Skip to main content

Region II Online Course Pilot: Numeracy and LD - Session 1 ANI-PD Guidelines

Course pilot participants: use this discussion thread to explore your thoughts on the recent research in adult numeracy instruction from the Numeracy Instruction and Adults with Learning Disabilities online course. **ALL LINCS community members are invited to join in!**

ANI-PD Guidelines coverPost a 'Reply' with your thoughts, using the following question to guide your reflections:

How might the information in “Building on Foundations for Success: Guidelines for Improving Adult Mathematics Instruction” (as expressed in the ANI-PD Guidelines) might impact your instructional practice? Why?

To enhance your understanding: Read and reply to other participants' posted plans. Check back to this discussion thread or bookmark the post to read and reply to others' responses or thoughts at a later date.

Reminder - If you have not already, you must create and/or login to your LINCS account and then have joined the Math and Numeracy group or the Disabilities in Adult Education group in order to post a Reply.

Comments

The book emphasizes the importance of being able to actually use math outside the classroom.   We absolutely need to be teaching in that context, which means that we have to do the hard work of figuring out how to get students to make that connection.   

"Word problems" have often been a nemesis for students, yet they're the purported "link" between arithmetic procedures and being able to apply them.   I know some teachers try to go from the other direction:   start with a "real life" application and work from there.   

I love the chart of algebra topics and where their study is actually needed.   

Missy Slone's picture
First

I think you are right! We have to have students up and out of seat learning math. It is necessary to find a way to get our students to make a connection and I attempt to do this by getting to know my students and teaching topics by relating to them and their life. 

Missy Slone's picture
First

After reading much of "Building on Foundations for Success: Guidelines for Improving Adult Mathematics Instruction" my take away was mainly related to the guidelines, adults’ goals for their participation in adult education programs and NMAP recommendations.

 

Guideline 1: Mathematics content should emphasize a consistent link between math and concepts learned and their use in context and form a coherent progression of learning.

Mathematic concepts build on each other; it is a must that mathematical learning is a progression. To be successful students should understand key concepts, achieve automaticity, develop flexible, accurate, and automatic execution of the standard algorithms, and use these competencies to solve problems.

How does this impact my instructional practice? Many times adults walk into the classroom with little or no foundational skills. When teaching mathematics to adult learners I always try to get to know the student. What is the student's interest, how is math used in their daily life, and where or do they work are a few of the questions I ask. I feel that knowing the student allows me to teach the student math in a way that is relevant to their lives. If students can relate a mathematical concept to their lives it becomes more meaningful to them and they tend to retain the information.

Guideline 2: The topics of fractions, decimals, percent, and reasoning with proportions are essential and should form the instructional foundation for adult mathematics education.

A student must develop some proficiency with fractions, decimals, percent, and proportions to be successful in algebra.

How does this impact my instructional practice? I tend to teach fractions, decimals, percent, and proportion together as a unit. My hopes in doing this is that students will make a connection and see how they are all related. Proficiency in these topics is very important in many goals of the adult learner including: managing everyday life tasks, being successful in the workforce, passing the GED Test, and even preparing for secondary education.

Guideline 3:  Algebraic thinking is essential for decision making in daily life and the workplace. Elements of algebra therefore should be introduced early to all students in adult mathematics instruction.

Algebra topics should be incorporated into mathematics curriculum long before the student gets to an algebra focused class.

How does this impact my instructional practice? As a mathematics instructor, I begin introducing the feared letter very early in my instruction. I begin as early as addition and subtraction and start with a blank space or question mark instead of a letter ( 2 +  ____ = 6). For some reason adults are less intimated by a blank space or symbol than they are by a letter (2 + x = 6).

Guideline 4: All content standards should be included in varying degrees at all levels of adult mathematics instruction.

The GED Test follows high schools standards and is now written with CCS in mind.

How does this impact my instruction? My attempt is to teach as much CCS related material to my adult students as possible in a limited time frame. Common core material is very important to some adult learners and not as important to others.  Knowledge of many common core standards in necessary in passing the GED Test which is an important goal to many of my learners. Common core is also important to students who have children in school and are learning by CCS. Is common core important to my learners who are entering the workforce? The concepts included in some of the standards are important but are they all important? Again, this is a place where I try to get to know my student. I want to know about their goals as an adult learner and go from there.

