Episode 318: Flexibility In Problem Solving: Making Mathematics Accessible
Look behind the scenes of the Georgia math standards revision for secondary education. Join us for a special episode of Classroom Conversations with Lya Snell and Kenneth Golden of the Georgia Department of Education!
Look behind the scenes of the Georgia math standards revision for secondary education. Join us for a special episode of Classroom Conversations with Lya Snell and Kenneth Golden of the Georgia Department of Education!
Ashley Mengwasser: Hello there. Thank you for joining us for another episode of Classroom Conversations. This podcast series is brought to you in partnership by Georgia Department of Education and Georgia Public Broadcasting. We are the platform for Georgia's teachers, and I am Ashley Mengwasser, a diehard teacher groupie. Speaking of fans, our audience knows that a few episodes ago, we spent some quality time together understanding the elementary math standards. If you haven't heard that episode, you might want to go back and listen. Today we are attacking mathematics standards revision and implementation for secondary education, total knockout style. And now, two introductions. Things here at GPB studios are just golden, Kenneth Golden. Kenneth is our teacher feature, a seventh grade teacher at Smitha Middle School in the Cobb County School District. Hey, Kenneth.
Kenneth Golden: Hey, how's it going?
Ashley Mengwasser: Now I understand you've been teaching for 100 years, or no, is that 10 years? Which is it, Kenneth?
Kenneth Golden: So, 10 years I've been teaching. I'm in my second year here at Cobb County and eight years with Gwinnett County.
Ashley Mengwasser: So, zeros matter before the decimal, my apologies. Math education taught me that. And we're blessed with a second guest. We're happy to have Dr. Lya Snell return for part deux. Lya is the Mathematics Program Manager at the Georgia Department of Education. Welcome back, Lya.
Lya Snell: Yes, thank you. Thank you for having me.
Ashley Mengwasser: You know, this is what we call an encore performance, and you're the first. Any heartfelt words, anyone you'd like to thank?
Lya Snell: No, it's amazing.
Ashley Mengwasser: Our very first encore. That's pretty special. I don't know if there will be more, but you're the first. It's nice to have both of you pros here today. Thanks for joining us. Kenneth, tell us how you got into mathematics education. This is always interesting.
Kenneth Golden: So, I'm starting out at Georgia State University undergraduate program, and I'm a business major going through a business learning community with my cohort. And it's my second semester, just finishing up with my accounting exam and I realized that I need something more fulfilling. So I got an opportunity to tutor some kids, tutor some elementary school kids. And I was tutoring, interestingly enough, in reading and math. And so I was tutoring in math and they were like, "Hey, we want you to be our teacher. Why can't you be our teacher?" And so I felt it. I was like, my dad's a teacher, my godmom was a teacher, and I've had some great teachers along the way, but I wanted to see myself more reflected in the classroom. I had a few teachers, but not enough so I just wanted to be that teacher that I rarely got in the classroom that had the level of engagement that I had with these kids. So that just set me on my journey to be a mathematics educator with a shout-out to Julie Pinto was one of the math educators who I strived to be like, so she's really amazing from Cobb County. So that's how I came into mathematics education.
Ashley Mengwasser: Well, I hope she's listening.
Kenneth Golden: Oh yeah.
Ashley Mengwasser: That was just beautiful. Lya, how about you? Honestly, do you ever tire of talking about math? What do you do in your spare time?
Lya Snell: You know, I am a math enthusiast through and through. I absolutely love mathematics. And I have a phrase that I often say, mathematics is the language of the universe, and I truly believe that. So my career has provided me the opportunity to encounter so many amazing people. From my start at Alabama State University where I was a math major and Dr. DeShields really encouraged me to go into education after I finished an internship in chemical engineering and realized that this wasn't the path that I really wanted. Like Kenneth said, I wanted something more fulfilling, and Dr. DeShields was right there saying, "You should really consider going into education." And so I tried it and loved it. Absolutely loved teaching, and I've taken that passion into leadership experiences and now, working at the Georgia Department of Education, able to work with teachers from all over the state to hopefully spread the love of mathematics and share that passion and like I always say, mathematize the world.
