This week sees the move from the LINCS Subject Matter Expert (SME) – model to that of a moderator-facilitated discussion groups. For the Math and Numeracy group, I will assume the role as moderator of this community of practice (CoP) and move from the title of SME. I am very excited to be continuing with this wonderful group!
I am not new to this community but let me re-introduce myself for those of you who have recently joined our group. My name is Brooke Istas and I currently teach mathematics at Cowley College in Kansas. For last eight years, I worked in our adult education program as the Instructional Coordinator/Mathematics Instructor in face-to-face, online, and blended classes; both in and out of the correctional settings. I am familiar with the difficulties that many of you have because I have had them, too. In addition, I have worked as the Subject Matter Expert for the Math and Numeracy Community of Practice for the past five years and have given trainings on mathematical and science concepts for LINCS.
Each of us brings a depth of knowledge and expertise to our community, I look forward to getting to know and learn as a member of this community. I welcome your feedback, questions, concerns, issues, thoughts and suggestions for making this community a place you value for answers to tough questions, resources to improve instructional strategies, look to others for help and support each week.
Whether you are new to this community or not, please feel free to introduce yourself and answer these two questions:
1. What is something you are struggling with right now in your program, classroom, or facility?
2. What are your current learning interests to help you improve or support what you are currently working on?
As we begin to post – I would like for those of us reading the responses to reply to posts that intersect with our own thoughts, challenges, or interests. If you are interested in something I mentioned in this introduction and want to now more, please post a reply to ask about it.
I teach math in a maximum security men's prison in Wisconsin. My current struggle right now is contending with students who only want to study algebra and geometry, yet they have yet to master the basics (addition, subtraction, multiplication, and division of whole numbers fractions and decimals). I try explaining to them that learning math is like building a skyscraper where algebra and geometry are the top floors. If you try to start building a skyscraper with the top floor without having a good, strong foundation, the building will collapse and if you try to start with algebra and geometry and you don't have a handle on the basics, you will have an extreme struggle on your hands.
I am currently taking the ANI numeracy training. I have learned many great new practices I have put to good use in the classroom. If anyone has an opportunity to take the classes I would strongly recommend it. Currently I am working on finding more practical applications for math to use as lessons to help the student understand that what they are learning is important and that it has real life applications.
Thank you Christine for posting! I can't say enough positive things about the ANI Training! I am an ANI Trainer and I love how the lessons are geared for adults AND there is a real-world connection! How many institutes have you been to?
Also, I will be in Wisconsin on April 30 and May 1 for a couple of presentations - will you be attending? If so, I would love to meet you face-to-face.
I have been to the first two sessions. I will be attending the third session on April 2nd and 3rd. I am very interested in becoming an ANI instructor for the DOC in Wisconsin. Do you have any information about becoming an instructor?
Where will you be on April 30th and May 1st? Maybe we can arrange to meet even though I'm not attending that institute.
I will be in Madison on April 30 and then I will be at Black River Falls on May 1 but returning to Madison later that day. Are you located near either of those locations?
In my experience as a math instructor for adult basic education, I found that geometry and algebra were great subjects with which to start math instruction, rather than waiting until all "the basics" have been mastered. That's because real-world applications give learners a reason to know those basics! In finding the perimeter and the square footage of a room in order to get a new carpet, one has to add and multiply after one has measured the sides of the room. There you have it, in one task: measurement, addition, multiplication! Geometry has been the place to start, once we get past the Greek words like hypoteneuse!
You bring up a great point - the College and Career Readiness Standards graphic that I found illustrates this idea of teaching algebra even at the lowest level. Of course, it doesn't look like the upper-level concepts but it could start with getting learners to see patterns. Have other instructors in the community taught any lessons that incorporate algebraic thinking with basic number sense?
One thing I do a *lot* with algebra is to plug in numbers to show how things work. So, when X + X = X ^2 in the student's mind, I plug in 3 and walk through the process to show that ... welp, no it doesn't. Then I'll use 25 ... Then I'll show how X + X = 2x (25 + 25 = 50) .... and try to reinforce the concept that if we have an x in a place, it could be *any* number and what we say it's equal to has to be true for any number.
