encouraged to work as teams in finding multiple solutions to real world problems, math will become relevant to all including the ELL.  Word problems will be ones encountered in business.  Team problem solving will take precedence over struggling in isolation.  With such a radical transformation of the classroom, ELLs will develop more confidence in dealing with math since it will finally be accessible.

This site is an excellent multimedia resource covering all areas of math through trigonometry.  Each level of math is accompanied by videos of real world application.  A video often times makes a world of difference to an ELL.  The visual component allows them to SEE the problem and hear the problem discussed.  Once the task is assigned by the teacher, this background information along with the low anxiety of working within a small group (or partner) has the potential to build an ELL's confidence in offering her/his ideas to solve the problem or task.  With a team work approach, students quickly learn that there is more than one way to come to an answer.  Isn't that the goal of team work in the real world?

MATH INTERACTIVES

Denise

ELL TEACHER PROS


Texas Instruments TI-1795-SV Desktop Calculator TI-1795SV
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Create a Direct Connection Between ALGEBRA and the REAL WORLD For Your Students:)

Often times, students go to math classes (here algebra), do the activities/exercises, might have some exposure to how the numbers and symbols in text might be applied in the world outside of class, and possibly get good grades.  BUT, what have they really learned?  Can they explain the connection between the subject and any actual application to solving problems?

Well, the new Common Core Standards in Math will be addressing this very same issue.  Teachers will be incorporating the necessary academic vocabulary into all lessons, expecting students to use it in speaking, recognize it when reading word problems, incorporate it in writing word problems, use it when explaining how they arrived at an answer, ask specific questions on problems they had in attempting to solve a problem, and be able to understand the terms when classmates or the teacher bring them into class discussion.

For ELLs, this process may need more support from the teacher, but it can still be achieved.  Since teachers will be recycling key vocabulary in reading, writing, listening, and speaking, ELLs will not only be exposed to it, but be able to actually insert it wherever necessary.  This focus will produce students who should be able upon finishing high school secure a well-paid job or go on to the university and do well and THAT is the end goal of the Common Core Standards in Math. 

DIRECT APPLICATION OF ALGEBRA TO REAL WORLD provides students with a detailed look at how the digits in the text actually solve exciting problems in the real world.  Teachers select one item (linear equations, quadratic equations, etc.) and then click on the link that accompanies it.  There they will find lessons, mini-movie clips (some come with a dvd that must be purchased, but most don't).

Here are some of the subject areas covered:

Predict future sports records based on past statistics
What qualities or characteristics would you look for in the material that is used to make an aquarium?
Build a two-dimensional "rover" and analyze its ability to climb over obstacles as you vary the diameter and spacing of its "wheels."
Find the exact equation for a new telescope mirror with a given light-gathering power and focal length. (from The FUTURES CHANNEL which you can subscribe to for FREE).

Hope your students enjoy this link.  Also, if you are American, happy July 4th:)

Denise


ELL TEACHER PROS

Khan Academy--114 Geometry Videos To Support Your Instruction

If you are looking to develop more review support in your math classes for your ELLs and others, you should take a look at Khan Academy.  It covers all areas of mathematics and science.  The videos are simple to follow and clearly would support a teacher's instruction.  Further, if you have ELLs in your classes, you can find translations in every subject.  Imagine having a newly arrived Mandarin only speaker and offering this site as a tool to access the content of your lesson.  The anxiety level of that ELL would definitely drop since he or she would not be totally in the dark in following your activity.  KHAN LANGUAGES lists all the languages available on the site.

For this post, I pulled out only one subject area--KHAN ACADEMY GEOMETRY.  Within this section are 114 videos all on geometry.  The total viewing time is slightly over 15 hours.  Though the amount of time on each subject component varies, they typically do not exceed 10 minutes more or less.  Access to the site is free and open to anyone.  Since ELLs typically need to jump two hurdles academically--language and content, they would benefit from such online support because it would provide them with additional practice in mastering the content.

Denise
ELL TEACHER PROS

PS  If you use CHROME as your browser, you may have a problem accessing my blog.  What you should do is ENTER the site (ignore the warnings--for some reason it has a problem with WORDPRESS BLOGS---and then bookmark it.  Once bookmarked, the problem is fixed:)

Have Students Who Need More Support in Math (and more)? This Site Might Help:)

Keeping to the theme of "test prep", this post will cover an easy to navigate website that allows students to review math from basic arithmetic through calculus.  It consists of number problems-no word problems.   This makes it possible for ELLs especially to review the math without struggling with the many language issues that arise in solving math word problems.  This site is a quick assessment of a student's grasp of key concepts.  Students may also retake the quizzes as often as they like.   

Since basic math is part of the site, even students as young as elementary school age would benefit from it.  Computers have infinite patience so those kids who need more time to master the process will have all the time they need.  Further, since the site is free (though you have to register), parents could continue to help them at home.  Since language is not an issue, parents who don't know English but who understand math, would be able to support their children  in honing their math skills at home.  Grades 6-8 (middle school) would have access to pre-algebra and algebra.  Again, the focus here is on computing answers to mathematical equations minus the language.  Once ELLs (and others) understand the layout and purpose of the equation, they are ready (with assistance) to start working on word problems through careful guidance on the part of the teacher and through carefully orchestrated small group OR partner learning activities.  Last, there is high school.  Every level of math from algebra through calculus is here.  Students can monitor their progress through immediate feedback.  If they did poorly, they will have enough specific feedback from the quizzes to know where they need more support from teacher. 

