Topics? Math and the CCRS

Hello Colleagues, We would like to offer a LINCS special event in the coming year to address the CCRS and math. What specific standards-based math topics would be most interesting and helpful to you?

Your suggestions will guide the planning.  Thanks for weighing in!

Cheers, Susan Finn Miller

Moderator, College and Career Standards CoP



I would like to see something about active learning with adult numeracy and how we can address CCRS expectations. Something like Steve Hinds's work with Active Learning in Adult Numeracy (ALAN) project that he has presented to ANN on.

Thanks, Susan, for soliciting ideas.  Here's one:

One of the major themes of the math CCRS is the coherence of math -- both within and between levels.  Effective teachers help students see the connections among math concepts and skills.

It might be helpful to have a special event that brings this notion of "coherence" to life by showing some of the ways in which particular math standards connect to others.  For example, by including the topic of proportional relationships, the intermediate standards involve extensions of lower-level standards related to fractions and decimals.  And fractions and decimals are themselves inter-related because they both describe parts of a whole. Perhaps a special event can be designed that walks participants through some of these connections with hands-on activities.  Participants would get a deeper understanding of the meaning of "coherence" in the CCRS, some train-the-trainer resources, and even some classroom lesson ideas.

Or, the "coherence" concept could be illustrated with other standards.  The main idea in this suggestion is to have the special event bring the CCRS notion of "coherence" to life.



Thank you, Christine, William and Michell, for these valuable suggestions. We will definitely incorporate your ideas into our planning.

If others have suggestions, please let us know!

Cheers, Susan Finn Miller

Moderator, CCS CoP

I tried an experiment this last year and I think others may wish to collaborate. It was pitched to me that in working with adult learners, we could concentrate on simply conceptual knowledge and the learners would have all the math skills they need to succeed other than the academic fields that require the precision of standard procedures. At first I was very suspect and critical of this suggestion but after getting to discuss this for hours and in playing with activities and what little resources I could find, I decided I might try this shift in focus from our ingrained procedure focus to a focus on simply building strong conceptual understanding. I was amazed with the results and continue to experiment and explore this year. 

Learners effectively play with math using manipulatives, simulations, constructions and other activities that are all active. Simply having activities is not enough though, we needed good questions that helped learners begin to formulate their own connections. Tie in a strong set of experiences to build estimation, justification, reflection and communication and my math students have been so much more confident in math with much more success on standard assessments. Learners share that the math they learn is something they can relate to and really understand the connections. As an example, learners were blown away when they learned how to perform all 4 basic operations on fractions simply by folding 4 or 5 strips of paper using unit fractions and estimation. None of that silly converting improper to mixed, finding common denominators, the many ways to simplify and many other fraction procedures that are akin to voodoo for most students. Sure, their answers were not precise and often could vary by a few 8ths, but for most of us in life those small variances will not matter. In carpentry there is a saying that precision is only limited to the space that molding and putty can cover things up.

I would like to see some collaboration and discussion around this concept of focusing primarily on conceptual development, estimation, reflection and communication. Sure, we would add in the symbols, algorithms and such, but it would be a reduced emphasis as to be thought of as "extra credit". For those wishing to go into the exact sciences, an equal split of conceptual and procedural is of course desired. For almost all of my adult ed students, the procedural learning almost gets in the way of what they wish to do in life. As I hear more and more from my students concerning the effectiveness of really "getting this math stuff" I am becoming more and more convinced that we might wish to think about how a shift in focus could benefit the field.


Thank you for these ideas and for sharing your standards-based math practices with us, Ed. There is strong interest among members for a focus on supporting students' conceptual understanding for our upcoming Math and CCRS special event.

Your experiment is fascinating. I am not surprised that students have responded so positively. I'd love to hear other math teachers' responses to your approach.

Cheers, Susan Finn Miller

Moderator, College and Career Standards


I saw a post today in a list serve that I feel is worth many reading.