One of the many awesome things I learned from this group is about teaching number sense and comprehension as "parts and wholes." I don't teach; I'm a tutor, but I do have students who struggle with anything like a word problem. Using Dorothea Steinke's framework that "if you know the whole and need to find a part, you'll subtract or divide. If you have the parts and you need to find a whole, you'll add or multiply."
So ... if students are used to working with that with plain ol' numbers, it could be easier (I haven't tried this, though) to recognize that if the "whole" is 40 and one of the parts is "x," then the other part has to be "40 - x." That's the key to a whole mess of otherwise terrifying Word PRoblems With Two Unknowns.
http://www.mathplayground.com/thinkingblocks.html has some really neat activities for working with word problems.
Hi Sue (and all).
Thanks for repeating the idea of "find the part" with subtraction and division and "find the whole" with addition and multiplication. Many, many of our math students are not used to thinking of numbers in relationship to each other - which is what math is. If anyone wants to learn more about this "two kinds of problems" approach, contact me at firstname.lastname@example.org
About X ...
I was working with a student once who thought X was always the same number, no matter which problem the letter was in. When I told the student that X would be the same number in THAT problem, but could represent a different number in a different problem, it made her see that unknown differently.
How often we assume students know something that seems so basic to us math-inclined people!
Another surprise to students is that the "X + X = 2x" and rules for combining like terms, etc. aren't arbitrary. WHen I show that no matter what you put in for x, "x + x = 2x" would always be true but "x + x^2" wouldn't, a gliimmer of understanding. (It's still ... abstract. )
I love the website you posted in this thread - this is a great way to show area models and how x^2 isn't the same at x + x. What are your thoughts about the Virtual Manipulative Library? They have some great things for Binomial Multiplication and Factoring of Polynomials. I was wondering if anyone in the community tries to use real-life examples to show x + x isn't x^x.
I do some geometry and number concepts but I teach the very basic level for math so it's hard to do area with student who do not even know the basic multiplication facts. The area model helps. But sometimes focusing on the basic facts is necessary.
If your students want to start with algebra and geometry but are lacking some "basic" math concepts, I'd recommend looking at Myrna Manly's Math Problem Solver. It's geared toward the old GED test, but it does a good job of integrating number sense with algebra and geometry, and I've found nearly all of it to still be relevent (I covered the answer grids with sticky notes so the students can write their exact answers without having to learn the grid). Depending on your students' levels, you may need to supplement or skip parts, but I have had good luck using it with a variety of folks. (Also--it looks like a "serious" math book, which is important to some students.)
In response to S Jones, this book starts with parts and wholes. The students begin by writing equivilent equations (3+9=12, 9+3=12, 12-3=9, 12-9=3) and move on to incorporating variables (10+y=15, y+10=15, 15-y=10, 15-10=y). I also like the fact that the students do a lot of work with addition and subtraction (including algebra, geometry, graphs, negative numbers, and word problems) before moving on to multiplication and division, and then fractions, percents and ratios.
I wouldn't use it as the only thing the students do all day (especially if you have weak readers or ESL students in your class), but I've had success using this book for the independent study portion of a class with students at 7.0-12.9+ on the TABE.
My problem is that in my low level math class, half of the students are ESL and the majority of them have reading levels that are less than 4th grade. I will look into that book and see what I can use and adapt for my classes.
Have you heard of the EMPOWER series from McGraw Hill? They have a great book that is on mental math but curriculum incorporates real-life, hands-on, lessons that push learners to use critical thinking and build on previous knowledge. My low-level learners love them - but I have only had a small number of ESL. Below is a link to the resource, oh, and they best part - the copyright for this book allows for you to copy the pages for instructional purposes!
Hope this helps!
Hi Brooke and Christine! I absolutely love this series by McGraw-Hill! Christine if you decide to go this way, you won't be disappointed!
