Posted in Education & Technology, Math Inquiry

Understanding Math & Technology

First, I want to start with saying that I  have a love hate relationship for mathematics. I get when students don’t understand math. I personally call it a “writer’s block.” Students say “I don’t know” for that very real reason and I trust and believe them (not all the time). This is something that has bothered me a lot, because I feel that math teachers know it all and that we (students) miraculously know the material too because we’ve been taught the concept (once).

Second, I want to acknowledge the fact that I am aware that my blogs within my math inquiry hasn’t been about technology per se. However, this is where I hope to redeem myself. I wanted to participate in this group as it was the most interesting and relevant to me as a math tutor. Yet, I didn’t know how to contribute to the technology portion of this. I didn’t even know where to begin. I mentioned this in my first math inquiry blog. Thus, I felt like that lost math student. How is a student suppose to get to the solution, know what they’re looking for, if they simply “don’t know?”

I was searching aimlessly at mathematical topics online, and most of what I was finding were math games or video tutorials. So, it wasn’t until a kind group member guided me and kindly handed me two applications to research, Tiger Algebra and Stack Exchange.

I won’t go into depth here about those two applications, but what I continued to encounter in exploring those two applications were my continuous frustrations with math and technology. What I mean by this is that students I work with that take remedial math and who are required to use an online software are often frustrated with the “learning technology” process. I will even admit that I assist them by entering their answers for them when working with them side by side. It bothers me to see students frustrated in entering the correct answer the wrong way (the software wants responses entered in a specific manner). Not to mention how time consuming this is for the students. By the time I painstakingly enter their response (it is not multiple choice), the students are halfway done working on the next problem. Graphing via some of these software are extremely cumbersome!

These are math students, not computer students who need to learn how to enter mathematics in a scientific way. Let alone these are the students who still have trouble working with a mathematical technology, the graphing calculator. Most students that I work with still don’t know how to effectively find appropriate windows for their graph, nor some know how to properly type in calculations to compute. They often forget their order of operations and that parenthesis and brackets makes all the difference.

So, going back to my first point, I feel that I can relate when students don’t get math. I know that very real feeling. I felt it as I searched for digital applications for this inquiry. Even with the ones that I explored, I was back at square one. I thought in my head, when am I going to use Stack Exchange? Honestly, probably never! It was over my head and I wasn’t sure what to make of it. I felt that I need to be a math genius to use that site. As with Tiger Algebra, this was really cool but I wonder if my college students will use this site effectively to help themselves as oppose to cheat themselves from the learning. It will take a certain skill set for one to incorporate technology into learning math in the classroom; and I must say that students who have math teachers like Dan Meyer and Mrs. Cathy Yenca are very fortunate.

In the meantime, I do wonder how I can build it in to my restricted tutoring sessions. I feel like I need to start studying up on this (digital math applications) as oppose to simply pull from the various topical worksheets bank that I have created over the years.

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Posted in Math Inquiry

Controversies on Math Homework

In continuing on my last blog entry regarding math homework, I thought I was going to sit down and write my two cents about it and call it a day on blogging. Well, I was wrong. I just spent the last several hours browsing through the internet about math inquiry (focusing on math games, math digital applications, and math homework). Wow, what I found online about math homework were some great perspectives and issues. The following are some to read/browse through: “Do Students Really Need Practice Homework,” “Study says more math homework doesn’t increase student achievement,” and “Homework: A Math Dilemma and What To Do About It.”

I didn’t realize it, but I have found that this is quite a controversial topic. Deciding whether homework should be mandatory or optional and whether homework should be graded were the top two reoccurring issues. Growing up (including college years), doing math homework or any assigned homework was a common educational practice. So, I find it fascinating to learn about these current homework dilemmas.

My personal take on homework in college are: it should be strongly recommended and graded to count no more than 5% of total grade. Out of context, that probably didn’t make any sense. How could I put a grade on something not required. Well, this is how I would do it. I would suggest at most 10-20 math problems to do as homework, but I would only grade between 3-5 problems out of the total suggested. I will even tell the students which 3-5 would be graded. So, if they chose to do just those few problems for HW grade, then that is fine by me.