Ashley Mengwasser: You told me this, that you, what is it, mathematize?
Lya Snell: Yes.
Ashley Mengwasser: You mathematize everything around you and you're a chess player.
Lya Snell: Oh, yes.
Ashley Mengwasser: Tell us more about that.
Lya Snell: Chess is one of my hobbies. I love to play chess and I love to reason through the game and try to figure out what the opponent is thinking in order to conquer them and to have a checkmate. So I do love chess and I also love to swim and traveling with family and making great memories with those are close to me.
Ashley Mengwasser: Well, if there's a math addiction, you have it. You have it. Good for you. Before we demystify mathematics, team, I thought maybe we could mystify ourselves with a little round of jokes. Who doesn't love humor? Just please don't think of this as your favorite new standup because it's not good material, number one. And number two, we're sitting down. All I can promise you are dad jokes, and I mean that literally, though. This is from, what is this website, fatherly.com. These are legitimate jokes by dads. You ready?
Kenneth Golden: Yes.
Ashley Mengwasser: Laugh or groan, here we go. Joke number one. What... I can't even. What did the math teachers say about Amazon Prime members?
Kenneth Golden: Oh lord.
Ashley Mengwasser: A groan on the first joke. Any ideas?
Kenneth Golden: Amazon Prime members.
Ashley Mengwasser: Prime being the keyword.
Kenneth Golden: Prime numbers, of course.
Lya Snell: They are not composite.
Ashley Mengwasser: Oh, you're so close. They are odd.
Kenneth Golden: Oh, nice.
Ashley Mengwasser: I feel attacked. I love Amazon Prime. What do you call dudes who love math? This one's good.
Lya Snell: Mathmadudes.
Ashley Mengwasser: Dudes who love math.
Kenneth Golden: Let's see.
Lya Snell: Mike.
Kenneth Golden: Math guy. Mike.
Ashley Mengwasser: Kenneth.
Kenneth Golden: Oh, is that me?
Ashley Mengwasser: No, that's not the answer, but it should be.
Kenneth Golden: I was like, "Yeah."
Ashley Mengwasser: You're a dude who loves math. The answer is algebros.
Lya Snell: Oh, nice.
Kenneth Golden: Algebros, nice. I love it.
Ashley Mengwasser: That's good. You're going to totally use this in your classroom, aren't you?
Kenneth Golden: Yes, yes.
Ashley Mengwasser: This one's fun. Why are parallel lines so tragic? You may get this one.
Kenneth Golden: Let's see. They never meet. They'll never come in contact with each other.
Ashley Mengwasser: They never meet.
Lya Snell: Oh, they never meet.
Ashley Mengwasser: They have so much in common, but they'll never meet. Nailed it. I like this one. What did the number zero say to the number eight?
Kenneth Golden: Oh, that's a nice belt.
Ashley Mengwasser: Kenneth, are you the author of this article on fatherly.com?
Kenneth Golden: I actually, my kids love my dad jokes. I do dad jokes all the time.
Lya Snell: I was going to say, "You thought you ate."
Ashley Mengwasser: Oh, that's good.
Kenneth Golden: I like that one. I like that one.
Ashley Mengwasser: That's good, too. Maybe too clever for fatherly.com. I didn't even know that you were my target audience here today, Kenneth. And here's the last one. What do you call an adventurous number?
Kenneth Golden: Adventurous number...
Lya Snell: Infinity.
Kenneth Golden: I like the way you think. Adventurous number. I'm stumped.
Ashley Mengwasser: A roamin' numeral.
Kenneth Golden: Roamin'.
Ashley Mengwasser: Roamin'.
Kenneth Golden: Roaming, got you.
Ashley Mengwasser: It's roaming, get it?
Kenneth Golden: I like what you're putting down.
Ashley Mengwasser: Okay. That's enough of that. We're officially off task. Time to refresh our memories. The new mathematics standards will take effect in 20, Lya's dying. They take effect in 2023. Is that right, Lya?
Lya Snell: That's right.
Ashley Mengwasser: What's the timeline? Give us the scoop.