It is especially important for parents and students that have felt they "can't do math". I have always felt that students struggle with math because we math teachers struggle to present more than what our text books and college lectures trained us to do. This article offered me much vindication in my believe that everyone can not only learn math, but can become confident and competent at very high levels in math; we simply need to improve our options in instruction. 

Maybe this article was aiming to sell a product more than inform, but many of the links do provide rich materials for our educational professionals to discuss. If we really dive into the College and Career Readiness Standards for Adult Ed, we find the Standards for Mathematical Practice ( page 48 is where they start) articulating common habits of effective mathematical thinkers. This is basically a Habits of Mind type list that focuses on proficient mathematicians. For most of us, trying to train learners in these 8 thinking practices seems impossible and impractical. I agree, these ways of thinking can NOT be taught so much as we need to create environments that elicit thinking opportunities that support these types of thinking. As the article linked above states, our brains grow as we experience frustration and failure. Are we providing our math students productive failure time that is supported by rich discussion and discovery? I am definitely not seeing much of that in any curriculum guides or standardized exams. If we truly want our learners to think and process at deep levels, our collective educational providers need to work together to explore positive ways to set the stage for our learners to think, fail, reflect, reset and try again. This simply can not be accomplished with most traditional forms of assessment we use. 

Perhaps math discussions centered around formulating ideas, ways, activities that promote thinking and positive failure cycles would be beneficial? I would love to hear ways instructors are fostering cycles of think, self assess, reflect on successes and failures, resetting approaches, and trying for more successes. 

Our Texas ASE Math trainers put their heads together and came up with the following topic suggestions: · Developmental Math: Its Foundational Principles · The X-Factor: Polynomials, Equations & Inequalities · Geometry & Measurement · Data Analysis, Statistics & Probability · Applying Math to Public Health · Math for Careers - How Math is used on the Job · Word problems" to illustrate mathematical comprehension in an applied way. · Linear equations, · Factoring quadratic equations, · Slope of the line, and slope intercept form of a linear equation. · Working with formulas and substitution, · Distributive property

Harriet Vardiman Smith

TRAIN PD @ TCALL, Texas A&M University

Thank you Harriet --and thanks to your colleagues, too! This is a great list of potential topics!

Would others like to suggest additional topics or to validate or even prioritize the topics identified by our Texas colleagues? Which of these topics would you put at the top of the list?

Cheers, Susan Finn Miller

Moderator, College and Career Standards CoP

There are at lots of different levels, like our students... 

Some of the basics like working with formulas and substitution are such critical concepts that, if we go back and work on that foundation, can open the doors to the higher math.   I'd like to see attention paid to making sure we're building conceptual knowledge as well as procedural.   

Harriet -

Thanks for using the term "foundational principles" for math.

Too many of our adult math learners are in the situation of "they don't know what they don't know."  It's like being color blind and having someone describe a bright, colorful picture to you.

The foundational principles or concepts many adults do not grasp are:

1) Each "1 more" on a number line is the same size. That is, the distance between 7 and 8 is the same as the distance between 37 and 38. Adults who do not have this concept use marks on their paper or use manipulatives to add. When they put the physical items together, they have to count all the pieces (or marks) from 1 to arrive at the total.

2) The whole amount (for example, 9) and all the parts inside it (for example, 6+3 or 2+2+2+2+1 or any other combination) exist AT THE SAME TIME. Adults who do not have this concept struggle with fraction and decimal concepts. This ability to keep parts and whole in mind at the same time is also critical to reading comprehension.

Throw in the common misunderstanding of the equal sign as an operation rather than a relationship, and you have normal adults with good reading skills who think they cannot understand math. They need to go back to these early concepts. Unfortunately, none of the adult math texts from major publishers teach these concepts. The incorrect assumption is that we all grow into understanding them.

What I'm saying about missing concepts has its base in research with children. I have extended it to adults. If you would like a copy of my recently published article that gives more background on this (Evaluating Number Sense in Workforce Students, MPAEA Journal of Adult Education, July 2015), contact me and I'll send my submitted article. The outcome of the evaluation: Of 86 workforce students, 74% lacked the part-whole coexistence concept. Of those 86, 14% also lacked the "same sized 1" concept on a number line.

