Research On The 7^th Grade Students' Learning Of The Key Steps In The Worked Examples About Mathematic Operation

Incomplete worked example learning has been an important issue in worked example learning research, but the learning effects of it have inconsistent conclusions. For instance, Paas (1992) found that the learning effects between incomplete and complete worked example did not have obvious difference, but Stark (1999) discovered that the learning effects of incomplete worked example were better than the complete worked example. Having analyzed the previous researches, we proposed that the learning effects of key steps in worked examples decided the worked example learning effects, namely, if the learners understood the key steps, they would master the worked examples, if they didn't understand the key steps, they would not get through the worked examples. Adopted the gap-filling method, the present research mainly tested the functions of the key steps and non-key steps in worked example learning, the effects of feedback in the incomplete worked example learning, and the validity of explaining, decomposing and integrating key steps in worked example learning.Study I included two experiments. During the phrase of experiment 1, a total of 120 7^th grade students chosen with a pre-test were shown four kinds of incomplete worked examples about scale operation and absolute value inequality operation and requested to fill up the deleted steps. In the experiment 2, a total of 90 7^th grade students were separately shown complete worked examples (CWE), incomplete worked examples deleted a key step (IWEK) or incomplete worked examples deleted a non-key step (IWEN), after learning the worked examples, they took part in the post-tests. Results showed that the last step of the worked examples about absolute value inequality operation was a key step. There was not significant difference between the effects of CWE and IWEN, the near transfer effects of CWE were obvious better than IWEK, and the far transfer effects between CWE and IWEK had no significant difference.There were 3 experiments in Study II. During the first phrase of experiment 3, a total of 90 7^th grade students were shown three kinds of incomplete worked examples about powers with the same base operation individually and requested to fill up the deleted steps. In the second phrase, 60 7^th grade students were respectively shown CWE or incomplete worked examples which deleted the key step and given feedback timely (IWEKF), then participated in the post-tests. Results showed that the learning effects of IWEKF were obviously higher than CWE. Experiment 4 was about the extraction operation worked example learning, the experiment design and procedure were the same as experiment 3. As a result, the effects between IWEKF and CWE had no significant difference. Experiment 5 firstly adopted the gap-filling method to identify the difficulty of the key steps in the worked examples of quadratic equation of one variable operation, and then participants were separately shown incomplete worked examples deleted a high difficulty key step (IEHKF) or a low difficulty key step (IELKF). The results showed that the near transfer effects of IEHKF were obviously lower than the IELKF, and the far transfer effects between IEHKF and IELKF had no obvious difference.Study III was composed of three experiments. Experiment 6 designed three kinds of worked examples about absolute value inequality operation, including the original worked example (OWE), every step explaining worked example (ESE) and key step explaining worked example (KSE). Experiment 7 designed worked example of extraction operation by decomposed key step simply (CKS) or amply (CKA). Experiment 8 designed worked example of quadratic equation of one variable operation by integrated key steps (IWE). The results indicated that the near transfer effects of KSE were obvious better than OWE and ESE, and far transfer effects of KSE were significant better than OWE, the learning effects of CKS and CKA were separately significant better than OWE, and the near transfer effects of IWE were significantly better than OWE, and the far transfer effects of IWE and OWE had no significantly difference.The above results suggested, (1) The key steps significantly influenced the effects of the incomplete worked example learning, but the non-key steps had no obvious effect on the incomplete worked example learning. (2) The incomplete worked example learning with feedback could improve the learning effects of powers with the same base operation obviously, but couldn't improve the learning effects of extraction operation, and the learning difficulty of the key steps significantly restricted the near transfer effects of incomplete worked example learning with feedback, but had no obviously constraint on the far transfer effects.(4) The key step explaining could promote the worked example learning obviously, and the every step explaining had little effect on the worked example learning. (5) Simply or amply decomposing the key steps all could significantly improve worked example learning. (6) Integrating key step worked examples could obviously promote near transfer effects of the quadratic equation of one variable operation, but could not improve the far transfer effects.