I want to be clear that I will not grade the 3-5 problems based on accuracy, but rather that students show their work. First, I believe that not grading for “correctness” removes the idea that one has to “copy” another to earn their undeserved HW grade. Second, I find that most students want to learn and put in the practice; so, I rather one tries and goes through the motion, even if it’s the wrong approach or attempt. Thus, just like an athlete who practices a drill or skill set, a student (most likely) isn’t going to intentionally do the work/ “practice” inaccurately.

For a daily math class in a college quarter system, I would provide the 10-20 suggested HW problems on every new topic section (this is often daily). However, I will not necessarily assign the 3-5 graded problems for each of those 10-20 suggested problems. The deadline for students to turn them in would be one day before the test on that section (this is approximately 2 weeks). The ideal is for students to turn them in the next day or two after assigned. However, I chose the day before test day because I recognize that students have other classes to balance into their schedule. Over the span of 2 weeks time also allows one to get help from classmates, teachers, and tutors from the Math Lab. More importantly, I want to provide feedback on the graded assignment; even with a day turnaround time, students can study/cram (not recommended) for next day’s test.

Overall, I believe that required, graded math homework provides structure to one’s learning. Just as it builds frustration as one doesn’t understand, it also builds confidence as one recognizes their learning. For those feeling frustrated, it should be a key indicator for them to seek help immediately. Students needs to recognize that they are not alone and that teachers want them to succeed in their math class!

Nevertheless, there is a lot to consider. I believe that “strongly suggesting” homework problems allows a college student to take responsibility for their own learning. Also, grading on it should’t be punitive to their overall grades. Homework needs to be purposeful to student’s learning, and immediate deadlines for homework submission may not be the most beneficial. Students math learning often progress at different pace, and allowing time to receive help and utilize free campus resources (including one-on-one tutoring) should be encouraged.

What are your take on this issue, math homework? Should it be mandatory? Should it be graded? Are my suggestions flawed (remember, I am NOT a teacher)? How can my take on homework be improved?

Posted in Math Inquiry

NO Math Homework! What!?

Okay, my paper clip image and title for this post is perhaps a bit misleading. Although I am not completely against the idea of no homework, I do understand how requiring it can be meaningless for some students and even detrimental to a student’s grade. Before I give some of my perspectives, I wanted to credit my group member’s blog for giving some blogging ideas for this week.

Based on the video posted on my group member’s site, it got me thinking about “how much should homework count?” Better yet, the question was rephrased to be thought of as “how much should practice count?” First, I love how Wormeli changes the word “homework” to “practice” indicating that the word “homework” carries “emotional baggage” which creates negative attitudes and even anxiety for students. Second, I also love how Wormeli says that “homework is practice, an extension of that which is already learned.” This is so true and I couldn’t agree more! It drives me so nuts when  teachers teach a concept but only shows one example, then worse, assign homework (HW) problems that are much more complex than what was taught. Thankfully, I didn’t have too much of this growing up. However, I find that this as an issue when students learn intermediate algebra in a college quarter system, which is fast pace. Students need the scaffolding required to build up their skills, especially in learning new concepts.

It’s not realistic to assign a whole bunch of HW problems that students are going to struggle through. I tell students all the time that it’s not worth coming back to me the next day and telling me that “I worked on math for 3 hours last night,” but didn’t get much done. It makes me wonder what did they do. I feel frustrated for them. It would have been more productive for them to “practice” owning the new knowledge (math concepts) as opposed to working problems so rehearsed. I try to steer them away from this by reminding them that they are not going to get the same exact problems on the quiz, test, or final! I also have other strategies when working with them. Students are so hung up in rote memorization on “how to work the problem.”

Take a look at my classmate’s blog post and check out her inquiry on Photomath and on Rich Wormeli’s awesome video. My classmate asked a great question that I will attempt to answer here. I think a great way to ensure students’ mastery at home without the use of Photomath is 1) ensure that students have taken good notes that they understand (so they can refer to it) 2) students ask for clarifications during class 3) students are able to answer conceptual questions to the learning goal (e.g. Why do we do that? Why can’t…be the answer? Can we…? If this is on…, then….? What is the opposite of…, so we…? etc…) I found that it’s also important to reiterate a lot of fundamental concepts especially when I notice that students don’t “own” it quite yet.

Watch the video that’s already embedded on classmate’s blog site, and let us know what you’re take on it. More to come on math homework in college and grading homework; so, stay tuned.