Lya Snell: So, the new standards were adopted unanimously by our State Board of Education.
Ashley Mengwasser: All right.
Lya Snell: August 26th, 2021. And they will be implemented in classrooms with students in fall of 2023. So we are actively preparing for that implementation and to get teachers and leaders ready for teaching those in the classroom with students.
Ashley Mengwasser: We've got some time, so we thought, hey, our teachers might just like a little help elucidating what's coming their way, and that's what we're going to do next. So let's talk about how a mathematical mindset is crucial for student success. How have you seen that to be true, Kenneth?
Kenneth Golden: So mathematical mindsets are super important in the classroom. And for teachers, that means facilitating a classroom where kids can make mistakes and be okay with that. It's this conversation between having a fixed mindset and a growth mindset. A fixed mindset says, I can't. And a growth mindset says, I'm not able to yet. And that word yet is so powerful in the classroom. Giving students an opportunity to just explore mathematics with the ability to be wrong and to learn from their mistakes is such an important driving factor for understanding the concepts in the classroom. Just having that ability to just be free with the math. So the mathematical mindset is super important and facilitating that is something that we are going to make sure that we try to push out to teachers as well.
Ashley Mengwasser: Lya, how's that crucial?
Lya Snell: It's absolutely crucial. There's not a such thing as a math person or not a math person. Everyone has the opportunity to learn math at high levels. So mathematical mindsets really bleed into counseling with students, guidance with school counselors, with leaders, with teachers, but also with parents and community at home. We often say in media, for example, in movies, they talk about math being this dreadful thing when actually, math is beautiful, math is a subject that should be explored by all because it is all around us. Everything that we do has some connection to mathematics. So giving students the opportunity to learn mathematics and focus on making sure that each and every student has the opportunity to be successful in the mathematics classroom and having the mindset that mathematics is for all, then that would help our learners tremendously.
Ashley Mengwasser: Ah, so it's the beauty in the process of learning math. How did you two participate in the development of Georgia's new K-12 math standards? Lya, you go first.
Lya Snell: We engaged with teachers and all congressional districts throughout the state of Georgia to review and revise the mathematics standards. We had the opportunity to pull together over 400 teachers in a room together, in multiple rooms, and thousands of constituents who provided feedback to participate in the review process. This was the largest involvement of teachers and stakeholders in the history of standards review, and we're really excited about that.
Teachers from all areas of the state, teachers from all grade levels had the opportunity to determine what the specific content needed to learn by students was for each grade level. That brought us to the place of having these adopted standards. And it's just been an honor for me to see this and lead this effort for the state and to come in contact with amazing teachers throughout the state who are passionate about making sure students have what they need to grow and be successful in any post-secondary opportunity that comes their way.
Ashley Mengwasser: Well done. Well, Kenneth, you were one of these teachers. Tell us about your role.
Kenneth Golden: So, like Lya said, we had this great opportunity to meet with tons of teachers who had the same passion that I did with how can we make the standards more accessible. And by accessible, we just mean how can we make the standards more clear for all the stakeholders involved. So I got a chance to lead the sixth grade team and just having those conversations, some hard conversations, and some really thoughtful conversations about having just a vertical talk about what's the logical progression going to look like, what should be taught now, what should be taught later, what's age and developmentally appropriate. We just had these conversations and found ways to just make it, like I said, more accessible. Make it feasible for parents to understand and students to understand and teachers to understand.
Ashley Mengwasser: Everyone to understand.
Kenneth Golden: Yes, yes.
Ashley Mengwasser: What is the main difference that you've seen in your perspective, Kenneth, between the old standards and these newbies?
Kenneth Golden: So, the biggest thing that I would say is, like I was talking about with the clear expectations, talking about that verbiage and talking about the intent. So we're going to be providing the resources within the standards so that teachers are able to deliver them effectively for their students. And just with that, where if I could explain it as if going to a destination, we're focusing more on the journey and the destination and the vehicle that students are using to get there.