I would love to have a set of them but budgetwise at this time we cannot order books.
I have great news - the original pilot for the EMPOWER series came from Teachers Investigating Adult Numeracy (TIAN) - these resources are similar to the ones in the EMPOWER Series and they are available online to you. Here is the link: http://tian.terc.edu/TIAN_teacher_resources.html. There are FIVE bundles that have lots of great activities - maybe this can be useful until you can get a set of books.
Hope this works!
In case you and others don't know, the purchase of the student book allows you to make copies for your students. If short on funds, you could purchase just one teacher edition and one student edition. The student books are also perforated and hole-punched, so it's easy to tear out the pages and copy what you need for the students you have that week. I keep mine in a three-ring binder with additional practice and other lessons between (or substituted for) the lessons in the book.
I also like the EMPower books, though I find that for my students, it's better to go a little bit slower than one lesson per class. We generally do the main activity one class and then spend the next class working on the concept some more, including going over homework, using the practice pages, and sometimes bringing in exercises from the internet or other books. This is also helpful for students who miss class, since there's less of a chance that they will be totally lost.
I don't know about everyone else, but I have found that students don't always generalize from examples as readily as the exercises seem to anticipate. This is something that I have to actively teach.
My name is Alfons Prince and though I've been a poster on LINCS sparingly, I check the forums frequently. I currently teach under-credited adult in Washington DC in mathematics. The school I teach at is uses blended learning to prepare students for the GED test, Accuplacer exams and several vocational certifications.
The major thing that my school is struggling with are the students' attendance. We can show gains if the students show up, however since the holiday season our attendance numbers have been mediocre at best. Within my class, I struggle with overcoming the students' hatred/fear/anxiety of/for math. Usually once I get past that barrier, students can learn the material they need. We have about 10-15 students that we are preparing to send to take the test in late May, so then I will have a great barometer of whether or not what I'm doing is working.
As for my own professional development, I want to learn about adult mindsets when approaching mathematics. I'm looking for any webinars, conferences, etc that will help me with this. I appreciate any assistance this forum has with that endeavor.
Welcome Alfons, thank you for your post!
I know that there are others that struggle with student persistence - I see it in our program here in Kansas, too. I hope that others in the community will chime in with their thoughts on how to retain learners. I know that the LINCS Resource Collection has some research-based practices. I found a few and I am posting their links below:
- Adult Learner Persistence
- Making it Worth the Stay: Findings from the New England Adult Learner Persistence Project
As far as your professional development, I know of some GREAT resources about adult mindsets about mathematics
I am sure there are others but these are just a couple that I have ran across. Thank you for sharing your struggles and needs with us!
Thank you Brooke for the links on retaining learners! It is information that I will definitely digest and put into practice at my school. I am also interested in the ANN group. I am also looking into attending the COABE conference next month. What are some things you suggest I attend?
Hello All - Alfons asked above the sessions he should attend at COABE; does anyone want to offer suggestions they have used in the past to help them navigate?
Greetings everyone! My name is Libby Serkies, and I work for the Central Illinois Adult Education Service Center. I work primarily from my home in Bloomington, IL as my office is located 2 hours away from me! I provide state-level professional development to adult ed teachers and programs throughout the state of Illinois - specializing in math instruction and Career and College Readiness.
I have been more of a lurker on the Lincs message boards, but very much want to become a regular poster/commenter! My response to Brooke's request to answer the following questions is below:
- What I am currently struggling with is how to get buy-in from some of our more "experienced" teachers about the need to not only include more rigorous content in our classes, but to adapt our instructional practices to reflect a shift to a more process oriented model (meaning that we don't focus our math instruction on finding the answer, but rather on understanding the math).
- My current learning interests include the Standards for Mathematical Practice, and integrating them into instruction.
I am excited to be here and to learn from all of you!
Thank you for posting and sharing your struggles with the group. I also struggle with helping other instructors in the shift from procedural knowledge to conceptual knowledge! Does anyone else in the community have any suggestions for Libby?