An Exploratory Comparison of a Traditional and an Adaptive Instructional Approach for College Algebra

This research effort compared student learning gains and attitudinal changes through the implementation of two varying instructional approaches on the topic of functions in College Algebra. Attitudinal changes were measured based on the Attitude Towards Mathematics Inventory (ATMI). The ATMI also provided four sub-scales scores for self-confidence, value of learning, enjoyment, and motivation. Furthermore, this research explored and compared relationships between students\u27 level of mastery and their actual level of learning. This study implemented a quasi-experimental research design using a sample that consisted of 56 College Algebra students in a public, state college in Florida. The sample was enrolled in one of two College Algebra sections, in which one section followed a self-adaptive instructional approach using ALEKS (Assessment and Learning in Knowledge Space) and the other section followed a traditional approach using MyMathLab. Learning gains in each class were measured as the difference between the pre-test and post-test scores on the topic of functions in College Algebra. Attitude changes in each class were measured as the difference between the holistic scores on the ATMI, as well as each of the four sub-scale scores, which was administered once in the beginning of the semester and again after the unit of functions, approximately eight weeks into the course. Utilizing an independent t-test, results indicated that there was not a significant difference in actual learning gains for the compared instructional approaches. Additionally, independent t-test results indicated that there was not a statistical difference for attitude change holistically and on each of the four sub-scales for the compared instructional approaches. However, correlational analyses revealed a strong relationship between students\u27 level of mastery learning and their actual learning level for each class with the self-adaptive instructional approach having a stronger correlation than the non-adaptive section, as measured by an r-to-z Fisher transformation test. The results of this study indicate that the self-adaptive instructional approach using ALEKS could more accurately report students\u27 true level of learning compared to a non-adaptive instructional approach. Overall, this study found the compared instructional approaches to be equivalent in terms of learning and effect on students\u27 attitude. While not statistically different, the results of this study have implications for math educators, instructional designers, and software developers. For example, a non-adaptive instructional approach can be equivalent to a self-adaptive instructional approach in terms of learning with appropriate planning and design. Future recommendations include further case studies of self-adaptive technology in developmental and college mathematics in other modalities such as hybrid or on-line courses. Also, this study should be replicated on a larger scale with other self-adaptive math software in addition to focusing on other student populations, such as K - 12. There is much potential for intelligent tutoring to supplement different instructional approaches, but should not be viewed as a replacement for teacher-to-student interactions

Inclusive Search for Anomalous Production of High-pT Like-Sign Lepton Pairs in Proton-Antiproton Collisions at sqrt{s}=1.8 TeV

We report on a search for anomalous production of events with at least two charged, isolated, like-sign leptons with pT > 11 GeV/c using a 107 pb^-1 sample of 1.8 TeV ppbar collisions collected by the CDF detector. We define a signal region containing low background from Standard Model processes. To avoid bias, we fix the final cuts before examining the event yield in the signal region using control regions to test the Monte Carlo predictions. We observe no events in the signal region, consistent with an expectation of 0.63^(+0.84)_(-0.07) events. We present 95% confidence level limits on new physics processes in both a signature-based context as well as within a representative minimal supergravity (tanbeta = 3) model.Comment: 15 pages, 4 figures. Minor textual changes, cosmetic improvements to figures and updated and expanded reference

Search for Kaluza-Klein Graviton Emission in ppˉp\bar{p} Collisions at s=1.8\sqrt{s}=1.8 TeV using the Missing Energy Signature

We report on a search for direct Kaluza-Klein graviton production in a data sample of 84 ${pb}^{-1}$ of \ppb collisions at $\sqrt{s}$ = 1.8 TeV, recorded by the Collider Detector at Fermilab. We investigate the final state of large missing transverse energy and one or two high energy jets. We compare the data with the predictions from a $3+1+n$-dimensional Kaluza-Klein scenario in which gravity becomes strong at the TeV scale. At 95% confidence level (C.L.) for $n$=2, 4, and 6 we exclude an effective Planck scale below 1.0, 0.77, and 0.71 TeV, respectively.Comment: Submitted to PRL, 7 pages 4 figures/Revision includes 5 figure