So what I mean by that is, focusing less on specific methods that students are using and assessing those specific methods and just encouraging students to find those patterns. And you'll see reasoning all throughout the standards focusing on that pattern, focusing on reasoning, for students to kind of come up with their own way and their own methods that make sense to them. So you'll definitely see that. You'll see teachers getting a clearer expectation and a clear picture of what's going on. So hopefully that comes through with the standards that'll be implemented.
Ashley Mengwasser: And this is true for the secondary education ones. Lya, what do you want to say about it?
Lya Snell: It is important to note that the change in the standards really focuses on students understanding what they are learning and focusing on reasoning. Every big idea that is incorporated in the new standards from kindergarten all the way through high school literally has the word reasoning, because that is important. And it also is important to note that the standards have included some instructional supports that help teachers as well as parents and students in the classroom as students are engaging in learning the specific concepts at each grade level. There are now suggestions for age appropriateness of standards. There are suggestions for relevance and application. There are specific ideas and suggestions provided that serve as examples of what that standard and learning objective actually means. There are also progressions documents that help explain the key concepts at each grade level and what's taught in the years prior, as well as what's taught in the years to come so that teachers and parents and students can actually see the progression of knowledge from kindergarten all the way through high school. We're excited about that new addition to the standards because it will provide for more clarity in understanding what the standards actually mean. Also, what's important to note is there is a greater focus on flexibility in problem solving, where students can solve problems in any way they see fit.
Ashley Mengwasser: You make it plain what the purpose is, and you root it in significance, which I imagine creates less resistance to the learning.
Lya Snell: Yes, absolutely. It makes it fun.
Ashley Mengwasser: Yeah.
Lya Snell: Mathematics is fun, so it makes it fun for learners and relevant.
Ashley Mengwasser: What would you like teachers to know about mathematics teaching and learning for students?
Kenneth Golden: I love it because math is so magical, but we don't want it to be so magical that it's-
Ashley Mengwasser: Inaccessible.
Kenneth Golden: Yeah, inaccessible. You want it to be where you have this environment where students are allowed to explore, giving students that opportunity to work on something concrete, getting hands on mathematics, then moving to a representational where students are able to draw diagrams, maybe, and then moving to the abstract. Working on that concrete to representational to abstract. And then just allowing students to just see those patterns themselves and genuinely and sincerely come up with things that make sense to them. Even in my classroom, I'm still learning from students that come up with new ways to do old math or the same math that students are just coming up with different ways to do everything. So I'm loving it.
Ashley Mengwasser: You roll with it.
Kenneth Golden: I roll with it.
Ashley Mengwasser: What math are you teaching right now?
Kenneth Golden: So, I'm teaching seventh grade math as well as a seventh/eighth math. So, it is an advanced class, the seventh to eighth.
Ashley Mengwasser: Of course. Of course. Lya, what do you want teachers to know about mathematics teaching and learning for students?
Lya Snell: Well mathematics, as we've discussed today, mathematics is an amazing subject with a lot of beauty. And so I would say in the implementation of the standards, find ways to make mathematics learning fun. There are expectations that are specifically outlined for each grade level and each high school course. And the concepts can be taught in a way where students get excited about learning mathematics, because there are so many interconnections between mathematics and also mathematics in other areas, showing where mathematics really is relevant in everyday life. So that's exciting with the new standards and having teachers get excited and then also letting their students be excited about teaching and learning of mathematics will help students engage at a greater level and also understand at a deeper level.
Ashley Mengwasser: And the message is not just, "Here are the new standards. Go have a good time." It's, there's support, there's backing. You have resources for educators. So let's start with that. What resources will exist that will help teachers implement the math standards in secondary education, Lya?
Lya Snell: So, we have several resources that we currently offer on georgiastandards.org, as well as our homepage at gadoe.org/mathematics. All of the frameworks and curriculum maps and grade-level comprehensive course overviews will be revised to align with the new standards. So that work is happening now. Georgia's teachers are absolutely amazing, so we have tapped into the amazing teachers and brought them together for each grade level and each high school course and they are taking the standards that have been adopted and now writing resources that include opportunities for engagement, opportunities for application and reflection for each unit, each grade level, each course that will all be released in time for implementation in fall of 2023.