We need to actively teach these concepts.

Dorothea Steinke


Please send it my way :)   

I see the same pattern, tho' not quite as severe, in the community college setting -- even with folks who place into our developmental classes.   I see it more pronounced in the students in our lowest level course, which most colleges don't even offer (and some of our admins would just as soon save money and not offer, since financial aid won't pay for it so we front the costs).   

That course is very strongly based in Dorothea's work (in fact, we'd have used her materials but they just weren't going to be done on time).   Basically, the students who attend it, pass it, tho' some also come in for office hours and Kathy's (the instructor) *amazing* tutelage.   

So, for instance, they work with fractions -- but with lots and lots of practice making 1.   3/4 + 4/4... Lots of practice with what zero is... no throwing in huge numbers just for fun.   Lots of manipulatives; lots of discussion of the concepts -- the "part/whole" concepts as well as the mathematical concepts.      

Thank you for your thoughtful posting and for offering to send your paper to members, Dorothea. This issue is clearly of central importance since such a significant percentage of adult literacy students are likely missing these foundational principles.

Does the paper discuss practical teaching strategies? What are the practical steps math teachers can take? Are there things math teachers should avoid doing?

Cheers, Susan Finn Miller

Moderator, College and Career Standards CoP

I I teach Math. I have used this strategy in my class.   It is rewarding for both the students and the teachers to have peer teaching and review.

It is rewarding to the students  because when they talk to each other, they communicate in their own language and at their own level.   When they find each other's weaknesses and strengths, coach each other, and critique each other's work, they don't feel alone.  Someone else feels what they feel.  They confirm that everybody can make mistakes and can learn from them.  Once they overcome their dilemma, they feel accomplished and take control over their own learning.

During Alicia’s class she engaged with students randomly as she moved around the room, making suggestions and helping where she was needed.  The students were able to learn from one another and collaborate regarding best writing practices and suggestions.  It allowed them not only to share their ideas and knowledge, but also to learn from those who might have more advanced writing skills.

I teach beginner and intermediate ESL.   I recognize the importance  of atonomy learning and do use peer review as a means of avoiding direct teacher corrections.  Leaves the student with more freedom to learn from one another. 

One specific, concrete, and descriptive observation I saw during Alicia's class was that she walked around the classroom to check on students as they discussed and collaborated with each other regarding what makes a good paragraph and how they can improve their own writing.

One specific, concrete, and descriptive observation is that the students were learning from each other and discussing the best way for the writing, they were giving each other ideas as well criticting each other's work in a good way to make their paragraphs. 

During Alicia's class, she walked around to check students as they were collaborating with each other about what makes a good paragraph and how they can improve their writing. I try to circle the room to help engage students in the activity, but at times some students feel that they are not very good at writing.... I hope to implement some activities to teach students that their brain is growing all the time and that they can and will eventually understand more concepts in learning. 

I agree, she did a good job of walking around and listening and offering suggestions to help her students. Her encouragement for the students helped build their confidence, and give them the ability to want to do more to help their peers. The engagement from the teacher, the engagement from student to student, and to oneself was motivating. This helped make the student feel in control of their learning.

One specific, concrete, and descriptive observation I saw during Alicia's class was that she walked around the classroom to check on students as they discussed and collaborated with each other regarding what makes a good paragraph and how they can improve their own writing.

Post-viewing activity

-I watched a lesson on Writing to Learn. The teacher had the students just jot down things that happened last week. The idea was to show them how brainstorming on paper helps them think of ideas. From there she had them choose an event and write more about it, then share together what they learned. I really appreciate how this lesson models learning strategies. My students HATE taking notes or writing anything down. Often, when I tell them to jot down some ideas, they ask me to look at it and tell me if they did it right. They need to learn that writing is a tool they can learn for their learning, not just what gets turned in. 