 

 

Aaron Kohring's picture
Fifty

Missy,

Thanks for your reflections on this topic.  I really was struck by what you said in Guideline 2- "I tend to teach fractions, decimals, percent, and proportion together as a unit. My hopes in doing this is that students will make a connection and see how they are all related."

Have you been involved with any of the ANI (Adult Numeracy Instruction) trainings through LINCS or has this been something you've been doing all along?

When so many traditional approaches show the instruction of fractions, decimals, percents, and proportion as separate topics, one can better understand why they can be such a challenge for many students when those connections and relationships aren't so explicitly taught and explored.

Aaron

Missy Slone's picture
First

I have taught in adult education for 14 years and I did not start out by teaching fractions, decimals, percent, and proportion together. However, after watching students struggle with these topics I saw that for the most part students don't make the connection between those topics. I started teaching the topics together and having discussions about how they relate. Money has been a good resource  to use in adult education when teaching these topics. 

I have never been involved with any of the ANI training's through LINCS. 

Thanks for your comments..

Carolyn_Hendrix's picture
Ten

I too have found that using money is always a good resource for teaching math concepts. They always have change in their purse or pocket we can pull out and manipulate to help them visualize whatever it is we are working on at the time.

hmunchd's picture
First

 

 

Disclaimer: I am a novice in this field! I have spent the past four years tutoring for a local literacy council in my state. Often, I floated over to the Adult Ed offices to be extra manpower during open study. The only consistent math students I can claim were all LD or Developmentally Disabled (I am not sure whether I am even using the current politically correct terms; please forgive if I am not). We worked mostly on very basic skills: adding single digits and counting money. The students in the Adult Ed program were more advanced, and I coached a little of everything. 

To follow the format of other participants...

Guideline 1: Mathematics content should emphasize a consistent link between math and concepts learned and their use in context and form a coherent progression of learning. I always strive to make an adult's lessons meaningful. I have performed all sorts of instructional gymnastics to find multiple examples, until one clicks with a student. 

Guideline 2: Fractions, decimals, percents, and reasoning with proportions are essential and should form an instructional core. Food (actual food), grocery store ads, play money, cell phone battery usage, and many other things are what I use. I do progressively (pretty much in the above order) teach these concepts. We can not get away from these things in life, and I try many things until one clicks. 

Guideline 3: Algebraic thinking is essential for decision making in daily life and the workplace. Elements of algebra should be introduced early to all students. I do this- what is a problem with a blank? Same thing, but I do not use the fear-inducing term "algebra" when I teach it. Only after the student shows a good, smooth mastery do I tell them they have been doing the very basics of algebra.

Guideline 4: All content strands should be included in varying degrees at all levels. As life is a tapestry, so  mathematics is woven into life. We do  a little of everything, though not always assigning a label.

I think I already do all of these things to some degree. I hope to find specific ways to refine what I do. There are many approaches to teaching this concepts, the key, in my experience, is matching the right approach (and sometimes it is simply patience and fortitude) to the student.

 

S Jones's picture
One hundred

I was a reading specialist at The New Community School in Richmond, Virginia for 5 years, and while I *mostly* did reading, I also worked w/ students in math, and that was my focus in my assorted graduate coursework.   Since then, I've been working with college students in the lowest math courses here, and helped design our "transitions" course.   Many of the students in there have lots of difficulty in math and/or actual diagnosed LDs.   

  One  "cardinal rule" for teaching at TNCS, which is *highly* successful, is to always, always start with visual-concrete and build towards abstract... and teach all the transitions along the way, and go back and review along the way.   Even more cardinal, though, was student engagement in what we were learning and why.   Now, they didn't have a whole lot of say in the skills part, but in reading the "oral reading" part of each lesson was from a book of student's choosing, and our work w/ words and sentences was individualized for their interests.   In our math course here, the "word problems" are home brewed and local... and we try to do lots with visuals and concrete materials, so the "area" concept is taught with Cheezits, which happen to be a square inch in size.   (The store brand is smaller, by the way... )

Chris Woodin from Landmark School has some awesome videos of teaching this "concrete-to-symbols" way on youtube -- see https://www.youtube.com/channel/UCYnlx2w7EX4jigFUqT2XVOA   

I'm trying to work up some apps to show how we can make interactive online stuff that isn't just worksheets and procedures and symbol manipulation. https://www.youtube.com/watch?v=FPXq89p6dtI  is a 35 second video of stage 1 ; https://www.youtube.com/watch?v=4b-8DD829RI is stage two.   https://www.youtube.com/watch?v=BSXkyjisZQs  is stage 3; those all have the visuals, and I want to have a "quiz" version with the option for peeking at what it would look like.   If you can do it without peeking you get a ton of points; if you have to peek you still get points... if you get it wrong, you "lose a life."   Hopefully that would mean that instead of guessing the user would stop and think.  