Ashley Mengwasser: To comprehensively support everything wherever teachers are. What do you think, Kenneth? What resources are teachers going to look forward to and love here?
Kenneth Golden: Yeah, in addition to what Lya said about us, because I'm on that committee tasked with writing the framework or the tasks that students will be able to have to explore the mathematics in context. I'm also a part of the virtual math specialist, which there are a few virtual math specialists that we provide video professional development that will allow teachers to make that bridge from the current standards we have now to what's going to happen next.
Ashley Mengwasser: That's cool.
Kenneth Golden: So, I get to be a part of that, and that's just amazing.
Ashley Mengwasser: Who doesn't love a video on demand this day in age?
Lya Snell: Absolutely. Yes. Yes. And I have to mention, Brooke, Janice, and Mike and Carla and Issa and our team, they on a monthly basis ensure that there's content preparing teachers to implement the standards. So we want to get teachers connected to that on-demand content so that they're prepared.
Ashley Mengwasser: And what are we going to do for our parents? I know so much of learning, it's not just happening in the classroom, it's starting there, but we want to reinforce that and undergird that at home with parents. What resources exist for our parents as they help their kids adjust to the new standards in mathematics?
Kenneth Golden: So, in addition to the resources that will be provided, like Lya said, my biggest thing is just the encouragement for parents to make use of the experiences that they have at home. So just as we say at our school, 30 minutes of reading a night will help you with your vocabulary and your stamina, your reading stamina. It's the importance of building that numeracy, and that's just a feel for numbers. So whether that's estimating the cost of groceries or estimating the cost of a bill when you go out to eat with your family, or just talking about percents and real-life taxes, tips and discounts, and helping students to estimate distances in real life. These are just some examples of ways that you can take, outside of the content, just helping students get a feel for numbers.
Ashley Mengwasser: A feel for numbers. I'm going to start using that. Whenever I'm having an off math day, my feel for numbers is weak today. Lya, what resources do you think that parents are going to love?
Lya Snell: So, one of my favorite resources that we're providing for parents, we've created in partnership with Georgia Public Broadcasting, and it's the Make Mathematics Count Georgia series where we offer specific videos where some of our celebrities throughout Georgia-
Ashley Mengwasser: Georgia celebs.
Lya Snell: Georgia celebs, come and talk about how important it is to learn mathematics at those levels. And then we also have parents who provide information on what is taught at each grade level so that other parents will know what to expect when it comes to their children's teaching and learning for each grade level. Additionally, for high school, we have guidance documents for high school graduation to provide information for parents on what the expectations are for students to earn a high school diploma or meet the mathematics requirements to earn a high school diploma. And also we have progressions documents that show parents what's taught from year to year. So, it shows the progression of content from each year so that they know what students are supposed to learn at each grade level and what they will learn in subsequent grade levels for them. Additionally, the evidence of student learning is provided to give more information about each expectation and learning objective and each standard and expectation for the grade level. So all of that is provided to really help parents have a full picture of what their children are supposed to learn at each grade level and course.
Ashley Mengwasser: Sounds like plenty. I want a window to your world, Kenneth. What math success stories have been memorable from your classroom?
Kenneth Golden: So, I remember my first year at the current school that I'm at now, we were talking about proportional relationships. And we were talking about it in context, so a proportional relationship problem. And we started off by building up this foundation of what we learned in elementary school, equivalent fractions. And that's all solving proportions is for in-context problem anyway, it's just setting up equivalent fractions. So, we talked about one half equaling two fourths, and of course we went through that and then we got to problems where there's a missing numerator or a missing denominator. And so, students would talk about, well, how can we multiply to get from one fraction to the next? And some fractions are easier than others. And then there was, I can't remember the context problem for this one, but I definitely remember the poster we made for the student. So the student was tasked, or the students were tasked with this problem where the fraction was like four over six equals 18 over something, and they had to figure out what that was.
Ashley Mengwasser: 18 over dun, dun, duh.
Kenneth Golden: Yes. So the students were like, "Well, Mr. Golden, we can't get from four to 18." And what they meant was they can't multiply a whole number to-
Ashley Mengwasser: To get 18.