One specific, concrete, and descriptive observation I saw during Alicia's class was that students were practicing learning from each other. It supports the sharing of best practices and build awareness about their own work. It also give the students opportunity to learn from, and give feedback to peers.

I am a GED Math instructor and this can really help me in the classroom. Also, I saw from this video how students were helping each other, which I encourage my students to set up groups outside of class to practice on the lesson for that week. 

I found the teacher's method of engaging her students in a learner-centered writing activity very powerful. They gently guided each other to correcting or editing their work. I'm an ESOL teacher and have usually taught beginning level students for 20 years. I look forward to teaching a high intermediate level class and providing students with strategies to read, write, and share. I will invite students to share contact information with each other so that they may collaborate. 

I agree, the teacher did a great job in providing students with needed space to assess their own skills development.  The peer interaction gave me a mountain of ideas of what I would like to see in my writing class.  

I agree, the teacher did a great job in providing students with needed space to assess their own skills development.  The peer interaction gave me a mountain of ideas of what I would like to see in my writing class.  

I really liked the video. I think learning from one another can really help the students feel more comfortable and sure of themselves. I will keep this in mind for my students.

I loved how the instructor set up the work stations with specific features to look for (with examples).  Their comments were then critiqued by others (so they couldn't blow off the assignment) and they couldn't leave the station until someone else agreed and initialed their comment.  Excellent way to keep students on track!

So cool how the students reported it helping their own writing!

I think they began to think more deeply about what writing should look like as they saw the many examples and had to reflect on what was correct or not.  Lots of critical thinking.  This instructor must've done work to prepare them to be so kind and open with each other.  Bravo!

During the video teacher was walking and monitoring students' discussions all the time providing feedback. Students were working with partners and checking their essays. They learned how to review and edit essays and compare their work with their classmates.

I noticed that as I do in the classroom the teacher continued to walk the classroom and monitor students. This is a good way to check group participation and student understanding.  

Using peer feedback was a very effective strategy in the video. It created a comfort level for students. Each student could identify their own mistakes while doing the peer review and one student went back to check his own work. This was much more effective than the instructor correct the work.

I like the method of peer feedback. I believe this strategy is helpful to all students and builds confidence. This strategy allows students to feel seen and supported. Peer feedback shows the students that we value them.

I felt that the use of peer feedback was an effective tool that was used between and among the learners.  It seemed that the process helped them to both better understand the materials and to reinforce their collective confidence to master the relevant content.  The use of this tool helped students to be able to learn from each other, rather than instructionally driven learning.

In the video, the teacher modeled literacy and learning strategies by writing a story about visiting the supermarket (using past and present tense). The teacher had a visual aid that showed what the supermarket looked like. The teacher directed the students talk with each other about what they ate yesterday (cooperation and collaboration). Each student recorded their findings on a piece of paper. The teacher assisted learners in managing errors by talking with each pair to clarify what each student ate yesterday, applying present/past tense (written and speaking).  

Peer review is often an excellent idea for adult students. They can give feedback to one another without feeling overwhelmed.

One particular strategy that Alicia uses is setting a goal. In this case, her goal was for students to discover the strengths and weaknesses in both their own and their peers' writing. By making this clear from the beginning, students demonstrated an understanding of the task and had meaningful conversations that fostered their learning. One student talked about improving his essay's introduction and using more examples, both of which meet the original goal of learning how to effectively revise his paper.

In what ways have teachers in your program worked together to boost learner motivation and persistence? 

In our AE program, we have had many discussions about how to help students overcome barriers. Whether it be about motivation for coming to class, test anxiety, or the need for getting Disability Services on board, we are always striving to put the needs of our students first so that they will attend class and continue to progress in their journey.

I thought the peer-tutoring in the ESL video was applicable to GED instruction as well. I have had success in teaching GED Math with students working in small groups together to solve problems. I also liked the way the instructor had the students standing up and moving from station to station; this showed a natural progression of learning with a finite end.