{And if you're *really* brave, just today I went through the steps to make the app I'm developing for exploring positive and negative integers sharable... except I left my tablet at home so I don't know yet if it really is or not ;)   Since this is an "unknown" source, if you have an android device with recent enough version of Android you'd still have to go to settings and security and okay "unknown sources" (it's entirely homemade so nothing devious in it...  the code's not even compressed so anybody could copy it for themselves...)     https://www.dropbox.com/s/t8n28c2yr321q3n/app-release.apk?dl=0   is where it resides...   }

 

Cindy Gray's picture
First

Hello,

 I teach GED classes at Goodwill Easter Seals in Alabama. Many of my students struggle with fractions, decimals, percents, and proportions. I have found that starting my students off with these topics has helped them a lot. But I usually go in order, fractions then decimals then percents... For some students it is just a refresher, since they have been out of school for some time. For others they have to learn these skills all over again. Once the students have mastered this topics it will help them when they have to solve more difficult problems.

For Guideline  4. I agree that all topics/content should be covered in varying degrees. In my classes I may have 2 students working on the same topic. But one student may be at a more advanced level than the other student. So being able to teach a topic/content at varying degrees is very instrumental in the success of the adult student.

kecondit's picture
First

I teach a lower level group of students and we're now winding up our spring semester. We normally move in a fairly predictable order for math, beginning with basic arithmatic and ending the semester with some very basic concepts in geometry.  Currently we're discussing lines & angles.  This week a student casually asked a question about fractions that he and a friend outside of class were discussing and we spent the entire rest of the class talking about fractions. The discussion was not just with that one student.  As I looked around the room, everyone was engaged in our conversation and some had retrieved notes from weeks ago and began to chime in.  In an effort to stay in tune with the curriculum outline, we checked off fractions and moved quickly on.  The Computational Fluency had not been achieved!  That day I went home and began thinking of how we need to revamp our curriculum so that these important concepts are woven into the brains rather than just allowed to pass through.  The next day I started this course.  My opportunity to work on curriculum for the coming year, the simple question about subject matter covered weeks ago, and this course are lining up to have an impact on what happens in the future for our program.  I'm excited about the possibilities.

elizabeth severson-irby's picture
First

All four of the guidelines are so important when teaching math.  Previously, I always "saved" algebra, but then realized you couldn't go very far into geometry without an understanding of at least basic algebra.  The more I have taught math, the earlier and earlier I introduce algebra.  This was frightening to me at first, but introducing it in a way that compliments the student's current level of understanding helps them build confidence in the area of algebra.  It makes it less scary, and it does not become this big looming thing that they dread.  Introducing algebra early helps them understand it piece by piece, so as it becomes more complex, they have a strong base to fall back on.  This also goes in line with introducing all strands early and often.  Math is much more integrated than previously taught.  There is not much one can teach in isolation that does not involve a concept from another strand.  Again, introducing the strands early and in small pieces allows students to develop a deeper understanding of how all the concepts are related, and teaches students how to think through problems using the knowledge base that they have.  For example, if you separate geometry and algebra, the students will view them as separate entities and not realize that solving for a missing side of a square involves the use of algebra concepts.  Finally, contextualizing math problems into real life situations that are of interest and relevant to the students helps them see how math is used daily.  A lot of times, students think that they never use math, and certainly don't use "complicated" math.  However, getting them to realize when and how they use math on a daily basis, gets them more interested in wanting to learn these concepts.

Ila Waite-Burns's picture
First

Florida’s teachers are now required to take 20 hours of students with disabilities training for their teaching certificate renewal.  We have a math standard’s based instruction professional development training for our adult educators.  I am very excited about how this course will enhance our math trainings and assist teachers still having challenges with instructional strategies.  I'm hoping when I finish this course, the puzzle pieces will fit together.

