Our middle school created Thunder Rolls: a couple days at the end of each quarter students are given a fresh chance to demonstrate a previously assessed standard. Often, using stations is a helpful model when running Thunder Rolls. Basically, you make a standard available for re-exploration and demonstration of understanding.
I suggested to our 8th grade math teacher to use Tutor.com as one of the stations (and then list the standards instead as a menu and the student can pick). Our 8th grade math teacher is open-minded and curious. She was intrigued and so gave it a shot. The teacher worked in advance to teach the students how to use Tutor.com to get that logistical piece out of the way. She set it up as a station (with a menu of standards to choose from). The outcome? The teacher said bluntly, “I wish I had been doing this the entire year.” Here’s what I what we learned from this first foray: 1. Students in general were afraid to speak to a tutor directly, but chatting was more palatable. 2. The chat was a barrier to some students as they struggled communicating technical information, but there were many students that took right to it. Here is one example of a significant learning moment recorded real-time in Tutor.com. Quick background: Mali (name changed for privacy) is English speaking. She comes from a lower income household. She is reserved, shy and incredibly gifted (can do a Rubics cube in seconds), but also withdraws from academics, particularly math, and struggled reaching out for help from the teacher (and never in front of others). Here’s her dialogue with a live tutor (abbreviated for key exchanges). Mali [00:00:02] I need help with irrational and rational numbers Madhu T (Tutor) [00:00:06] Thanks for signing on! How are you? Mali [00:00:23] Im ok [00:00:27] how are you Madhu T (Tutor) [00:00:35] I am well, thank you for asking! [00:00:45] I see you are working on rational and irrational numbers [00:00:52] Was there a problem you were looking at? Mali [00:01:12] no Madhu T (Tutor) [00:01:33] Would you like to learn how to identify or differentiate between the two? Mali [00:01:55] could we do both Madhu T (Tutor) [00:02:03] Sure! [00:02:15] Rational numbers are numbers that can be expressed as a fraction [00:02:20] They can be positive or negative [00:02:24] Here are some examples [00:02:57] See that decimal? Do you know how we can write it as a fraction? Mali [00:03:16] no Madhu T (Tutor) [00:03:22] That's ok, I can explain [00:03:35] Nearly all decimals can be expressed as a fraction [00:03:44] First, we write the number without any decimal [00:03:57] Then a 1, followed by some zeroes [00:04:15] How do we know how many zeroes? We count the number of digits after the decimal point [00:04:27] Three digits, hence 1000 [00:04:31] Did that make sense? Mali [00:04:40] yes Madhu T (Tutor) [00:04:44] [00:05:00] Repeating decimals can also be written as fractions, hence they are also rational [00:05:25] Finally, let's look at whole numbers [00:05:31] For example: 19 [00:05:38] Can we write 19 as 19/(something)? Mali [00:06:06] cant we write it as 19/1 Madhu T (Tutor) [00:06:14] That's right! Well done [00:06:23] That is why, whole numbers are also rational [00:06:39] Rational is another word for 'fraction' [00:06:45] Any questions before we look at Irrational? Mali [00:07:14] so whole numbers and fractions are rational numbers Madhu T (Tutor) [00:07:24] Correct. Also, repeating decimals Mali [00:07:30] ok Madhu T (Tutor) [00:07:33] And any other decimals that can be successfully written as fractions Mali [00:07:45] ok thanks Madhu T (Tutor) [00:07:57] Irrational numbers cannot be written as fractions [00:08:03] The most common example is pi [00:08:19] And square-roots that do not simplify into repeating decimals [00:08:39] These are Irrational Mali [00:09:25] how do you simplify square roots to figure out if its irrational Madhu T (Tutor) [00:09:44] Good question! Are you familiar with square roots in general? Mali [00:09:58] a little bit Madhu T (Tutor) [00:10:07] What is the sqrt(9) = Mali [00:10:28] 3 Madhu T (Tutor) [00:10:40] Very good! And this is a rational number, because 3/1 [00:11:02] On the other hand, if we look at sqrt(7), we will need to use a calculator and it will give us a lengthy decimal [00:11:33] Square roots that give us neat answers, say even like sqrt(12.25) = 3.5 [00:11:37] Would be rational [00:11:52] However, lengthy decimal root means Irrational [00:11:55] Did that help? Mali [00:12:03] yes very much It worked in at least these ways: 1. The teacher could potentially use the recorded chat, along with a follow-up demonstration with a series of problems, as an assessment piece and update the students understanding of a standard. 2. The chat gave this talented, shy student direct, personalized feedback on a particular math question while in a classroom of 27 other students.
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