Kenneth Golden: To get from four to 18. So I prompted the question, "Well, how close can you get?" And they said, "Well, we can do four times four, get us to 16." And I said, "Well, four times five is what?" And they say, "Oh, that's too much." So you see the kids reasoning and they say, "Okay, well it's got to be somewhere in between," right? So they're thinking about it being somewhere in between. And I know they've gone through one step equation. So we just set it up, 4x = 18, four times something equals 18. And you hear this kid shout out in the back, "We just divide, we just divide."
Ashley Mengwasser: Amazing.
Kenneth Golden: So, the kid is just dividing, doing 18 divided by four. "It's 4.5, Mr. Golden. It's 4.5, it's 4.5." And so you see a student with that joy of identifying and realizing that they just multiply by 4.5, they eventually come up with their own strategy. "Mr. Golden, for all these problems, I'm just going to divide and then multiply." And I talk them through, "Well, how did you get that?" "Well, it's the inverse and then whatever I do on the top, I do on the bottom." And you hear them go through this and they're trying to get to an understanding. And once the kid did that, let's call the kid Bob, and we called it Bob's method and we just slammed it on a poster. We post it up and the kids are, every class period is like, "Oh, I'm just going to use Bob's method." And then we had Katie's method and Jerry's method and we just posted it up. So that's just something-
Ashley Mengwasser: That's such empowerment for them.
Lya Snell: Yes, ownership.
Kenneth Golden: Yes, ownership in the math.
Ashley Mengwasser: I'm too sensitive, I'm going to cry. I could never be a teacher. Okay. Well, Kenneth, you have to do us more favors before you leave. We want to hear some of your teaching tips, some golden nuggets.
Kenneth Golden: It's interesting. My wife is, we're having our second child and we call her golden nugget, so.
Ashley Mengwasser: Oh my gosh. How beautiful.
Kenneth Golden: So, every time I hear golden nugget, I think of my wife.
Ashley Mengwasser: Well, now it means something less exciting today. It's about teaching tips, but hopefully it's still good.
Kenneth Golden: So, two things I would say in the secondary mathematics from six to 12, continue the use of manipulatives. I don't care how old a kid is or whatever it is, that ability to touch the math is super important. So, increase your use of algebra tiles, increase your use of color tiles, increase your use of protractors, get the models in the students' hands so that they can touch the math and be able to make those connections. And then continue, if you haven't started already, Pamela Harris does some awesome work with number strings and talking about how we can make patterns and purposeful problems. So I would encourage teachers to take, do a warmup or a starting activity or an engagement activity to do a number string or do a number talk. Continue the work that teachers in elementary school have been working so hard on. Just continue the work throughout middle school. So just put things in the kids' hands and just work on those number strings and number sense talks.
Ashley Mengwasser: Do you endorse this message, Dr. Lya Snell?
Lya Snell: Absolutely. I love those golden nuggets.
Ashley Mengwasser: I'm so glad. Well, thank you both so much, Dr. Lya Snell and Kenneth Golden, for just a window into the future for Georgia's secondary math teachers. Kenneth, we really appreciate your golden nuggets. You need to trademark that.
Kenneth Golden: Oh, there we go. I can see it now.
Ashley Mengwasser: Get on it. And Dr. Lya Snell from Georgia DOE, winning the superlative of most guest appearances so far. Way to go. Can we get some claps for her? Thank you, Kenneth. Where can fans send your fan mail? We can call it Snell mail. Where can they send it, Lya?
Lya Snell: Well-
Ashley Mengwasser: Do you have a PO Box?
Lya Snell: I do want to share that we have additional resources. All of our math, amazing math specialists, Mike and Carla and Janice and Issa, all of our resources are available and all of our contact information is available on the GADOE webpage, gadoe.org/mathematics. And also all of the resources we referenced today can be found there.
Ashley Mengwasser: Okay, so bookmark those sites, teachers, and get ready for the rollout because as you've heard, it's going to be lit. However the mathematics standards grow and evolve in Georgia, one standard remains the same. You're a great teacher. Goodbye.