S Jones's picture
One hundred

   I'm exploring our adult ed resources geared towards the career paths... http://www.iccb.org/iccb/wp-content/pdfs/adulted/tdl_bridge_curriculum/tdl_context_math/C_TDL_Math_Resources.pdf   has  "Transportation Distribution and Logistics Bridge Curriculum & Resources" including a neat link to a guy explaining rectangular prism volume rather thoroughly on a moving truck.   If they dont' have it, I'll try to design some more-student-engaged activities to come after that ... 

Carolyn_Hendrix's picture
Ten

How might the information in “Building on Foundations for Success: Guidelines for Improving Adult Mathematics Instruction” (as expressed in the ANI-PD Guidelines) might impact your instructional practice? Why?

 

The guidelines helped me step back and take a look at the broad picture, which is what we want our students to do as they develop the skills to pass the high school equivalency test.  We also want them to make that transfer of skills to their everyday life activities, now and into the future.  Although we discuss making a connection of a particular concept to life, everyone may not fully realize the various avenues in which the concepts might be utilized.

Carolyn_Hendrix's picture
Ten

How might your current understanding of math disabilities or math difficulties impact your instructional practice?

 

How might your current understanding of math disabilities or math difficulties impact your instructional practice?

 

My current understanding of math disabilities and math difficulties is broad and runs deep.  I have a child who was diagnosed with a learning disability in math (dyscalculia).  He was in elementary school at the time and I was working on my master’s degree while teaching GED and Workforce development classes.

 

I sought information from every avenue available to me so I would be able to help him.  I have utilized that information over the years to assist my GED students

 

I have put the things learned to practice in my GED classes. I use peer-to peer, modeling, manipulatives, questioning etc.  I have the students show their work so that I can see how they arrived at the answer.  I ask them to explain to me how they arrived at the answer.  I ask them if their method works every time.  I have them show me by making up three to five more problems of their own and solving them in the same way.  We talk through problems, especially word problems.

durenclee's picture
Fifty

Carolyn - I have re-posted this for you over in the Numeracy Session 2 Thread:

https://community.lincs.ed.gov/discussion/online-course-numeracy-and-ld-definitions-math-difficulties-and-disabilities

 

S Jones's picture
One hundred

That is a great "low floor, high ceiling" task -- some folks' problems will be very similar to the ones they've been doing, and other students can really get creative with it. 

Carolyn_Hendrix's picture
Ten
  • Has your thinking about accommodations for math changed? How?
  • What are some accommodation practices you plan to continue using? What are some you want to try? Why? What might you need to be successful?
  • Regarding accommodations: What questions would you like to discuss with peers? What topics or ideas would you like to learn more about?

My thinking about accommodations has changed by being reminded that there are options I may not be utilizing in my class.  I plan to continue using manipulatives, peer-to-peer and inquiry learning.  I want to try using more realia to help students relate what we are doing to their daily life.  I will need to accumulate real world objects, tools and devices in order to be successful in this endeavor.

 

I would like to know what others utilize in the classroom regarding accommodations.  Has anyone done their own videos, developed their own games, made their own manipulatives?

 

 

 

S Jones's picture
One hundred

I've been playing with making manipulatable number lines for an Android App game -- you can download it from https://www.dropbox.com/s/t8n28c2yr321q3n/app-release.apk?dl=0   (tho' you have to set your device in the security settings to accept from "unknown" sources).   

My friend uses Cheezits as manipulatives for teaching area (they are, happly, just about a square inch apiece).   

I've been making little videos for a while, too... there's a few of them (as well as some Powerpoints) at http://library.parkland.edu/friendly.php?s=mat094cas  (my problem is I keep finding better ways to do things...) 

Aaron Kohring's picture
Fifty

Carolyn,

I have reposted your response in the Part 3 section: https://community.lincs.ed.gov/discussion/online-course-numeracy-and-ld-accommodations#comment-15805

I will also add a suggestion.

Aaron

Ila Waite-Burns's picture
First

Prior to working for the state office, I was a teacher for varying exceptionalities.  In my classroom, students displayed the characteristics that have been discussed so far.  In lesson three, regarding response accommodations, mind maps and flow charts were given as two examples to use with students.  Has anyone tried one of these? 

Aaron Kohring's picture
Fifty