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)

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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Breaking Down the Language of MATH for ELLs!

To support ELLs in accessing math content and language, teachers will need to do quite a bit of language clarification.  Some of this will entail the rewriting of questions from passive voice (ex.  16 subtracted from 32 equals 16) to active voice (32 minus 16 equals 16).  Other situations will entail words with multiple meanings such as GROSS.  In conversation it means disgusting, but in math, it means total income from sales. 

If ELLs try dictionary definitions, they will be lost.  Instead, this paper from NYU School of Education addresses how to make the language of math problems accessible through a variety of ways.  First, wall charts that have vivid easy to follow definitions to assist students in determining the correct usage.  Then there are graphic organizers such as venn-diagrams where, math "pictures" with their labels could be laid out in such a way as to show ELLs differences and similarities (difference:  rhombus, square, rectangle---similarity:  all 3 have 4 sides).  Of course, there is also the need to highlight key vocabulary students need to know to be able to figure out what is being asked of them.  With a document camera or an iPad, this can be done with ease.  To build this skill, have paper handouts with word problems on them, have them highlight must-know words (with ERASABLE HIGHLIGHTERS), and then discuss meanings.  If they highlighted the wrong words, they can erase them--no waste of paper for you and no loss of confidence for them.  One of the strongest ways to support them is to have them keep math journals (inexpensive composition books will do here).  They will note everything they learn there as well as problems they encountered and then solved.  With a record to refer to in doing future problems, they are not starting from ground zero.


There are many more ideas here along with additional website resources (majority are free, but not all).  Save the PDF in your DropBox folder and refer to it as needed.  Think of it as a free e-book on math:)
ELLS+MATHEMATICS

Denise


ELL TEACHER PROS

OfficeMax Pen Style Chisel Tip Erasable Highlighters, 5 Colored
Composition Book, 7 1/2" x 9 3/4", Wde Ruled

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

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

FREE Video Support and More in BASIC Math THROUGH Calculus:)

If you have your own website or a blog for your students in your math class, you might want to add this one. The videos are delivered through engaging teachers who really seem to enjoy all phases of math instruction. If you want kids to develop an interest in math, you need to be enthusiastic about it. Teacher enthusiasm about her/his subject can be quite infectious:)

This site could be that extra support for those (especially ELLs) who need more time to process the information. Students can watch them at home as often as they like for free. If browsing for videos doesn't offer exactly what you want, check by book. Click on the copy you are using in your class, and all the videos will be listed in the order that they appear in the textbook.

Students can also input problems on their own if they need help in solving them, but they will only receive the answer. If they need the steps that take you to the answer, there is a fee. However, students can always bring the problem to class where the problem could be solved in class either in small groups or whole class discussion.

Students can also get help from the MATH HELP forum. Immediate answer only responses are free.


BRIGHTSTORM -- free support for your math classes:)

Denise

ELL TEACHER PROS

A Site That Will Solve Math Problems? Sounds Impossible, But It's True!

Math has a language of its own teachers correctly say. Like science, it is akin to learning to function in another language. This situation becomes a bit more complicated when you have ELLs trying to learn the language of math in a language that is not their own. Teachers are English speaking and often times are not able to fully explain complex topics in enough detail to make the content accessible to ELLs. Dictionaries come into play, but most kids (including many EOs) are not really familiar with how to use a dictionary effectively. A glossary might surface sometimes, but a glossary only works if the ELL is proficient in her/his home language. If the student is a limited bilingual (not proficient in either language), s/he will find the glossary difficult to navigate.

MATH PROBLEM SOLVER is a site that might be a good resource to support weaker students (ELLs especially) in math class (ANY math class--from basic arithmetic through calculus). Students find the area of math that the class is working on and then input a problem that they need help in solving. The program not only gives the answer, but also the steps followed to arrive at the correct answer. Though it is in English, it is not overly wordy so ELLs won't become lost in math language. That component will make more sense as the ELL feels more comfortable answering questions with minimal English. When the solving becomes clear, the language associated with it will make more sense.

I have some other sites to assist struggling students which I will bring in this month. Again, everything I share is FREE.

Denise

ELL TEACHER PROS