This site also has a few other areas students can assess themselves in as well:
Languages--English, German, French, and Spanish
Geography--Americas, Africa, Asia, and Europe
Science--Cells, anatomy, elements, and conversion.
These activities are not as in depth as the math, but still serve as a quick overview review of major concepts covered in class.

THAT QUIZ

Hope your students benefit from the site's offerings:)

Denise

ELL TEACHER PROS

The History of Maths! Absolutely Fascinating to Watch:)

Have your students ever wondered how math came into existence?  Of course those few who find the subject exciting need little encouragement here, but for those who do, these sites will provide incredible insight behind numbers and how they came into being:)  As a non-math person, I found this BBC series quite engaging in that its delivery is totally accessible to non-math individuals.  Further, in these videos, every segment of humanity is recognized from every continent.  If you have ELLs in your classes, you see some wide smiles when their culture is showcased.

HISTORY OF MATHS

In HISTORY OF MATHS, you will discover the many paths of discovery humans took along the way trying to find patterns and solve puzzles.  Egyptians were acknowledged at length in their handling of complex mathematics.  Land and taxes were the driving force:)


CONTINUTATION OF EGYPTIAN MATH
This section continues where the introduction left off.   The Babylonians are explored here along with their contributions to math.  Here the links to astronomy and math are a major focus in the clip.  Quadratic equations were also born in Babylonia.  Last, but not least, the concept of ZERO was touched on, but not fully addressed for 1000 years.


HISTORY OF MATH IN ASIA  The 13th century was the golden age of math in China.  Many of the formulas developed were linked also to astronomy.  India is also covered here and the fact that their number system laid the ground for our present day 9 number system.  They also created the number zero (now 0-9 was a reality). 


HISTORY OF MATH IN EUROPE You will travel through Italy and France.  The journey over the history of math in Europe then explores the major contributions of Newton and others to the field of mathematics.

I only wish that such a program as this BBC one had been available when I was in school many years ago.  For me, math class consisted of doing lots of exercises with no history or tie-in to the real world.  I loved this series. 

Denise


ELL TEACHER PROS

Mathematics for ELLs:)

Mathematics can be quite challenging for many ELLs.  The concepts are delivered to them in yet another language---the language of mathematics.  Often times, ELLs have some of the basic terms such as add, subtract, etc., but when word problems enter the picture, they are lost.  Take for example the many ways the function of ADDING is expressed in math problems:  plus, in addition, total, sum, etc.  For the ELL to just know one form of ADD, he will be ill prepared to solve problems where the word ADD is expressed in many ways.  Further, ELLs may not easily see the connection between the math textbook and the real world.  Unless a link is established between the two, the ELL will continue to fall behind his/her English speaking peers. 

How can a bridge to success be established?  Two sites I have here offer some suggestions that may help the classroom teacher build ELL self-confidence in mastering mathematics!

HISTORY OF ALGEBRA AND GEOMETRY
In the above site, students will see a detailed review of the history of many areas of mathematics.  This is a way to build cultural pride since the contributions of pre-Greeks are addressed.  In fact, here students will see that many cultures were working with higher thinking math before the Greeks!  Such information can be empowering for many of these students.  Teachers who weave in the achievements of ancient cultures (representative of the students in the class especially) will see a pride in ancestral achievements and that can be a major motivator.

MATH INSTRUCTION FOR ELLS
Colorin Colorado is a powerhouse of everything and anything related to meeting the needs of ELLs at all grade levels.  For this post, I pulled their section on making math accessible to ELLs.  Here there are some excellent tips to turn the incomprehensible to comprehensible with ease.  A few of the suggestions are allowing students to collaborate with bilingual peers.  The class would still be conducted in English, but ELLs would be able to clarify tasks with peers.  Another strategy is to address vocabulary with multiple meanings.  Take the example given here where the question is to FIND X.  The task here is to FIND THE ANSWER and not FIND the X.  Teachers should also identify  KEY VOCABULARY before the lesson so that they will be ready to support ELLs with clear ELL-friendly definitions to support them throughout the lesson.  You will also find some additional math links towards the end of the article as well.

Denise

ELL TEACHER PROS

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MATH: From Textbook to REAL WORLD CAREERS!

If you are a math teacher, you have probably heard your students wonder how algebra could ever be used in the real world. They never seem to make the connection that mathematics does have a life beyond the classroom:)

The site, MATH IN THE REAL WORLD, takes algebra and shows its direct connection to music, the clothing industry, and the world of video games. You see the professionals in each field talking about how math is instrumental in their line of work first. Such insight will open up a lively class discussion as students try to make the connection, but then the website goes a bit further in that students in the film are presented with a REAL WORLD problem in the assigned industry to solve as a team. Every student is actively engaged in a team approach to solving the assigned task.

When the classroom teacher is done having students in his/her class come up with possible solutions (and there is almost always more than one), the teacher may click on the link which shows how the student teams arrived at viable solutions to each of the problems. Here is where the classroom teacher can lead the class in making comparisons of the two approaches (class approach and the one or ones used by the students in the videos).

I wish my math teachers had put a "face" on math for me a zillion years ago. I might have learned to like it:)

Denise

ELL TEACHER PROS