Search for lepton flavor violating decays of a heavy neutral particle in p-pbar collisions at root(s)=1.8 TeV

We report on a search for a high mass, narrow width particle that decays directly to e+mu, e+tau, or mu+tau. We use approximately 110 pb^-1 of data collected with the Collider Detector at Fermilab from 1992 to 1995. No evidence of lepton flavor violating decays is found. Limits are set on the production and decay of sneutrinos with R-parity violating interactions.Comment: Figure 2 fixed. Reference 4 fixed. Minor changes to tex

Measurement of the average time-integrated mixing probability of b-flavored hadrons produced at the Tevatron

We have measured the number of like-sign (LS) and opposite-sign (OS) lepton pairs arising from double semileptonic decays of $b$ and $\bar{b}$-hadrons, pair-produced at the Fermilab Tevatron collider. The data samples were collected with the Collider Detector at Fermilab (CDF) during the 1992-1995 collider run by triggering on the existence of $\mu \mu$ and $e \mu$ candidates in an event. The observed ratio of LS to OS dileptons leads to a measurement of the average time-integrated mixing probability of all produced $b$-flavored hadrons which decay weakly, $\bar{\chi} = 0.152 \pm 0.007$ (stat.) $\pm 0.011$ (syst.), that is significantly larger than the world average $\bar{\chi} = 0.118 \pm 0.005$.Comment: 47 pages, 10 figures, 15 tables Submitted to Phys. Rev.

Search for Long-lived Charged Massive Particles in anti-p p Collisions at s**1/2 = 1.8 TeV

We report a search for production of long-lived charged massive particles in a data sample of 90 pb^{-1} of \sqrt{s} = 1.8 TeV p anti-p collisions recorded by the Collider Detector at Fermilab (CDF). The search uses the muon-like penetration and anomalously high ionization energy loss signature expected for such a particle to discriminate it from backgrounds. The data is found to agree with background expectations, and cross section limits of \cal{O} (1) pb are derived using two reference models, a stable quark and a stable scalar lepton.Comment: 14 pages, 3 figure

Search for Higgs Bosons Decaying into b anti-b and Produced in Association with a Vector Boson in Proton-Antiproton Collisions at 1.8 TeV

We present a new search for $H^{0}V$ production, where $H^0$ is a scalar Higgs boson decaying into $b\bar{b}$ with branching ratio $\beta$, and $V$ is a $Z^{0}$ boson decaying into $e^{+}e^{-}$, $\mu^{+}\mu^{-}$, or $\nu\bar{\nu}$. This search is then combined with previous searches for $H^{0}V$ where $V$ is a $W^{\pm}$ boson or a hadronically decaying $Z^{0}$. The data sample consists of $106 \pm 4$ pb$^{-1}$ of $p\bar{p}$ collisions at $\sqrt{s}=1.8$ TeV accumulated by the Collider Detector at Fermilab. Observing no evidence of a signal, we set 95% Bayesian credibility level upper limits on $\sigma(p\bar{p}\to H^{0}V)\times\beta$. For $H^0$ masses of 90, 110 and 130 GeV/$c^{2}$, the limits are 7.8, 7.2, and 6.6 pb respectively.Comment: 6 pages, 3 figures, to be submiited to PR

Measurement of the polar-angle distribution of leptons from W boson decay as a function of the W transverse momentum in proton-antiproton collisions at sqrt{s}=1.8 TeV

We present a measurement of the coefficient alpha_2 of the leptonic polar-angle distribution from W boson decays, as a function of the W transverse momentum. The measurement uses an 80+/-4 pb^{-1} sample of proton-antiproton collisions at sqrt{s}=1.8 TeV collected by the CDF detector and includes data from both the W->e+nu and W->mu+nu decay channels. We fit the W boson transverse mass distribution to a set of templates from a Monte Carlo event generator and detector simulation in several ranges of the W transverse momentum. The measurement agrees with the Standard Model expectation, whereby the ratio of longitudinally to transversely polarized W bosons, in the Collins-Soper W rest frame, increases with the W transverse momentum at a rate of approximately 15% per 10 GeV/c.Comment: 47 pages, 16 figures, submitted to Physical Review